We provide statistics practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on statistics skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of statistics Questions

Question No | Questions | Class |
---|---|---|

1 | The variance of the scores 2,4,6,8,10 is ( A cdot 2 ) B. 4 ( c .6 ) ( D ) | 11 |

2 | If ( x ) is increased by ( k ) then ( sigma ) changes to ( mathbf{A} cdot k+sigma ) в. ( k sigma ) c. ( k sqrt{sigma} ) D. remains unchanged | 11 |

3 | If the standard deviation of ( n ) observations ( x_{1}, x_{2}, dots, x_{n} ) is 4 and another set of ( n ) observations ( boldsymbol{y}_{1}, boldsymbol{y}_{2}, dots, boldsymbol{y}_{n} ) is ( 3 . ) The standard deviation of ( n ) observations ( x_{1}-y_{1}, x_{2}- ) ( boldsymbol{y}_{2}, dots, boldsymbol{x}_{boldsymbol{n}}-boldsymbol{y}_{n} ) is A . 1 в. ( frac{2}{sqrt{3}} ) ( c .5 ) D. data insufficient | 11 |

4 | Given n real numbers ( a_{1}, a_{2}, dots a_{n}, ) the value of ( x ) for which sum of the square of all the deviations is least is A ( cdot a_{1}+a_{2}+ldots+a_{n} ) В – ( 2left(a_{1}+a_{2}+ldots+a_{n}right) ) c. ( a_{1}^{2}+a_{2}^{2}+ldots a_{n}^{2} ) D. ( frac{a_{1}+a_{2}+ldots+a_{n}}{n} ) | 11 |

5 | Suppose values taken by a variable ( boldsymbol{X} ) are such that ( a leq x_{i} leq b ) where ( x_{i} ) denotes the value of ( X ) in the ( i^{i h} ) case for ( boldsymbol{i}=mathbf{1}, mathbf{2}, dots . boldsymbol{n} . ) Then ( ^{text {A } cdot} frac{a^{2}}{4} leq operatorname{Var}(X) ) В . ( (b-a)^{2} geq operatorname{Var}(X) ) c. ( a leq operatorname{Var}(X) leq b ) D ( cdot a^{2} leq operatorname{Var}(X) b^{2} ) | 11 |

6 | If the mean of the data : 7,8,9,7,8,7 ( lambda, 8 ) is ( 8, ) then the variance of this data is A . B. 1 ( c cdot frac{9}{8} ) D. 2 | 11 |

7 | For two data sets, each of size ( 5, ) the variance are given to be 4 and 5 and the corresponding means are given to be 2 and ( 4, ) respectively. The double of the variance of the combined data set is A . 13 B. 12 ( c .5 .5 ) D. 10 | 11 |

8 | Find constant of variation and write equation of variation for given below. ( mathbf{A} quad boldsymbol{p} boldsymbol{a} frac{mathbf{1}}{boldsymbol{q}}: boldsymbol{i} boldsymbol{f} boldsymbol{p}=mathbf{1 5} t h e boldsymbol{n} boldsymbol{q}=boldsymbol{4} ) ( mathbf{B} quad boldsymbol{z} boldsymbol{a} frac{mathbf{1}}{boldsymbol{w}} ; boldsymbol{w} boldsymbol{h} boldsymbol{e} boldsymbol{n} boldsymbol{z}=mathbf{2} ) ( c quad s a frac{1}{r^{2}} ; i f s=4 t h e n t=5 ) D ( x ) a feacl ( sqrt{y} ; ) if ( x=15 ) | 11 |

9 | If the mean of a binomial distribution is ( 25, ) then its standard deviation lies in the interval A ( cdot[0,5] ) в. [0,6] c. [0,25] ] D. [0,28 | 11 |

10 | The mean deviation from the data ( mathbf{3}, mathbf{1 0}, mathbf{1 0}, mathbf{4}, mathbf{7}, mathbf{1 0}, mathbf{5} ) ( mathbf{A} cdot mathbf{3} ) B . 2 c. 3.75 D. 2.57 E. None of these | 11 |

11 | ( fleft{f_{i} x_{i}=75 text { and } sum f_{i}=15, ) then find right. the mean ( bar{x} ) | 10 |

12 | Identify the mode for the following data: Number ( mathbf{0} ) 12 ( mathbf{6} ) ( mathbf{9} ) Frequency ( quad 4 quad 8 ) A . 18 B. 12 c. Both A and B D. 6 | 10 |

13 | A distribution has mean=8.7, median ( =8.5 ) and mode ( =7.3 . ) The distribution is A. Positively skewed B. negatively skewed c. symmetrical D. none of these | 11 |

14 | Calculate mode for the following data shows the number of colour pencils the students have in a class. ( begin{array}{lllll}text { Colour } & mathbf{0}- & mathbf{5}- & mathbf{1 0}- & mathbf{1 5}- \ text { Pencils } & mathbf{5} & mathbf{1 0} & mathbf{1 5} & mathbf{2 0}end{array} ) Number of students 17 13 ( mathbf{A} cdot 11 ) B. 15 ( mathbf{c} cdot 19 ) D. 16 | 10 |

15 | 46. If the mean deviation of the numbers 1,1 + d. 1 + 2d. 1 + 100d from their mean is 255, then d is equal to: 12000 (a) 20.0 (b) 10.1 (c) 20.2 (d) 10.0 | 11 |

16 | If mean: median of a certain data is 2 3, what is the ratio of its mode and mean? A .3: 2 B. 5: 2 ( c .3: 5 ) D. 2: 3 | 10 |

17 | If the variable a is of discrete type then the frequency distribution can be represented by A. scatter diagram B. bar diagram c. a pie chart | 11 |

18 | Find the mode for the following frequency table. Wages(Rs.) ( quad 250 quad 300 quad 350 ) Number of workers 15 16 | 10 |

19 | For the values ( x_{1}, x_{2} dots dots x_{101} ) of a distribution ( x_{1}<x_{2}<x_{3}<dots . .< ) ( x_{100}<x_{101} . ) The mean deviation of this distribution with respect to a number will be minimum when k is equal to A. ( x_{1} ) в. ( x_{5} ) c. ( x_{50} ) D. ( frac{x_{1}+x_{2}+ldots . .+x_{101}}{101} ) | 11 |

20 | If mean of a series is 40 and variance ( 1486, ) then coefficient of variation is A .0 .9021 B. 0.9637 c. 0.8864 D. 0.9853 | 11 |

21 | Find the mean deviations about the mean for the following data: Marks ( i ) ( begin{array}{ll}10- & 2 \ 20 & 3end{array} ) ( begin{array}{ll}20- & 3 \ 30 & 4end{array} ) 30 obtained 40 Number of 2 student | 11 |

22 | The time(in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below. Time (in ( sec ) ( begin{array}{llll}5- & 10- & 15- & 20- \ 10 & 15 & 20 & 25end{array} ) No. of people If variation is ( 36.76, ) so calculate standard deviation of the data. | 11 |

23 | Find the median value from the given table by drawing the curve of the values. begin{tabular}{|l|l|} hline Weight (in kg) & No of students \ hline Less than 38 & 0 \ hline Less than 40 & 3 \ hline Less than 42 & 5 \ hline Less than 44 & 9 \ hline Less than 46 & 14 \ hline Less than 48 & 28 \ hline Less than 50 & 32 \ hline Less than 52 & 35 \ hline end{tabular} A . 18.5 B. 16.5 c. 17.5 D. 21.5 | 10 |

24 | Which of the following are true or false? a) T-distribution varies from+infinity to infinity b)The variance of ( t ) distribution and the variance of normal distribution become closer and closer as the size of the sample increases. A. both (a) and (b) are true B. both (a) and (b) are false c. (a) is true but (b) is false D. (a) is false but (b) is true | 11 |

25 | Find the Coefficient of Variation for Factory ( boldsymbol{B} ) A ( .0 .15555 % ) B. ( 0.25714 % ) c. ( 0.36934 % ) D. ( 0.42548 % ) | 11 |

26 | By what percentage was the maintenance cost in ( 1997-1998 ) was lower compared to ( 1999-2000 ? ) A . ( 33.55 % ) B. ( 69.07 % ) ( c .54 .23 % ) D. ( 67.12 % ) | 9 |

27 | Median is independent of change of A . only origin B. only scale c. origin and scale D. neither origin nor scale | 10 |

28 | Find the mean ( begin{array}{llllll}x: & 10 & 30 & 50 & 70 & 89 \ f: & 7 & 8 & 10 & 15 & 10end{array} ) ( mathbf{A} cdot 55 ) B. 65 ( mathbf{c} cdot 45 ) D. 95 | 10 |

29 | Consider the following statements: 1. The mean and median are equal in symmetric distribution. 2. The range is the difference between the maximum value and the minimum value in the data. 3. The sum of the areas of the rectangle in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis. Which of the above statements are correct? A. 1 and 2 only B. 2 and 3 only c. 1 and 3 only D. 1,2 and 3 | 11 |

30 | Mean deviation can be calculated from A. mean B. median c. mode D. any of the above | 11 |

31 | The mean deviation of ( a^{3}+b^{3} ) and ( a^{3}- ) ( b^{3}(text { when }(a & b>0) ) is A ( cdot a^{3} ) в. ( b^{3} ) ( c cdot 2 a^{3} ) D. ( 2 b^{3} ) | 11 |

32 | The marks in the science of 80 students of class ( X ) are given below: Find the mode of the marks obtained by the students in science. ( begin{array}{lllll}text { Marks: } & begin{array}{l}0- \ 10end{array} & begin{array}{l}10- \ 20end{array} & begin{array}{l}text { 20- } \ text { 30 }end{array} & begin{array}{l}text { 30- } \ 40end{array}end{array} ) Frequency: ( quad 3 quad 5 ) 16 12 | 10 |

33 | If the median of data ( mathbf{3 1}, mathbf{3 3}, mathbf{3 5}, boldsymbol{x}, boldsymbol{x}+mathbf{1 0}, mathbf{4 8}, mathbf{4 8}, mathbf{5 0} ) is ( mathbf{4 0} ) than find the value of ( x ) | 10 |

34 | Mean deviations of the series ( a, a+ ) ( boldsymbol{d}, boldsymbol{a}+mathbf{2} boldsymbol{d}, ldots, boldsymbol{a}+boldsymbol{2 n} boldsymbol{d} ) from its mean is A ( cdot frac{n(n+1) d}{(2 n+1)} ) в. ( frac{n d}{2 n+1} ) c. ( frac{(n+1) d}{2 n+1} ) D. ( frac{(2 n+1) d}{n(n+1)} ) | 11 |

35 | Mode of the following frequency distribution ( begin{array}{lccccc}mathrm{x}: & 4 & 5 & 6 & 7 & 8 \ mathrm{f}: & 6 & 7 & 10 & 8 & 3end{array} ) A. 5 B. 6 ( c cdot 8 ) D. 19 | 10 |

36 | A college teacher has the following absentee record of 50 students of a class for the whole year. Find the median. ( begin{array}{lllll}text { Number } & mathbf{0}- & mathbf{4}- & mathbf{8}- & mathbf{1 2}- \ text { of days } & mathbf{4} & mathbf{8} & mathbf{1 2} & mathbf{1 6}end{array} ) Number of students A. 11.66 B. 12.66 c. 13.66 D. 10.66 | 10 |

37 | The median of a set of 9 distinct observations is ( 20.5 . ) If each of the largest 4 observations of the set is increased by ( 2, ) then the median of new set : A. is increased by 2 . B. is decreased by 2. c. is two times the original median. D. remains the same as that of the original set. | 10 |

38 | 72. Which of the following graphical representations of data repre- sents cumulative frequencies ? (1) Pie-chart (2) Histogram (3) Frequency polygon (4) Ogive | 9 |

39 | Incomes of the families in a locality are given. Find the mode of the data. ( begin{array}{lllll}text { Income } & 1- & 201 & 401 & 600 \ text { (in Rs.) } & 200 & 400 & 600 & 800end{array} ) 10 16 Number of families | 10 |

40 | T-distribution is symmetrical like normal distribution and its mean value is A. zero B. – – ( c ) D. | 11 |

41 | If the standard deviation is small, we define a new variable known as A. student’s F-distribution B. student’s T-variable c. chi-square distribution D. student’s G-variable | 11 |

42 | 12. In an experiment with results were available: with 15 observations on x, the following [2003] Ex2 = 2830, Ex = 170 One observation that was 20 W was replaced by the correct variance is (a) 8.33 © 188.66 rvation that was 20 was found to be wrong an d by the correct value 30. The corrected [2003] (b) 78.00 (d) 177.33 on th | 11 |

43 | Find the mode for the following data: 22 26 Term 30 Frequency ( quad 3 quad 5 quad ) 10 ( quad 2 ) A . 22 B . 30 ( c cdot 34 ) D. None of these | 10 |

44 | The median and standard deviation (S.D.) of a distribution will be, If each term is increased by 2 A. median and S.D. will increased by 2 B. median will increased by 2 but S.D. will remain same c. median will remain same but S.D. will increased by 2 D. median and s.D. will remain same | 11 |

45 | Find median: Wages per ( mathbf{3 8} quad mathbf{4 5} quad mathbf{4 8} quad mathbf{5 5} ) day is Cumulative igure ( quad 14 quad 22 quad 29 quad 39 ) figure | 10 |

46 | Assertion The variance of the series ( boldsymbol{a}, boldsymbol{a}+boldsymbol{d}, boldsymbol{a}+ ) ( mathbf{2} boldsymbol{d}, boldsymbol{a}+mathbf{3} boldsymbol{d}, ldots boldsymbol{a}+boldsymbol{2 n d} ) is ( frac{boldsymbol{n}(boldsymbol{n}+mathbf{1})}{mathbf{3}} boldsymbol{d}^{2} ) Reason The sum and the sum of squares of first ( n ) natural numbers ( frac{n(n+1)}{2} ) and ( frac{n(n+1)(2 n+1)}{6} ) respectively A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

47 | The range of the data 7,9,7,5,9,9,18,6,8,9 is: A. 7 B. 8 ( c cdot 9 ) D. 13 | 11 |

48 | The distribution given below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. ( begin{array}{llll}text { No. of } & mathbf{2 0}- & mathbf{6 0 -} & mathbf{1 0 0 -} \ text { wickets } & mathbf{6 0} & mathbf{1 0 0} & mathbf{1 5 0}end{array} ) Bowl No. of owlers 16 | 10 |

49 | The sum of 12 observations is ( 600, ) then their mean is A . 20 B. 30 c. 40 D. 50 | 10 |

50 | How many employees get to work in more than 100 minutes? A . 20 B. 15 ( c cdot 4 ) D. 58 | 9 |

51 | Range of data 7,8,2,1,3,13,18 is? A . 10 B. 15 c. 17 D. None of the above | 11 |

52 | Find the mean for the following distribution ( begin{array}{lllll}text { Marks } & begin{array}{l}10- \ 20end{array} & begin{array}{l}20- \ 30end{array} & begin{array}{l}text { 30- } \ 40end{array} & begin{array}{l}text { 40- } \ 50end{array}end{array} ) Frequency 6 8 13 | 10 |

53 | Find the mean of first six natural numbers. A . 3.6 B. 7 ( c .3 .5 ) D. None of these | 10 |

54 | 1,2,3,6,8 is a set of five positive integers whose mean is 4 and median is 3. Write down two other sets of five positive integers, each having the same mean and median as this set. | 10 |

55 | NIVE, HUL Syircudlu Suppose a population A has 100 observations 101, 102, …………., 200 and another population B has 100 obsevrations 151, 152, ……………. 250. If V and V represent the variances of the two populations, respectively then A is [2006] (a) I (b) ? (c) 4 (d) ? | 11 |

56 | Mode of the distribution begin{tabular}{lccccc} Marks & 4 & 5 & 6 & 7 & 8 \ No. of students & 3 & 5 & 10 & 6 & 1 \ hline end{tabular} ( mathbf{A} cdot mathbf{6} ) B. 10 ( c cdot 8 ) ( D cdot 4 ) | 10 |

57 | The height of 30 boys of a class are given in the following table : Height in cm Frequency [ begin{array}{ll} 120-129 & 2 \ 130-139 & 8 \ 140-149 & 10 \ 150-159 & 7 \ 150-159 & 3 end{array} ] If by joining a boy of height ( 140 mathrm{cm}, ) the median of the heights is changed from ( M_{1} ) to ( M_{2}, ) then ( M_{1}-M_{2}, ) in cm is A . ( 0 . ) B . -0.1 c. 0 D. 0.2 | 10 |

58 | Represent the following data by histogram and hence compute mode. Price o 22 24 sugar 18 20 per kg [ 20 ] 22 24 26 (in Rs.) Number of f weeks 4 8 22 A. 21.2 Rs. B. 22.2 Rs. c. 23.2 Rs. D. 24.2 Rs. | 9 |

59 | Find the median class for the following data given below: ( begin{array}{llll}text { Number } & mathbf{0}- & mathbf{1 0}- & mathbf{2 0}- \ text { of cars } & mathbf{1 0} & mathbf{2 0} & mathbf{3 0}end{array} ) Frequency 7 13 A . ( 30-40 ) в. ( 40-50 ) c. ( 50-60 ) D. ( 60-70 ) | 10 |

60 | In a series of ( 2 n ) observations, half of them equal ( a ) and remaining half equal ( -a . ) If the ( S . D . ) of the observations is 2 then ( |a| ) equals A ( cdot frac{1}{n} ) B. ( sqrt{2} ) ( c cdot 2 ) D. ( frac{sqrt{2}}{n} ) | 11 |

61 | : *2-………….., xn are any real numbers and n is any postive integer, then (1982 – 2 Marks) 2 » -Ź< <{}x) – Šx = (3 (9) Žx{z^{}x) (a) none of these (c) N (d) none of these i=1 | 11 |

62 | If ( n=10, bar{x}=12 ) and ( sum x^{2}=1530 ) then calculate the coefficient of variation. A . 20 B . 25 c. 30 D. 35 | 11 |

63 | How to derive the Mode formula for grouped data? | 10 |

64 | Constructing a frequency distribution A. is one of the most common means of summarizing data. B. begins by recording the number of times a particular value occurs C. is the basis for construction of a percentage distribution. D. All of the above | 11 |

65 | Determine the mode of the following data. begin{tabular}{llllll} Marks & 10 & 16 & 12 & 19 & 13 \ Number of Students & 3 & 3 & 4 & 2 & 6 \ hline end{tabular} A . 12 B . 13 c. 14 D. 20 | 10 |

66 | The distribution below gives the weights of 30 students of a class. Find the median weight of the students ( begin{array}{lllll}text { weight } & 40- & 45- & 50- & 55- \ (text { in } mathrm{kg}) & 45 & 50 & 55 & 60end{array} ) 8 6 No. of students ( quad 2 ) begin{tabular}{ll|l|l} Weight tin & 60- & 65- & 70- \ Kg) & 65 & 70 & 75 \ Ma of & & & end{tabular} No. of students 3 If A .46 .67 g в. 12.12 кв ( c .75 .12 mathrm{kg} ) D. ( 56.67 mathrm{kg} ) | 10 |

67 | The mean of a distribution is 14 and standard deviation is 5. What is the value of the coefficient of variation? ( mathbf{A} cdot 57.7 % ) B. ( 45.7 % ) c. ( 35.7 % ) D. None of these | 11 |

68 | Find the mode of the following: ( mathbf{1 8}, mathbf{1 4}, mathbf{2 2}, mathbf{2 3}, mathbf{1 4}, mathbf{1 8}, mathbf{1 7}, mathbf{2 8}, mathbf{2 8}, mathbf{1 4}, mathbf{2 5}, mathbf{1} ) A . 12 B. 13 c. 14 D. 15 | 10 |

69 | For ( boldsymbol{X} rightarrow boldsymbol{B}(boldsymbol{n}, boldsymbol{p}), ) if ( boldsymbol{n}=mathbf{2 5}, boldsymbol{E}(boldsymbol{x})=mathbf{1 0} ) then ( S . D .(x)= ) A ( .2 sqrt{6} ) B. 2.4 c. ( 2 sqrt{10} ) D. ( sqrt{2.4} ) | 11 |

70 | Find the value of ( z ) using shortcut method whose arithmetic mean is 2.5 A . 14 B . 15 c. 16 D. 17 | 10 |

71 | Find the mean deviation about mean and median for the following data. begin{tabular}{ccccc} multirow{2}{*} {( boldsymbol{C I} )} & ( mathbf{1}- ) & ( mathbf{6}- ) & ( mathbf{1 1}- ) & ( mathbf{1 6}- ) \ & ( mathbf{5} ) & ( mathbf{1 0} ) & ( mathbf{1 5} ) & ( mathbf{2 0} ) end{tabular} [ begin{array}{l} 2 \ 2 end{array} ] | 11 |

72 | The runs secored in a cirect match by 11 players is as follows: ( mathbf{9}, mathbf{1 5}, mathbf{1 2 1}, mathbf{5 1}, mathbf{1 0 1}, mathbf{8 1}, mathbf{5 0}, mathbf{1 6}, mathbf{8 2}, mathbf{1 1}, mathbf{1 1} ) Find the mean, mode and median respectively of this data. A .48,11,51 в. 49,81,11,51 c. 49,90,11,50 D. 49,81,11,50 | 10 |

73 | Find the median of the following frequency distribution ( begin{array}{llll}text { Class } & begin{array}{l}4- \ 8end{array} & begin{array}{l}text { 8- } \ 12end{array} & begin{array}{l}text { 1 } \ text { 1 }end{array}end{array} ) ( 12- ) 16 20 Frequency 9 16 1 | 10 |

74 | Find the mean deviation about mean for the data in ( mathrm{Ex} 9 ) and 10 . ( begin{array}{lll}text { Income per day } & text { No of persons } \ 0-100 & 4 \ 100-200 & 8 \ 200-300 & 9 \ 300-400 & 10 \ 400-500 & 7 \ 500-600 & 5 \ 600-700 & 4 \ 700-800 & 3end{array} ) | 11 |

75 | 54. Let x, , X ,…..r et xi , Xn,…., xn be n observations, and let X be their Srithmetic mean and o- be the variance. 20121 Statement-1: Variance of 2×1,2×2,…, 2x, is 402. Statement-2: Arithmetic mean 2x,, 2×2, …, 2x, is 43. (a) Statement-1 is false, Statement-2 is true. Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1. (c) Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1. (d) Statement-1 is true, statement-2 is false. | 11 |

76 | Find the actual lower and upper class limits and also the class marks of the classes : ( 1.1-2.0,2.1-3.0, ) and ( mathbf{3 . 1}-mathbf{4 . 0 .} ) | 11 |

77 | The table below shows the daily expenditure on food of 25 households in a locality. Daily expenditure (in Rs.) ( quad ) No. of households ( 100-150 ) 150-200 200-250 250-300 2 300-350 Find the mean daily expenditure on food by a suitable method. A . 211 B. 201 c. 215 D. 209 | 10 |

78 | The mean of four observations is ( 3 . ) If the sum of the squares of these observations is 48 then their standard deviation is A. ( sqrt{7} ) B. ( sqrt{2} ) ( c cdot sqrt{3} ) D. ( sqrt{5} ) | 11 |

79 | Find the mean deviation about the median for the following data: ( boldsymbol{x}_{i} quad 3 quad 6 quad 9 quad 12 ) [ f_{i} quad 3 quad 4 quad 5 quad 2 ] | 11 |

80 | 75. If the standard deviation of the numbers -1, 0, 1, kis where k>0, then k is equal to: [JEEM 2019-9 April (a) 2V6 (b) 2. (d) V6 | 11 |

81 | Which of the following are measures of dispersion? A. Standard Deviation,Median,Range B. Standard Deviation,Mode,Range c. standard Deviation, Variance,Range D. Mean,Mode,Median | 11 |

82 | Find the coefficient of range for the given data ( mathbf{5 9}, mathbf{4 6}, mathbf{3 0}, mathbf{2 3}, mathbf{2 7}, mathbf{4 0}, mathbf{5 2}, mathbf{3 5}, mathbf{2 9} ) A . 0.46 B. 0.44 ( c .0 .56 ) D. 0.124 | 11 |

83 | Find the mean, mode and median of marks obtained by 20 students in an examination. The marks are given below. ( begin{array}{lllll}text { Marks } & 0- & 10- & 20- & 3 \ 10 & 20 & 30 & 4end{array} ) No. of 1 1 4 tident | 10 |

84 | Calculate the coefficient of variation (C.V.) of the following data: 40,36,64,48,52 | 11 |

85 | A group of 50 house owners contributes money towards children’s education of their street. The amount of money collected is shown in the table below: (use direct method). A . Rs. 27 B. Rs. 17 c. Rs. 10 D. Rs. 23 | 10 |

86 | Per day expenses of 25 families of the frequency distribution of a Dhani of a village is given as follows. Per day 25 ( begin{array}{lll}text { 35- } & text { 45- } & text { 55 }end{array} ) expense ( quad 35 quad 45 quad 55 quad 65 ) (In Rs.) Number of families Find the mean expense of families by Direct Method. | 10 |

87 | If the median of the data ( boldsymbol{x}_{1}, boldsymbol{x}_{2}, boldsymbol{x}_{3}, boldsymbol{x}_{4}, boldsymbol{x}_{5}, boldsymbol{x}_{6}, boldsymbol{x}_{7}, boldsymbol{x}_{8} ) is ( boldsymbol{alpha} ) and ( boldsymbol{x}_{1}<boldsymbol{x}_{2}<boldsymbol{x}_{3}<boldsymbol{x}_{4}<boldsymbol{x}_{5}<boldsymbol{x}_{6}<boldsymbol{x}_{7}< ) ( x_{8}, ) then the median of ( x_{3}, x_{4}, x_{5}, x_{6} ) is ( A cdot alpha ) в. ( frac{alpha}{2} ) c. ( frac{alpha}{3} ) D. ( frac{alpha}{4} ) | 10 |

88 | In histogram, the height of rectangle shows A. width of the class B. upper limit of the class c. lower limit of the class D. frequency of the class | 9 |

89 | 1. Assertion: The marks in maths of 7 students are as follows: 53, 61, 78, 68, 62, 8, 48. Here, range = 78 – 8 = 70. Reason: Range is defined as the difference between the highest and lowest values of observations in a data. _ __ _ yomole ofrandom | 9 |

90 | The first of two samples has 100 items with mean 15 and ( S . D .3 . ) If the whole group has 250 items with mean 15.6 and ( s . d=sqrt{13.44}, ) find the standard deviation of the second group. A . 5 B. 4 ( c cdot 6 ) D. 3.52 | 11 |

91 | The value of ( X^{2} ) describes the magnitude of the difference between A. two normal distributions B. expected and observed frequency c. both (A) and (B) D. two samples | 11 |

92 | Variance of first 20 natural number is A ( frac{133}{4} ) в. ( frac{379}{12} ) ( ^{c} cdot frac{133}{2} ) D. ( frac{399}{4} ) | 11 |

93 | 64. The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is: [JEE M 2015] (a) 15.8 (b) 14.0 (c) 16.8 (d) 16.0 | 9 |

94 | Calculate the mean using step deviation method. begin{tabular}{|l|l|l|l|l|} hline Number of pages & 20 & 40 & 60 & 80 \ hline Number of articles & 3 & 6 & 9 & 12 \ hline end{tabular} ( mathbf{A} cdot 62 ) B. 63 ( mathbf{c} cdot 64 ) D. 65 | 10 |

95 | The coefficient of variation of two distributions are 60 and ( 70 . ) The standard deviation are 21 and 16 respectively, then their mean is This question has multiple correct options A . 35 B . 23 c. 28.25 D. 22.85 | 11 |

96 | Now, we construct rectangles with class-limits as bases and respective adjusted frequencies as heights. Draw a histogram for the marks of students given below: begin{tabular}{|l|c|c|c|c|c|} hline Marks: & ( 0-10 ) & ( 10-30 ) & ( 30-45 ) & ( 45-50 ) & ( 50-60 ) \ hline No. of students: & 8 & 32 & 18 & 10 & 6 \ hline end{tabular} | 9 |

97 | A student scores the following marks in five test: ( 45,54,41,57,43 . ) His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six test is A ( cdot frac{10}{sqrt{3}} ) в. ( frac{100}{sqrt{3}} ) c. ( frac{130}{3} ) D. ( frac{10}{3} ) | 11 |

98 | The degree to which numerical data tend to spread about value is called A. mean B. variation c. median D. mode | 11 |

99 | ( mathbf{1 0} ) ( mathbf{2 0} ) ( mathbf{3 0} ) 40 ( f quad 5 quad 7 quad 15 quad 13 ) From the given distribution, calculate mean deviation about mean. A .1 .021 B. 11.231 c. 10.256 D. 12.214 | 11 |

100 | The mean of the following distribution is 15. Find the value of a ( begin{array}{lll}text { C.I. } & text { 5 } & text { 10 }end{array} ) 15 ( mathbf{2 0} ) ( mathbf{2 5} ) Freq 6 a 6 5 10 | 10 |

101 | If in a moderately asymmetrical distribution mean and mode are ( 9 a, 6 a ) respectively then median is equals, ( mathbf{A} cdot 6 a ) B. ( 9 a ) ( c cdot 8 a ) D. ( 15 a ) | 10 |

102 | The mean deviation from mean of observations ( 5,10,15,20, dots .85 ) is A. 43.71 B. 21.17 ( c .38 .7 ) D. None of these | 11 |

103 | Find the approximate value of mode for the following data: ( begin{array}{lllll}text { Class } & 7- & 14- & 21- & 28 \ text { interval } & 14 & 21 & 28 & 35end{array} ) Frequency 4 3 A . 30 B. 32 c. 31 D. 35 | 10 |

104 | Following 10 observations are arranges in ascending order as follows. ( mathbf{2}, mathbf{3}, mathbf{5}, mathbf{9}, boldsymbol{x}+mathbf{1}, boldsymbol{x}+mathbf{3}, mathbf{1 4}, mathbf{1 6}, mathbf{1 9}, mathbf{2 0} ) If the median of the data is 11 , find the value of ( x ) | 10 |

105 | The sum of the squares of deviation of 10 observations from their mean 50 is ( 250, ) then coefficient of variation is A . 10% B. 40% c. 50% D. none of these | 11 |

106 | toppr LoGil JOIN NOW Q Type your question curve and determine the median. | 10 |

107 | Calculate the coefficient of range for the following data: ( begin{array}{llll}text { Heights } & 120- & 125- & 130- \ text { in cm. } & 124 & 129 & 134end{array} ) No. of students 9 | 11 |

108 | A random survey of the number of children of various age group playing in a park was found as follows: Draw a histogram to represent the data | 9 |

109 | The mode of the following discrete series is: 12 ( boldsymbol{x}_{i} quad 1 quad 3 quad 5 quad 6 ) ( f_{i} quad 5 quad 7 quad 3 ) 8 ( mathbf{A} cdot mathbf{3} ) B. 12 c. 8 D. 6 | 10 |

110 | Test scores out of 100 for a class of 20 students are as follows: 93,84,97,98,100,78,86,100,85,92,55 Find the interval that contains the median A. ( 81-90 ) В. ( 71-80 ) c. ( 71-90 ) D. None of these | 10 |

111 | Find the mean and variance for the following frequency distribution ( begin{array}{lllll}text { Classes } & begin{array}{l}0- \ 30end{array} & begin{array}{l}text { 30- } \ 60end{array} & begin{array}{l}text { 60- } \ text { 90 }end{array} & begin{array}{l}text { 9 } \ text { 1 }end{array}end{array} ) 120 Frequencies 2 3 | 11 |

112 | The contents of 100 match boxes were checked to determine the number of matches they contained. No. of ( quad 35 quad 36 ) 37 matches No. of match ( begin{array}{ll}text { 12 } & text { 15 }end{array} ) boxes Calculate the mean number of matches per box A . 38 B. 42 c. 67 D. 51 | 10 |

113 | If ( X, Y ) are independent then ( S D(X- ) ( boldsymbol{Y}) ) is: ( mathbf{A} cdot S D(X)-S D(Y) ) в. ( S D(X)+S D(Y) ) c. ( sqrt{S D(X)+S D(Y)} ) D. None of these | 11 |

114 | The mean salary paid per week to 1000 employees of an establishment was found to be Rs. ( 900 . ) Later on, it was discovered that the salaries of two employees were wrongly recorded as Rs. ( mathbf{7 5 0} ) and Rs. ( mathbf{3 6 5} ) instead of Rs. ( mathbf{5 7 0} ) and Rs. ( 635 . ) Find the corrected mean salary. A . 900.90 B. 1,115 c. 1,225 D. 900.09 | 10 |

115 | The sum of the squares deviations for 10 observations taken from their mean 50 is ( 250 . ) The coefficient of variation is A . ( 10 % ) B . ( 40 % ) c. ( 50 % ) D. none of these | 11 |

116 | The mean of ( x_{1} ) and ( x_{2} ) is ( M_{1} ) and that of ( boldsymbol{x}_{1}, boldsymbol{x}_{2}, boldsymbol{x}_{3} ldots . . boldsymbol{x}_{4} ) is ( boldsymbol{M}_{2} ) then the mean of ( a x_{1}, a x_{2}, frac{x_{3}}{a}, frac{x_{4}}{a} ) is? A. ( frac{a M_{1}+M_{2}}{2} ) ( ^{mathbf{B} cdot} frac{a M_{1}+left(frac{M_{2}}{a}right)}{2} ) c. ( frac{1}{2 a}left[left(a^{2}-1right) M_{1}+M_{2}right] ) D ( cdot frac{1}{2 a}left[left(a^{2}-1right) M_{1}+2 M_{2}right] ) | 10 |

117 | The mean deviation of a frequency dist. is equal to A ( frac{sum d_{i}}{sum f_{i}} ) в. ( frac{sumleft|d_{i}right|}{sum f_{i}} ) ( c cdot frac{sum f_{i} d_{i}}{sum f_{i}} ) D ( cdot frac{sum f_{i}left|d_{i}right|}{sum f_{i}} ) | 11 |

118 | Find the mean deviation about the mean for the following data. | 11 |

119 | The sum of the squares of deviations of a set of values is minimum when taken about A . ( A M ) в. ( G M ) с. ( H M ) D. median | 11 |

120 | The sum of the squares of deviations of 10 items about mean 50 is 250 .The coefficient of variation is A . 10% B. 50% c. 30% D. none of these | 11 |

121 | 71. A line graph (1) shows trend over time (2) compares structures (3) makes comparisons (4) None of the above | 9 |

122 | If ( sum_{i=1}^{9}left(x_{i}-5right)=9 ) and ( sum_{i=1}^{9}left(x_{i}-5right)^{2}= ) ( 45, ) then the standard deviation of the 9 ( operatorname{times} x_{1}, x_{2}, dots, x_{9} ) is A . 9 B. 4 ( c cdot 3 ) ( D cdot 2 ) ( E ) | 11 |

123 | Find the mean of the following frequency distribution: ( begin{array}{lllll}text { Class } & 10- & 30- & 50- & 70- \ text { interval: } & 30 & 50 & 70 & 90end{array} ) Frequency: ( quad 5 quad 8 ) 12 20 | 10 |

124 | A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. ( begin{array}{lllll}text { Number } & 0- & 6- & 10- & 14- \ text { of days } & 6 & 10 & 14 & 20end{array} ) Numbe of student | 10 |

125 | The mean square deviation of a set of ( n ) observation ( x_{1}, x_{2}, ldots x_{n} ) about a point ( c ) is defined as ( frac{1}{n} sum_{i=1}^{n}left(x_{i}-cright)^{2} ) The mean square deviations about -2 and 2 are 18 and 10 respectively, the standard deviation of this set of observations is A . 3 B. 2 ( c . ) D. None of these | 11 |

126 | The number of students absent in a class were recorded for 120 days and the information is given in the following frequency table: No. of students absent ( x ) No. of [ operatorname{days}(f) ] 50 Find the mean number of students absent per day. | 10 |

127 | Find the mean deviation from the median for the following data: [ begin{array}{ccccc} x_{1} & 6 & 9 & 3 & 12 \ f_{1} & 4 & 5 & 3 & 2 end{array} ] | 11 |

128 | If ( bar{X} ) is the mean of ( x_{1}, x_{2}, x_{3}, dots, x_{n} ) Then, the algebraic sum of the deviations about mean ( bar{X} ) is A. 0 в. ( frac{bar{X}}{n} ) ( c cdot n bar{X} ) D. none of these | 11 |

129 | If s.d,of ( X ) is ( sigma ), then s.d.of the variable ( U=frac{a X+b}{c} ) where ( a, b, c ) are constants is A ( cdotleft|frac{c}{a}right| sigma ) B ( cdotleft|frac{a}{c}right| sigma ) ( c cdotleft|frac{b}{c}right| ) D. ( frac{c^{2}}{a^{2}} sigma ) | 11 |

130 | 52. In the afternoon, a student read 100 pages at the rate of 60 pages per hour. In the evening, when she was tired, she read 100 more pages at the rate of. 40 pages per hour. What was her average rate of reading, in pages per hour ? (1) 60 (2) 70 (3) 48 (4) 50 | 10 |

131 | ( mathbf{3} quad mathbf{5} quad mathbf{7} quad mathbf{9} quad mathbf{1 1} ) ( boldsymbol{x}_{boldsymbol{i}} ) ( f_{i} ) ( i ) ( 6 quad 8 quad 15 quad 25 quad 8 ) Find the Mean Deviation (M.D) about the mean ( mathbf{A} cdot 2.1 ) B . 2.25 c. 2.09 D. 2.71 | 11 |

132 | If the standard deviation for the marks obtained by a student in monthly tests is 36 then the variance is ( A cdot 6 ) B. 36 ( c cdot 1296 ) D. None of these | 11 |

133 | Find the mean deviation about the median for the following data. ( mathbf{1 3}, mathbf{1 7}, mathbf{1 6}, mathbf{1 1}, mathbf{1 3}, mathbf{1 0}, mathbf{1 6}, mathbf{1 1}, mathbf{1 8}, mathbf{1 2}, mathbf{1 7} ) | 11 |

134 | 28. Let x1, x2 , ………….. Xn ben observations such that 52 = 400 and > x; = 80. Then the possible value of n among the following is (a) 15 (b) 18 (c) 9 (d) 12 [2005] | 11 |

135 | The S.D. of 1,2,3,4,5,6,7 is A .4 B. 2 ( c cdot sqrt{7} ) D. none of these | 11 |

136 | The weight of coffee (in gms) in 70 packets is given below. Determine the modal weight of coffee in packets 202 ( quad 203 ) Packe A . ( 201 mathrm{gms} ) в. ( 201.70 mathrm{gms} ) ( c cdot 202 g m s ) D. 202.70 gms | 10 |

137 | If the mean of the numbers ( a, b, 8,5,10 ) is 6 and their variance is ( 68, ) then ( a b ) is equal to A . 6 B. 7 c. 12 D. 14 E . 25 | 11 |

138 | Find the mean deviation from the mean of the following data: [ boldsymbol{x}_{1} ] [ begin{array}{ccccccccc} 2 & 5 & 6 & 8 & 10 & 12 \ hline & f_{1} & 2 & 8 & 10 & 7 & 8 end{array} ] | 11 |

139 | Find the median of the following data: 2,7,3,15,12,17 and 5 | 10 |

140 | Calculate the mean deviation about the mean of the set of first ( n ) natural numbers when ( n ) is an even number | 11 |

141 | Find the average of 2,3,4,5,10,13 | 10 |

142 | Find the mean of the following frequency distribution: ( begin{array}{llll}text { Class } & text { 0- } & text { 6- } & text { 1 } \ text { interval: } & text { 6 } & text { 12 } & text { 1 }end{array} ) ( 12- ) 18 3 24 Frequency: ( quad 7 ) 10 | 10 |

143 | Lowest value of variance can be: ( A cdot 1 ) B. – c. 0 D. None of these | 11 |

144 | The median of the following observations ( 11,12,14,(x-2),(x+ ) 4) ( ,(x+9), 32,38,47 ) arranged in ascending order is ( 24 . ) Find the value of ( x ) and hence find the mean. | 10 |

145 | Calculate the mean of the following data, using direct method: ( begin{array}{lllll}text { Class } & begin{array}{l}25- \ 35end{array} & begin{array}{l}35- \ 45end{array} & begin{array}{l}45- \ 55end{array} & begin{array}{l}55- \ 65end{array}end{array} ) 10 8 Frequency 6 | 10 |

146 | 54. If the average of x and (x+0) is M, then the average of x2 and 2 is: (1) 1 – M (3) 2M2-1 (2) 1 – 2M (4) 2M2 + 1 | 9 |

147 | The mean of the numbers ( a, b, 8,5,10 ) is 6 and the variance is ( 6.80, ) then which of the following gives possible values of ( a ) and ( b ) A ( . a=0, b=7 ) В. ( a=5, b=2 ) c. ( a=1, b=6 ) D. ( a=3, b=4 ) | 11 |

148 | If sum of the 20 deviations from the mean is 100 , then find the mean deviation | 11 |

149 | Find the mean deviation about the mean of the following data: ( mathbf{1 5}, mathbf{1 7}, mathbf{1 0}, mathbf{1 3}, mathbf{7}, mathbf{1 8}, mathbf{9}, mathbf{6}, mathbf{1 4}, mathbf{1 1} ) A . ( 3 . ) B. 3. ( c .3 .3 ) D. 3. | 11 |

150 | There are five times the number of two wheelers as there are three wheelers. The no of four wheelers are equal to the number of two wheelers. Find the average number of wheel per vehicle | 10 |

151 | The standard deviation of ( mathbf{9}, mathbf{1 6}, mathbf{2 3}, mathbf{3 0}, mathbf{3 7}, mathbf{4 4}, mathbf{5 1} ) is A. 7 B. 9 c. 12 D. 14 E . 16 | 11 |

152 | 59. Average age of A, B and C is 84 years. When D joins them the average age becomes 80 years. A new person, E, whose age is 4 years more than D, replaces A and the average of B, C, D and E becomes 78 years. What is the age of A? (1) 50 years (2) 60 years (3) 70 years (4) 80 years | 9 |

153 | The mean of all the factors of 12 is A ( cdot 3 frac{2}{3} ) в. ( 4 frac{3}{2} ) ( c cdot frac{2}{3} ) D. 12 | 10 |

154 | Find the mode for the following data: Students ( begin{array}{lll}mathbf{1 0} & mathbf{1 4} & mathbf{2 0}end{array} ) ( mathbf{3 0} ) Frequency ( quad 2 quad 2 ) A . 10 B . 20 c. 60 D. 30 | 10 |

155 | Weight of 40 eggs were recorded as given below weight in grams 90- 95- 100( begin{array}{ll}85- & 5 \ 90 & 5end{array} ) 104 ( operatorname{gram} ) 90 94 Number of eggs 12 14 Find the modal weight. | 10 |

156 | Standard deviation is calculated from the Harmonic Mean (HM) A . Always B. Sometimes c. Never D. None of these | 11 |

157 | In a study of diabetic patients in a village, the following observations were noted: ( begin{array}{llll}text { Age in } & mathbf{1 0}- & mathbf{2 0}- & mathbf{3 0}- \ text { years } & mathbf{2 0} & mathbf{3 0} & mathbf{4 0}end{array} ) No. of ( ^{f}_{n t s}^{2} ) patien Calculate the mean and standard deviation. Also interpret the results | 11 |

158 | Sum of all components in normalized histogram is equal to A . 0 B. c. 100 ( D ) | 9 |

159 | Find the mean deviation about mean for the following data: [ text { Score }(boldsymbol{x}) quad boldsymbol{6} quad boldsymbol{2 0} ] 18 Frequen [ 2 ] 11 ( (f) ) | 11 |

160 | The mean marks scored by 40 students were found to be ( 60 . ) Later it was observed that a score of 48 was misread as ( 84 . ) Then the correct mean is ( mathbf{A} cdot 58 ) B. 58.2 c. 59.1 D. 59 | 10 |

161 | The mode of the following data is 50 Calculate the value of ( X ) Marks ( quad begin{array}{ccc}50- & 60- & 70- \ 60 & 70 & 80end{array} ) Students 1 2 A . 3 в. 2.8 ( c .5 ) D. | 10 |

162 | The largest value in the collection of data is ( 7.44 . ) If the range is ( 2.26, ) then find the smallest value in the collection A . 5.18 B. 9.70 ( c .2 .26 ) D. 1.13 | 11 |

163 | Length of 40 bits of wire, correct to the nearest centimetre are given below. Calculate the variance. ( begin{array}{lllll}text { Length } & 1- & 11- & 21- & 31- \ mathrm{cm} & 10 & 20 & 30 & 40end{array} ) No. of bits ( quad 2 quad 3 ) | 11 |

164 | If the mean of following frequency distribution. is ( 2.6, ) then the values of is ( begin{array}{llllll}x_{i} & 1 & 2 & 3 & 4 & 5end{array} ) ( f_{i} quad 5 quad 4 quad ) f ( quad 2 quad 3 ) ( A cdot 3 ) B. c. 8 D. None of these | 10 |

165 | The total runs scored by two cricket players Arun and Bharath in 15 matches are 1050 and 900 with standard deviation 4.2 and 3.0 respectively. Who is better run getter? Who is more consistent in performance? | 11 |

166 | he variance of first 50 even natural numbers is (JEE M 2014] (2) 437 (6 437 (0) 833 (d) 833 | 11 |

167 | The exam scores of all 500 students were recorded and it was determined that these scores were normally distributed. If Jane’s score is 0.8 standard deviation above the mean, then how many, to the nearest unit, students scored above Jane? | 11 |

168 | Compute the age specific death rate for the following data: Number of deaths ( begin{array}{ll}text { Age } & text { Population (in } \ text { Group } & text { thousands) } \ text { (years) } & text { thousands) }end{array} ) 5 Below 5 360 ( _{5}-30 ) na begin{tabular}{l|l} Above & \ 30 & 10 end{tabular} 280 | 11 |

169 | The variance of first ( n ) natural numbers, is ( ^{text {A } cdot frac{n+1}{2}} ) B. ( frac{n^{2}+1}{12} ) c. ( frac{n^{2}-1}{6} ) D. ( frac{n^{2}-1}{12} ) | 11 |

170 | The mean deviation of the data ( mathbf{2}, mathbf{9}, mathbf{9}, mathbf{3}, mathbf{6}, mathbf{9}, mathbf{4} ) from the mean is A . 2.23 в. 2.57 c. 3.23 D. 3.57 | 11 |

171 | Draw the histogram of the following frequency distribution: ( begin{array}{ll}text { Class-Interval } & text { Frequency } \ 0-9 & 5 \ 10-19 & 8 \ 20-29 & 12 \ 30-39 & 18 \ 40-49 & 22 \ 50-59 & 10end{array} ) | 9 |

172 | On approximately how many days was the 2 p.m temperature above ( 70^{circ} ) F? A. Approx. 12 B. Approx. 39 C. Approx. 93 D. None of these | 9 |

173 | If the difference between the standard deviation and variance of a data is 12 then find the sum of the variance and standard deviation of that data A . 20 B . 15 c. 18 D. 22 | 11 |

174 | If the difference between the mode and median is ( 2, ) then the difference between the median and mean (in the given order) is? A .2 B. 4 c. 1 ( D ) | 10 |

175 | How many students weight less than 35 kg? (a) 38 (b) 24 (c) 16 (d) 18 | 9 |

176 | loss of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete ass is 72, then what is the average of the girls? [2002] (2) 3 (6) 65 (c) 68 (d) 74 Sum of two forces is 18 N and resultant | 9 |

177 | The mean of the following data is 50 Find the value of a and hence the frequencies of 30 and 70 [ begin{array}{cccccc} boldsymbol{X} & mathbf{1 0} & mathbf{3 0} & mathbf{5 0} & mathbf{7 0} & mathbf{9 0} \ boldsymbol{F} & mathbf{1 7} & mathbf{5 a + 3} & mathbf{3 2} & mathbf{7 a – 1 1} & mathbf{1 9} end{array} ] A .28 and 34 B. 68 and 24 c. 28 and 24 D. None of these | 10 |

178 | Find the median class of the following distribution. ( begin{array}{ll} text { Weight }operatorname{(in} k g) & text { Number of students } \ 45-47 & 7 \ 47-49 & 5 \ 49-51 & 8 \ 51-53 & 12 \ 55-57 & 2 \ 57-59 & 10end{array} ) | 10 |

179 | The means of five observations is 4 and their variance is ( 5.2 . ) If three of these observation are ( 1,2, ) and ( 6, ) then the other two are A .2 and 9 B. 3 and 8 c. 4 and 7 D. 5 and 6 | 11 |

180 | Find the mean deviation about median for the following data. begin{tabular}{lllll} multirow{2}{*} {( boldsymbol{C I} )} & ( mathbf{2 0}- ) & ( mathbf{3 0 -} ) & ( mathbf{4 0 -} ) & ( mathbf{5 0 -} ) \ ( mathbf{3 0} ) & ( mathbf{4 0} ) & ( mathbf{5 0} ) & ( mathbf{6 0} ) end{tabular} 18 | 11 |

181 | Which of the following is not a measure of central location? A. Mean B. Median c. mode D. Variance | 11 |

182 | Find the mean deviation about the median for the following continuous distribution: ( begin{array}{lllll}text { Marks } & 0- & 10- & 20- & 30- \ text { obtained } & 10 & 20 & 30 & 40end{array} ) No. of body 6 ( 8 quad 14 ) | 10 |

183 | Mean of marks obtained by 10 students is 30 Marks obtained are ( mathbf{2 5}, mathbf{3 0}, mathbf{2 1}, mathbf{5 5}, mathbf{4 7}, mathbf{1 0}, mathbf{1 5}, boldsymbol{x}, mathbf{4 5}, mathbf{3 5} ) Find the value of ( x ) A . 25 B. 37 c. 69 D. 17 | 10 |

184 | Calculate the mode ( begin{array}{ccccccc}boldsymbol{x} & 3 & 6 & 9 & 12 & 15 & 18 \ f & 6 & 8 & 11 & 4 & 10 & 7end{array} ) ( mathbf{A} cdot mathbf{9} ) B. 11 c. 12 D. 15 | 10 |

185 | Calculate the mode for the following data: begin{tabular}{lllll} Score & 14 & 16 & 18 & 20 \ Frequency & 2 & 4 & 4 & 8 \ hline end{tabular} A . 14 B . 16 c. 18 D. 2 | 10 |

186 | The donations given to an orphanage home by the students of different classes of a secondary school are given below. ( begin{array}{ll}text { Class } & text { Donation by each } \ & text { students }(text { in } R s)end{array} ) No. of students donated ( _{5} ) vı vıl 7 vııl 10 Ix 15 ( x ) 20 Find the mean, median and mode of the data A. Rs.11.26, Median = Rs.10; Mode = Rs.10 B. ( R s .1 .26, ) Median ( =R s .10 ; ) Mode ( =R s .10 ) c. ( R s .11 .26, ) Median ( =R s .20 ; ) Mode ( =R s .10 ) D. None of these | 10 |

187 | The variance of first ‘ ( n ) ‘ natural number is A ( frac{n^{2}+1}{12} ) B. ( frac{n^{2}-1}{12} ) c. ( frac{(n+1)(2 n+1)}{6} ) D. None of these | 11 |

188 | The coefficient of mean deviation from median of observations 40,62,54,90,68,76 is A .2 .16 B. 0.2 ( c .5 ) D. None of these | 11 |

189 | The mean of 100 observations is 50 If one of the observations which was 50 is replaced by 150 the resulting mean will be A . 51 B. 52 ( c .51 .5 ) D. 53 | 10 |

190 | The lower limit of the modal class of the following data is : ( begin{array}{lllll} & 0 & 10 & 20 & 30 \ text { c.l. } & – & – & – & – \ & 10 & 20 & 30 & 40end{array} ) Frequency ( quad 5 quad 8 quad ) 13 ( quad ) 7 A . 10 B. 30 c. 20 D. 50 | 10 |

191 | The demand of different shirt sizes, as obtained by a survey, is given. Calculate the Mode. Size ( 38 quad 39 ) Number of persons(wearin it) | 10 |

192 | The variance of following: begin{tabular}{lllll} multirow{2}{*} { Age } & multirow{2}{*} { ( mathbf{2 0}- ) ( mathbf{2 5} )} & ( mathbf{2 5}- ) & ( mathbf{3 0}- ) & ( mathbf{3 5}_{-} ) \ & & ( mathbf{3 0} ) & ( mathbf{3 5} ) & ( mathbf{4 0} ) end{tabular} begin{tabular}{l|c|c} Number & \ of & 170 \ persons end{tabular} 15 80 45 ( mathbf{A} cdot 62.62 ) B . 56.56 c. 7.93 D. 9.24 | 11 |

193 | Find the mode when median is 12 and mean is 16 of a data. | 10 |

194 | If the mean deviation about mean ( mathbf{1}, mathbf{1}+boldsymbol{d}, mathbf{1}+mathbf{2} boldsymbol{d}, dots mathbf{1}+mathbf{1 0 0} boldsymbol{d} ) from their mean is ( 255, ) then the ( d ) is equal to A . 10 B. 20 c. ( 10 . ) D. 20.2 | 11 |

195 | Calculate the mean of the following frequency distribution. ( begin{array}{llll}text { Class } & mathbf{9 0 -} & mathbf{1 0 0 -} & mathbf{1 1 0 -} \ mathbf{1 0 0} & mathbf{1 1 0} & mathbf{1 2 0}end{array} ) Frequency 8 78 | 10 |

196 | 57. The average of 11 numbers is 63. If the average of first six numbers is 60 and the last six numbers is 65, then the 6th number is (1) 57 (2) 60 (3) 62 (4) 64 | 9 |

197 | The sum of 100 observations and the sum of their squares are 400 and 2475 respectively. Later on, three observations, 3,4 and ( 5, ) were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is. A . 8.00 B. 8.50 c. 8.25 D. 9.00 | 11 |

198 | Let ( x_{1}, x_{2}, dots dots dots, x_{n} ) be n observations such that ( sum x_{i}^{2}=400 ) and ( sum x_{i}=80 ) Then a possible value of ( n ) among the following is A . 15 B. 18 ( c cdot 9 ) D. 12 | 11 |

199 | The monthly profits earned by shops of a shopping complex are shown as the following frequency distribution. Draw ogive curve for the below data. Profit (in 05- 25- 45 thousano ( begin{array}{lll}text { 25 } & text { 45 } & text { 65 }end{array} ) Rs) No. of shops | 10 |

200 | Consider the table given below Marks ( begin{array}{llll}0- & 10- & 20- & 30- \ 10 & 20 & 30 & 40end{array} ) Number of Students [ begin{array}{lll} 18 & 27 & 20 end{array} ] 12 The arithmetic mean of the marks given above is A . 18 B. 28 ( c cdot 27 ) D. 6 | 10 |

201 | The mean deviation of ( frac{a+b}{2} ) and ( frac{a-b}{2}(text { where a and } b>0) ) is? ( A cdot frac{b}{2} ) в. ( frac{a}{2} ) ( c cdot a ) D. | 11 |

202 | The formula of students t-distribution is A ( cdot t=frac{s}{sqrt{n}} ) в. ( t=frac{|bar{X}-mu|}{s} ) c. ( quad t=frac{|bar{X}-mu|}{frac{s}{sqrt{n}}} ) D. ( quad t=frac{sqrt{n}}{s} ) | 11 |

203 | Calculate the mean deviation about mean for the data given here: ( begin{array}{lccc}text { Class } & mathbf{5} & mathbf{1 5} & mathbf{2 5} & mathbf{3 5} \ text { interval } & & & end{array} ) Frequency ( quad 5 quad 3 quad 9 quad 12 ) ( mathbf{A} cdot 10.2 ) B. 10.4 c. 10.5 D. 11.4 | 11 |

204 | Class ( begin{array}{cccc}2- & 4- & 6- & 8- \ 4 & 6 & 8 & 10end{array} ) ( 10- ) 12 interval frequency ( 2 quad 4 quad 6 ) 10 5 What is the mode for the grouped data? A .10 .5 B. 12.5 c. 13.7 D. 9.1 | 10 |

205 | Find the variance for the following data: 6,4,8,5,2,17 | 11 |

206 | Find ( bar{x} ) using shortcut method. A . 37 B . 38 c. 39 D. 40 | 10 |

207 | Calculate the missing frequency ( f ) from the following distribution, it is being given that the median of the distribution is 24 class ( begin{array}{ll}0- & 10- \ 10 & 20end{array} ) 30 40 25 Frequency | 10 |

208 | The measurements (in ( mathrm{mm} ) ) of the diameters of the heads of the screws are given below. Calculate the mean diameter of the head of the screws. ( begin{array}{ll}36- & 39- \ 38 & 41end{array} ) ( begin{array}{ll}33- & 3 \ 35 & 3end{array} ) ( begin{array}{ll}text { Diameter } & text { 3. } \ text { (in mm) } & text { 3) }end{array} ) Number of 3 screws ( left(f_{1}right) ) | 10 |

209 | The median of the following distribution is ( 35 . ) Find the value of ( a ) and ( b ) ( begin{array}{ll}text { Class – Interval } & text { Number of Workers } \ text { 0-10 } & 10 \ text { 10-20 } & text { 20 } \ text { 20-30 } & text { a } \ text { 30-40 } & text { 40 } \ text { 40-50 } & text { b } \ text { 50-60 } & text { 25 } \ text { 60-70 } & text { 15 } \ text { Total } & text { 170 }end{array} ) | 10 |

210 | Find the median from the following data. ( begin{array}{lllll}text { Marks } & 0- & 10- & 30- & 60- \ & 10 & 30 & 60 & 80end{array} ) No. of students , an a 15 30 A . 10 B . 20 c. 30 D. 40 | 10 |

211 | If the standard deviation of the values 2,4,6,8 is ( 2.33, ) then the standard deviation of the values 4,6,8,10 is ( mathbf{A} cdot mathbf{0} ) в. 2.58 c. 4.66 D. None of these | 11 |

212 | Histogram are a great way to show results of A . categories B. continuous data c. both ( A ) and ( B ) D. None of these | 9 |

213 | Find the least number of children in the interval ( 20-30 ) hours? 4.1 в. 15 ( c .25 ) D. 45 | 9 |

214 | The maximum bowling speed (kms/hour) of 33 players at a cricket coaching centre is given below: Find the modal bowling speed of players. Bowling 85 ( begin{array}{ll}100 & 115end{array} ) speed ( (mathrm{kms} / mathrm{hr}) ) ( begin{array}{lll}text { DO } & 115 & 130end{array} ) No. of Players A. Rs. 101kms/hour B. Rs.106 kms/hour c. Rs.115 kms/hour D. Rs.118 kms/hour | 10 |

215 | The mean deviation from the mean for the set of observations -1,0,4 is A. Less than 3 B. Less than 1 c. Greater than 2.5 D. Greater than 4.9 | 11 |

216 | Find the arithmetic mean of the following data. A . 59.35 B . 57.35 c. 61.35 D . 52.35 | 10 |

217 | In a series of observations, ( mathrm{S.D.}=7 ) and mean is 28 , the coefficient of variation is A .4 B . ( 1 / 4 ) c. 25 D. 12.5 | 11 |

218 | Calculate mean deviation from the median of the following data: ( begin{array}{llll}text { Class } & 0- & 6- & 1 \ text { interval: } & 6 & 12 & 1end{array} ) 8 一年 18 Frequency: ( quad 4 ) 5 | 11 |

219 | Khilona earned scores of 97,73 and 88 respectively in her first three examinations. If she scored 80 in the fourth examination, then her average score will be A. increased by 1 B. increased by 1.5 c. decreased by 1 D. decreased by 1.5 | 11 |

220 | The largest of 50 measurements is 3.84 kg. If the range is ( 0.46 mathrm{kg} ), find the smallest measurement. A . ( 3.38 mathrm{kg} ) B. 2.38kg. c. ( 6.38 mathrm{kg} ) D. None of these | 11 |

221 | How many students watched TV for less than 4 hours? ( A, 34 ) В. 32 ( c, 24 ) ( D, 30 ) | 9 |

222 | toppr Q Type your question ( begin{array}{llllll}text { Life } bmod e & 0- & 20- & 40- & 60- & 80 \ text { Hrs.) } & 20 & 40 & 60 & 80 & 100end{array} ) No. of electric bulbs [ 82 ] begin{tabular}{lll} 31 & 36 & 38 & 42 \ hline end{tabular} Find the modal life of the electric bulbs. | 10 |

223 | What is the arithmetic mean of the squares of first five natural numbers? ( mathbf{A} cdot mathbf{9} ) B. 11 c. 13 D. 15 | 10 |

224 | Probability density functions are always A. decreasing B. increasing c. positive D. negative | 9 |

225 | MATHEMATICS begin{tabular}{lcccc} Classes & ( 0- ) 10 & ( 10- ) 20 & ( 20- ) 30 & ( 30- ) 40 \ Frequencies & 5 & 8 & 15 & 16 \ hline end{tabular} | 9 |

226 | Let ( X ) be a variate taking values ( x_{1}, x_{2}, ldots . . x_{n} ) and ( Y ) be a variate taking values ( y_{1}, y_{2}, dots . y_{n} ) such that ( y_{i}= ) ( mathbf{6} boldsymbol{x}_{boldsymbol{i}}+mathbf{3} ; quad boldsymbol{i}=mathbf{1}, boldsymbol{2}, ldots boldsymbol{n} . ) If ( boldsymbol{V} boldsymbol{a} boldsymbol{r}(boldsymbol{Y})=boldsymbol{3 0} ) then ( sigma_{X} ) is equal to A ( cdot frac{5}{sqrt{6}} ) в. ( sqrt{frac{5}{6}} ) c. 30 D. ( sqrt{30} ) | 11 |

227 | Find the median of the following values: 37,31,42,43,46,25,39,45,32 | 10 |

228 | Find the median for the following data given below: ( begin{array}{lllll}text { Class } & 0- & 2- & 4- & 6 \ text { interval } & 2 & 4 & 6 & 8end{array} ) Frequencies 3. 2 3 A . 5.3 в. 5.4 c. 5.1 D. 5.6 | 10 |

229 | Find mode for the following data. ( begin{array}{lllll}text { Employees } & 0- & 10- & 20- & 30 \ text { salary } & 10 & 20 & 30 & 40end{array} ) No. of employees | 10 |

230 | The mean deviation about median from the data ( mathbf{3 4 0}, mathbf{1 5 0}, mathbf{2 1 0}, mathbf{2 4 0}, mathbf{3 0 0}, mathbf{3 1 0}, mathbf{3 2 0} ) is ( mathbf{A} .50 ) B. 52.8 c. 55 D. 45 | 11 |

231 | Compute Mean deviation about median for the following Frequency distribution. Variable( ( x ) ( mathbf{1 0} ) ( mathbf{1 5} quad mathbf{2 0} quad mathbf{2 5} ) Frequency [ f) ] A . 10.5 в. 10.1 c. 13.2 D. 12.1 | 11 |

232 | Mean of 10 observations is 50 and their standard deviation is ( 10 . ) If each observation is subtracted by 5 and then divided by ( 4, ) then the new mean and standard deviation are A ( .22 .45,2.5 ) В. 11.25,2.5 c. 11.5,2.5 D. 11,2.5 E . 11.75,2.5 | 11 |

233 | Arithmetic mean for ungrouped data can be calculated by A. assumed mean method B. direct method c. step deviation method D. all of the above | 10 |

234 | The standard deviation of a data is 6 when each observation is increased by 1, then the S.D. of the new data is A . 5 B. 7 ( c .6 ) D. | 11 |

235 | begin{tabular}{llllll} C.I. & ( 0- ) 4 & 4 8 & ( 8- ) 12 & ( 12- ) 16 & 16 20 \ hline end{tabular} 19 Find the mode of the following data A. 10.6 B. 12 c. 12.6 D. 8 | 10 |

236 | The ages (in years) of a family of 6 members are 1,5,12,15,38 and 40 The standard deviation is found to be 15.9 After 10 years the standard deviation is A . increased B. decreased c. remains same D. none of these | 11 |

237 | The variance of ( 10,10,10,10,10, ) is A . 10 B. ( sqrt{10} ) ( c .0 ) D. 5 | 11 |

238 | The age distribution of 400 persons in a colony having median age 32 is given below [ begin{array}{llll} text { Age } sin & 20- & 25- & 30- \ text { Years) } & 25 & 30 & 35 end{array} ] Frequency 75 Then, ( (x-y) ) is : A .10 в. 20 c. -10 D. – 20 | 10 |

239 | The sum and sum of squares corresponding to length ( X ) (in ( mathrm{cm} ) ) and weight ( boldsymbol{y} ) (in ( g m) ) of 50 plant products are given below: [ begin{array}{l} sum_{i=l}^{50} boldsymbol{X}_{i}=mathbf{2 1 2}, sum_{i=l}^{50} boldsymbol{X}_{i}^{2}= \ mathbf{9 0 2 . 8}, sum_{i=l}^{50} boldsymbol{y}_{i}=mathbf{2 6 1}, sum_{i=l}^{50} boldsymbol{y}_{i}^{2}=mathbf{1 4 5 7 . 6} end{array} ] Which is more varying the length or weight? | 11 |

240 | In a study of two groups, the following results were obtained Group Sample size 20 Sample mean 22 Sample standard deviation 10 Which of the following statements is correct? A. Group A is less variable than Group B because Group A’s standard deviation is smaller. B. Group A is less variable than Group B because Group A’s sample size is smaller. C. Group ( A ) is less variable than Group ( B ) because Group A’s sample mean is smaller D. Group A is less variable than Group B because Group A’s coefficient of variation is smaller. | 11 |

241 | Find the coefficient of variation. A. 72.66 B. 81.24 ( c cdot 264 ) D. 330 E. None | 11 |

242 | The standard error of two means is equal to ( ^{mathrm{A}} cdot sqrt{frac{sigma_{1}^{2}}{n_{1}}+frac{sigma_{2}^{2}}{n^{2}}} ) в. ( frac{sigma}{sqrt{n-1}} ) c. ( frac{sigma}{sqrt{n+1}} ) D. ( sqrt{frac{P_{1} Q_{1}}{sqrt{n_{1}}}+frac{P_{2} Q_{2}}{n_{2}}} ) | 11 |

243 | If the mean deviation of number ( 1,1+ ) ( boldsymbol{d}, mathbf{1}+mathbf{2} boldsymbol{d}, dots, mathbf{1}+mathbf{1 0 0} boldsymbol{d} ) from their mean is ( 255, ) then the ( d ) is equal to :- A . 20.0 B. 10.1 c. 20.2 D. 10.0 | 11 |

244 | The mean square deviation of set of ( n ) observations ( x_{1}, x_{2}, ldots . . x_{n} ) about a point ( c ) is defined as ( frac{1}{n} sum_{i=1}^{n}left(x_{i}-cright)^{2} ) The mean square deviation about -2 and 2 are 18 and 10 respectively, then standard deviation of this set of observations is A . 3 B. 2 c. 1 D. none of these | 11 |

245 | The median of 230 observations is 46 Find ( a ) and ( b ) ( begin{array}{lllll}text { Class } & begin{array}{l}10- \ 20end{array} & begin{array}{l}20- \ 30end{array} & begin{array}{l}text { 30- } \ 40end{array} & begin{array}{l}text { 40- } \ 50end{array}end{array} ) Frequency 12 30 ( a ) | 10 |

246 | The mean and median of 100 items are 50 and 52 respectively. The value of largest item is ( 100 . ) If was later found that it it 110 and not ( 100 . ) The true mean and median are: A. 50.10,51.5 B . 50.10,52 ( c .50,51.5 ) D. none of these | 10 |

247 | The Coefficient of Variation is given by: A. ( frac{text { Mean }}{text { Standard deviation }} times 100 ) B. ( frac{text { Standard deviation }}{text { Mean }} ) c. ( frac{text { Standard deviation }}{text { Mean }} times 100 ) D. ( frac{text { Mean }}{text { Standard Deviation }} ) | 11 |

248 | The mean of the following natural numbers ( 1,2,3, dots 10 ) is A . 6.5 в. 4.5 ( c .5 .5 ) D. 5.4 | 10 |

249 | If the variance of the series of the form ( 5 x_{1}+7 ) is 225 then standard deviation of the series of the form ( 7 x_{1}+5 ) is A .21 B. 44 c. 484 D. 22 | 11 |

250 | Heights of the pupils of a particular school are given. Draw greater than cumulative curve and find the median height from it. ( 110-quad 120 ) ( begin{array}{ll}90- & 100- \ 100 & 110end{array} ) Height (in ( mathrm{cm} ) ) 120 13. Number of pupils | 10 |

251 | For two data sets, each of size of ( 5, ) the variances are given to be 4 and 5 and the corresponding means are given to be 2 and ( 4, ) respectively. The variance of the combined data set is : A ( cdot frac{11}{2} ) B. 6 c. ( frac{13}{2} ) D. | 11 |

252 | The mean of a dist. is ( 4 . ) if its coefficient of variation is ( 58 % ). Then the S.D. of the dist. is A .2 .23 в. 3.23 c. 2.32 D. None of these | 11 |

253 | A group of 10 observations has mean 5 and ( S . D .2 sqrt{6} ) another group of 20 observations has mean 5 and ( mathrm{S.D.} 3 sqrt{2} ) then the S.D. of combined group of 30 observations is A ( cdot sqrt{5} ) B. ( 2 sqrt{5} ) ( c cdot 3 sqrt{5} ) D. none of these | 11 |

254 | Find variance for the following data: ( begin{array}{lllll}text { Wages } & begin{array}{l}125- \ 175end{array} & begin{array}{l}text { 175- } \ 225end{array} & begin{array}{l}text { 225- } \ 275end{array} & begin{array}{l}text { 275- } \ 325end{array}end{array} ) workers 2 १९ 14 A . 7935.69 в. 7935.56 c. 7835.89 D. 7835.16 | 11 |

255 | The table shows Paula’s scores in a revision test out of ( 20 . ) Find the median score for the subject. Maths Science History Geography | 10 |

256 | Find the mean deviation about the mean for data. ( boldsymbol{x}_{i} quad 5 quad 10 ) 20 15 5 6 ( f_{i} quad ) 7 ( quad 4 ) | 11 |

257 | The marks obtained by 20 students of Class ( X ) of a certain school in a English paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students using step deviation method. A . 61 B. 62 ( c cdot 63 ) D. 64 | 10 |

258 | Find the standard deviation of ( mathbf{9}, mathbf{1 6}, mathbf{2 3}, mathbf{3 0}, mathbf{3 7}, mathbf{4 4}, mathbf{5 1} ) | 11 |

259 | Assertion The variance of first ( n ) natural numbers is ( frac{n^{2}-1}{6} ) Reason The sum of the first ( n ) odd natural numbers is ( n^{2} ) and the sum of squares of first ( n ) odd natural numbers is ( frac{n}{3}left(4 n^{2}-1right) ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

260 | Which of the following statements is true of a measure of dispersion? A. Mean deviation does not follow algebraic value B. Range is crudest measure c. coefficient of variation is a relative measure D. All the above statements | 11 |

261 | Coefficient of deviation is calculated by the formula: A ( cdot frac{bar{X}}{sigma} times 100 ) в. ( frac{bar{X}}{sigma} ) ( ^{mathrm{c}} cdot frac{sigma}{bar{X}} times 100 ) D. ( frac{sigma}{bar{X}} ) | 11 |

262 | Calculate mean deviation about median begin{tabular}{lllll} Scores & 145 & 155 & 165 & 175 \ Frequency & 4 & 6 & 10 & 18 \ hline end{tabular} A. 11.56 B. 6.66 c. 11.25 D. 10.56 | 11 |

263 | Let ( bar{X} ) and M.D. be the mean and the mean deviation about ( bar{X} ) of ( n ) observations ( x_{i}, i=1,2, ldots . ., n . ) If each of the observations is increased by 5 then the new mean and the mean deviation about the new mean, respectively, are : A. ( bar{X}, ) М.D. в. ( bar{X}+5, M . D ) c. ( bar{X}, M . D .+5 ) D. ( bar{X}+5 m, M . D .+5 ) | 11 |

264 | The table below shows the members in “Stree-Sakti Kudambasree” Sorted according to their ages. Number of members Age group in the 20-30 ( 30-40 ) ( 40-50 quad 10 ) ( 50-60 ) ( 50-60 ) ( 60-70 ) ( 70-80 ) 35 Total a. If the members are arranged in increasing order of gas, the member at what position is taken as media? b. What is assumed to be age of the member at the 13 th position? c. Find the median of the ages. | 10 |

265 | Find mode for the following data: ( begin{array}{llllll}mathbf{x} & mathbf{2}- & mathbf{4}- & mathbf{6}- & mathbf{8}- & mathbf{1 0} \ mathbf{4} & mathbf{6} & mathbf{8} & mathbf{1 0} & mathbf{1 2} mathbf{2}end{array} ) 2 2 1 A . 11 в. 12 c. 13 D. 14 | 10 |

266 | The number of candy bars students brought to school the day after Halloween are given in the table. What is the mode? begin{tabular}{|c|c|} hline Number of Candy Bars & Number of Students \ hline 0 & 1 \ hline 1 & 1 \ hline 2 & 1 \ hline 3 & 3 \ hline 4 & 0 \ hline 5 & 4 \ hline 7 & 2 \ hline 8 & 2 \ hline end{tabular} 4 ( B ) ( c ) ( D ) | 10 |

267 | The mean and S.D of 100 observations are 50 and 4 respectively. Find the sum of squares of observation. | 11 |

268 | The scores of 10 students in a class test are given as 44,54,46,63,55,42,34,48,70,38 Calculate the mean deviation about the median. A . 8.6 B. 6.6 ( c .7 .6 ) D. 8.8 E . None of these | 11 |

269 | The mean of the numbers ( a, b, 8,5,10 ) is 6 and the variance is ( 6.80 . ) Then which one of the following gives possible values of ( a ) and ( b ? ) A ( . a=0, b=7 ) В. ( a=5, b=2 ) c. ( a=1, b=6 ) D. ( a=3, b=4 ) | 11 |

270 | According to above histogram, Which group has the maximum number of workers? 4.810 B. 820 ( c cdot 830 ) ( D cdot 840 ) | 9 |

271 | The relation connecting the measures of central tendencies is : A. mode ( =2 ) median -3 mean B. mode ( =3 )median -2 mean c. mode( =2 )median+3 mean D. mode ( =3 )median+2 mean | 10 |

272 | Find the mode of the following data ( begin{array}{ll}text { Class Interval } & text { Frequency } \ 10-20 & 7 \ 20-30 & 12 \ 30-40 & 20 \ 40-50 & 11 \ 50-60 & 8end{array} ) | 10 |

273 | The mean of five numbers is 0 and their variance is ( 2 . ) If three of those numbers ( operatorname{are}-1,1 ) and ( 2, ) then the other two numbers are : ( mathbf{A} cdot-5 ) and 3 B. – 4 and 2 c. -3 and 1 D. -2 and 0 E . -1 and -1 | 11 |

274 | If the mean deviation of number ( 1,1+ ) ( boldsymbol{d}, mathbf{1}+mathbf{2} boldsymbol{d}, dots, mathbf{1}+mathbf{1 0 0} boldsymbol{d} ) from their mean is ( 255, ) then the ( d ) is equal to: A . ( 10 . ) B. 20.2 c. 20 D. 10 | 11 |

275 | Find variance for following data: ( begin{array}{lllll}text { Marks } & mathbf{0}- & mathbf{5}- & mathbf{1 0}- & mathbf{1 5}- \ & mathbf{4} & mathbf{9} & mathbf{1 4} & mathbf{1 9}end{array} ) Frauency ( quad 2 quad 5 quad 7 ) 3 ( A cdot 7 ) в. 55 c. 64 D. 78 | 11 |

276 | Q Type your question_ expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure: begin{tabular}{ll} Expenditure (in Rs.) & No. of families \ ( 1000-1500 ) & 24 \ ( 1500-2000 ) & 40 \ ( 2000-2500 ) & 33 \ ( 2500-3000 ) & 28 \ ( 3500-4000 ) & 22 \ ( 4000-4500 ) & 16 \ ( 4500-5000 ) & 7 \ hline end{tabular} A. 2662.5 B . 2642.5 c. 2600.5 D. 2505.5 | 10 |

277 | If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately 2005] (a) 22.0 (b) 20.5 (c) 25.5 (d) 24.0 1 . | 10 |

278 | 62. The mean value of 20 observa- tions was found to be 75. but later on it was detected that 97 was misread as 79. Find the cor- rect mean. (1) 75.7 (2) 75.8 (3) 75.9 (4) 75.6 | 9 |

279 | Find the mode for the following data: (4 and ( 5) ) ( begin{array}{lllll}text { class } & 0- & 7- & 14- & 21- \ 7 & 14 & 21 & 28end{array} ) Area 26 31 35 | 10 |

280 | Draw a frequency polygon of the following data using histogram. ( begin{array}{llll}text { class } & mathbf{0}- & mathbf{1 0}- & mathbf{2 0}- \ text { interval } & mathbf{1 0} & mathbf{2 0} & mathbf{3 0}end{array} ) 一年 Frequency 5 10 25 | 9 |

281 | The marks in science of 80 students of class ( X ) are given below. Find the mode of the marks obtained by the students in science c… ( begin{array}{llll}0- & 10- & 20- & 30- \ 10 & 20 & 30 & 40end{array} ) Freq. 1 3 A. 17.36 B. 36.56 c. 53.17 D. 75.12 | 10 |

282 | What is the range of the data: ( mathbf{4 8}, mathbf{6 5}, mathbf{2 7}, mathbf{2 3}, mathbf{4 4}, mathbf{4 1}, mathbf{2 5}, mathbf{7 0}, mathbf{4 9} ? ) | 11 |

283 | Find the median for the grouped data given below: ( begin{array}{lllll}text { Marks } & 50- & 60- & 70- & 80 \ & 60 & 70 & 80 & 9000end{array} ) Students 3. 3 4 A. 53.75 в. 63.75 c. 73.75 D. 83.75 | 10 |

284 | The librarian at the public library counted the number of books on each shelf. The lowest number of books contained by any of the self is Books per shel ( A ) B. ( c . ) ( D ) | 9 |

285 | The variance of first ( n ) natural numbers is A ( frac{n^{2}+1}{12} ) в. ( frac{n^{2}-1}{12} ) c. ( frac{n(n+1)(2 n+1)}{6} ) D. none of these | 11 |

286 | Find the median height for the following data: Height(cm) ( quad begin{array}{ccc}50- & 100- & 150- \ 100 & 150 & 200end{array} ) Number of 2 tuder A. ( 123.33 mathrm{cm} ) в. ( 133.33 mathrm{cm} ) c. ( 143.33 mathrm{cm} ) D. ( 153.33 mathrm{cm} ) | 10 |

287 | Following table gives frequency distribution of time (in minutes) taken by a person in watching T.V. on a day. Time ( quad ) 30 ( quad 40 quad 50 quad 60 ) ne in ( min ) ( begin{array}{llll}text { 40 } & text { 50 } & text { 60 } & text { 70 }end{array} ) No. of 19 14 persons Obtain modal time taken for watching a T.V. by persons on a day. A. ( 51.22 . ) minutes B . 53.22 . minutes c. 57.22 . minutes D. ( 59.22 . ) minutes | 10 |

288 | Calculate mean deviation about mean for the given data. Score ( (x) quad 6 quad 20 ) 3. 8 11 Frequency ( begin{array}{ll}text { (f) } & text { (f) } 7end{array} ) 27 A. 3.117 B. 3.217 c. 4.212 D. 6.21 | 11 |

289 | Find the mean and standard deviation respectively for the following data. Year 10 20 30 40 Number of persons (cumulative) 32 51 1 A . 34.95 , 4.01 B. 32.95, 2.97 c. 34.95,1.99 D. 32.95 , 3.49 | 11 |

290 | The mean of five observations is 4.4 and the variance is ( 8.24 . ) Three of the five observations are 1,2 and ( 6 . ) The remaining two are ( mathbf{A} cdot 9,4 ) в. 7,6 c. 6,5 D. 10,3 | 11 |

291 | Represent the following data using suitable graphical representation. No. of [ begin{array}{llll} text { words } & mathbf{3 0}- & mathbf{4 0 -} & mathbf{5 0 -} \ text { typed } & mathbf{3 9} & mathbf{4 9} & mathbf{5 9} \ text { per } & & end{array} ] ( operatorname{minute} ) No. of typists 15 | 9 |

292 | If mean ( =(3 text { median }-text { mode }) x, ) then the value of ( x ) is A . 1 B. 2 ( c cdot frac{1}{2} ) D. ( frac{3}{2} ) | 10 |

293 | The mean deviation from the mean 10 of the data ( 6,7,10,12,13, alpha, 12,16 ) is A . 3.5 B. 3.25 5 ( c .3 ) D. 3.75 5 | 11 |

294 | Let ( x_{1}, x_{2}, ldots, x_{n} ) be ( n ) observations such that ( sum x_{i}^{2}=400 ) and ( sum x_{i}=80 . ) Then a possible value of ( n ) among the following is : A. 15 B. 18 ( c cdot 12 ) D. | 11 |

295 | Calculate Mean deviation about median for the given data ( begin{array}{llll}text { Marks } & begin{array}{l}100- \ 110end{array} & begin{array}{l}110- \ 120end{array} & begin{array}{l}120- \ 130end{array}end{array} ) Frequency 4 A . 10.5 в. 31.5 c. 12.5 D. 66.16 | 11 |

296 | The following table given the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers. [ begin{array}{llll} text { Wages } & 125- & 175- & 225- \ text { (Rs) } & 175 & 225 & 275 end{array} ] Number of workers | 11 |

297 | Let ( x_{1}, x_{2}, dots . . x_{n} ) be values taken by a variable ( boldsymbol{X} ) and ( boldsymbol{y}_{1}, boldsymbol{y}_{2}, dots dots boldsymbol{y}_{n} ) be the values taken by variable ( Y ) such that ( boldsymbol{y}_{i}=boldsymbol{a} boldsymbol{x}_{i}+boldsymbol{b} ; quad boldsymbol{i}=mathbf{1}, boldsymbol{2}, ldots boldsymbol{n} . ) Then A ( . operatorname{Var}(Y)=a^{2} operatorname{Var}(X) ) B. ( operatorname{Var}(X)=a^{2} operatorname{Var}(Y) ) c. ( operatorname{Var}(X)=operatorname{Var}(X)+b ) D. none of these | 11 |

298 | Find the mean deviation about the median of the following data: ( mathbf{1 1}, mathbf{3}, mathbf{8}, mathbf{7}, mathbf{5}, mathbf{1 4}, mathbf{1 0}, mathbf{2}, mathbf{9} ) A . 2.8 B. 3 ( c .3 .3 ) D. 2.9 | 11 |

299 | Following is the distribution of the size of certain farms from a taluka (tehasil) Find median size of farms. ( operatorname{size} ) ( begin{array}{ll}text { of } & 5 \ text { farm } & -end{array} ) 15 25 35 (in 25 ( 35 quad 45 ) [ 15 ] acres No. of 2 25 farms A . 33.60 Acres B. 37.60 Acres c. 38.60 Acres D. 40.60 Acres | 10 |

300 | Calculate M.D about Mean for the given data begin{tabular}{lcccc} Size of item & 4 & 6 & 8 & 10 \ hline end{tabular} [ text { Frequency } quad 2 quad 1 quad 3 ] 6 A . 6.12 в. 5.12 c. 2.44 D. 3.44 | 11 |

301 | If mean of following data is 215 then find ( k ) ( begin{array}{lllll}text { Class } & 0- & 10- & 20- & 30- \ & 10 & 20 & 30 & 40end{array} ) 1 4 | 10 |

302 | Median of the following freq. dist. ( boldsymbol{x}_{i} quad boldsymbol{3} quad boldsymbol{6} ) ( mathbf{1 2} ) ( mathbf{1 0} ) ( f_{i} quad 3 quad 4 quad 2 ) 13 ( A cdot 7 ) B. 10 c. 8.5 D. None of these | 10 |

303 | Q Type your question an apartment are groupea as roılows: The mean length of the plants is 33.43 years using direct method. Find y in the table ( begin{array}{ll}text { Age(years) } & text { Number of people } \ 0-10 & 10 \ 10-20 & 15 \ 20-30 & 26 \ 30-40 & mathrm{Y} \ 40-50 & 23 \ 50-60 & 16 \ 60-70 & 3 \ 70-80 & 1end{array} ) A . 23 B . 28 c. 15 ( D ) | 10 |

304 | On approximately what percent of the days was the 2 p.m temperature above ( 40^{circ} F ) but less than ( 70^{circ} F ? ) a A. Approx. ( 50 % ) B. Approx. ( 70 % ) c. Approx. ( 60 % ) D. None of these | 9 |

305 | From the data given below state which group is more variable ( boldsymbol{A} ) or ( boldsymbol{B} ) ( begin{array}{llllll}text { Marks } & begin{array}{l}10- \ 20end{array} & begin{array}{l}20- \ 30end{array} & begin{array}{l}30- \ 40end{array} & begin{array}{l}text { 40- } \ text { 50 }end{array} & begin{array}{l}text { 50 } \ 60end{array}end{array} ) Group A 32 33 17 25 begin{tabular}{l|l|l|l} Group & 10 & 20 & 30 \ B & (年) & (年) end{tabular} | 11 |

306 | If the average of the following data is 100. Find the value of ( p ) begin{tabular}{|c|c|c|c|c|c|c|} hline( x: ) & 10 & 20 & 30 & 40 & 50 & 60 \ hline( f: ) & 2 & 4 & ( p ) & 8 & 10 & 12 \ hline end{tabular} A . -26 B. -28 c. -25 D. -24 | 10 |

307 | Find the standard deviation of the numbers 62,58,53,50,63,52,55 | 11 |

308 | Coefficients of variation of two distributions are 50 and 60 and their arithmetic mean are 30 and 25 respectively. Difference of their standard deviation is ( mathbf{A} cdot mathbf{0} ) B. ( c .1 .5 ) D. 2.5 | 11 |

309 | For a certain frequency distribution, the values of Median and Mode are 95.75 and 95.5 respectively. Find the Mean A . 95.175 B. 95.475 c. 95.875 D. 96.975 | 10 |

310 | The mean of the ungrouped data is given by ( ^{mathrm{A}} cdot operatorname{Mean}=frac{sum x_{i}}{sum f} ) B. ( operatorname{Mean}=frac{sum x}{n} ) c. ( operatorname{Mean}=frac{sum f x}{sum n} ) D. mean ( =a+frac{sum f x}{sum n} ) | 10 |

311 | Find the mean deviation about the mean for the following data: ( begin{array}{ll}text { Marks obtained } & text { No. of students } \ text { 0-10 } & 5 \ text { 10-20 } & 8 \ text { 20-30 } & 15 \ text { 30-40 } & 16 \ text { 40-50 } & 6end{array} ) | 11 |

312 | Given mean ( =12, ) mode ( =3 . ) Find median. A ( cdot 12 ) B. 2 ( c cdot 9 ) D. | 10 |

313 | For a collection of data, if ( sum x= ) ( mathbf{3 5}, boldsymbol{n}=mathbf{5}, sum(boldsymbol{x}-mathbf{9})^{2}=mathbf{8 2}, ) then find ( sum x^{2} ) and ( sum(x-bar{x})^{2} ) | 11 |

314 | Variance remains unchanged by change of A. scale B. origin c. both D. none of these | 11 |

315 | Assertion The variance of first ( n ) even natural numbers is ( frac{n^{2}-1}{4} ) Reason The sum of first ( n ) natural even numbers is ( n(n+1) ) and the sum of squares of first ( n ) natural numbers is ( frac{n(n+1)(2 n+1)}{6} ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

316 | If ‘ ( x^{prime} ) varies inversely as ‘ ( y^{prime} ) and ( x=7 ) when ( boldsymbol{y}=mathbf{9} ) (a) Find constant of variation ( (k) ) (b) Write equation of variation. (c) Find ‘ ( y^{prime} ) when ( x=9 ) | 11 |

317 | The following table shows the age distribution of cases of a certain disease admitted during a year in a particular hospital ( begin{array}{ll}text { Age } & text { 5 } \ text { (in } & text { – } \ text { Years) } & text { 14 }end{array} ) 15 25 34 24 44 No. of 6 11 ( begin{array}{ll}21 & 23end{array} ) case Find the nearest integer to the modal age. | 10 |

318 | The modal class of the following frequency distribution is class ( begin{array}{cc}0- & 10- \ 10 & 20end{array} ) 30 40 Frequency 15 17 A . ( 20-30 ) в. ( 10-20 ) c. ( 30-40 ) D. ( 40-50 ) | 10 |

319 | The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Runs scored ( quad ) Number of batsmen tsmen ( 3000-4000 ) Is ( ^{4000}-5000 ) ( begin{array}{lll}5000-6000 & 9 \ 6000-7000 & 7 \ 7000-8000 & 6 \ 8000-9000 & 3 \ 9000-10000 & 1 \ 10000-11000 & 1end{array} ) and Find the mode of the data. | 10 |

320 | Find the decreased maintenance cost in the year ( 2000-2001 ) when compared to 1999 to 2000 listopran ( A .100 ) в. 120 ( c .1500 ) D. 150 | 9 |

321 | Wurks) deviation I WS SULU The marks obtained by 40 students are groupe frequency table in class intervals of 10 maks each. Thi and the variance obtained from this distribution ar to be 40 and 49 respectively. It was later discovered th observations belonging to the class interval (21-30 included in the class interval (31-40) by mistake. Fina mean and the variance after correcting the error. ouped in a ch. The mean ion are found ered that two 1_30) were ke. Find the (1982 – 3 Marle. | 11 |

322 | A survey regarding the height (in cm) of 51 girls of class ( X ) of a school was conducted and the following data was obtained: ( begin{array}{ll}text { Height in } mathrm{cm} & text { Number of Girls } \ text { Less than } 140 & 4 \ text { Less than } 145 & 11 \ text { Less than } 150 & 29 \ text { Less than } 155 & 40 \ text { Less than } 155 & 46 \ text { Less than } 165 & 51end{array} ) Find the median height. | 10 |

323 | Consider the following statements: 1. Coefficient of variation depends on the unit of measurement of the variable. 2. Range is a measure of dispersion 3. Mean deviation is least when measured about median. Which of the above statements are correct? A. 1 and 2 only B. 2 and 3 only c. 1 and 3 only D. 1,2 and 3 | 11 |

324 | Find the modal age of 100 residents of a colony from the following data: Age in yrs (more 10 20 ( quad 30 ) than o equal to) No. of 00 persons | 10 |

325 | Let ( r ) be the range of ( n(forall n geq 1) ) observations ( boldsymbol{x}_{1} boldsymbol{x}_{2} ldots, boldsymbol{x}_{boldsymbol{n}} ) if ( boldsymbol{S}= ) ( sqrt{frac{sum_{t=1}^{n}left(x_{i}-bar{x}right)^{2}}{n-1}}, ) then ( ^{mathbf{A}} cdot_{S}<r sqrt{frac{n^{2}+1}{n-1}} ) в. ( s geq r sqrt{frac{n}{n-1}} ) c. ( s=r sqrt{frac{n}{n-1}} ) D. ( s<r sqrt{frac{n}{n-1}} ) | 11 |

326 | Mean proportion of 64 and 225 will be – A ( cdot 120 ) B. 90 ( c cdot 60 ) D. 30 | 10 |

327 | Find the mean deviation from the mean of the following data, using the step deviation method: begin{tabular}{|l|l|} hline Marks & No. of students \ hline ( 0-10 ) & 6 \ hline ( 10-20 ) & 5 \ hline ( 20-30 ) & 8 \ hline ( 30-40 ) & 15 \ hline ( 40-50 ) & 7 \ hline ( 60-70 ) & 3 \ hline end{tabular} | 11 |

328 | The marks obtained by the students of class 6 are shown: ( mathbf{0}-mathbf{1 0} quad mathbf{1 0}-mathbf{2 0} quad mathbf{2 0}-mathbf{3 0} ) ( mathbf{3 0}-mathbf{4 0} ) 15 32 55 Find the mean of the data. | 10 |

329 | The variance of observations 112,116,120,125,132 is A . 58.8 B. 48.8 c. 61.8 D. None of these | 11 |

330 | The one which is the measure of the central tendency is A. mode B. mean deviation c. standard deviation D. coefficient of correlation | 10 |

331 | The algebraic sum of deviations of ten observations about 15 is ( 70 . ) The mean is A . 22 B. 25 c. 20 D. none of these | 11 |

332 | The standard deviation of 25 numbers is ( 40 . ) if each of the numbers is increased by ( 5, ) then the new standard deviation will be A . 40 B. 45 c. ( _{40}+frac{21}{25} ) D. None of these | 11 |

333 | Identify the shape of this histogram. A. Symmetric B. Skewed right C. Skewed left D. Rotational | 9 |

334 | Batsman ( A ) gets and average of 64 runs per innings with standard deviation of 18 runs, while batsman ( B ) get an average score of 43 runs with standard deviation of 9 runs in an equal number of innings. Discuss the efficiency and consistency of both the batsmen | 11 |

335 | Find the median for the following data shows that distance covered by 200 people to perform their IT project. ( begin{array}{ccc}mathbf{5}- & mathbf{1 5}- & mathbf{2 5}- \ mathbf{1 5} & mathbf{2 5} & mathbf{3 5}end{array} ) Distance(km) Number of people 60 40 A. ( 12 mathrm{km} ) B. ( 13 mathrm{km} ) ( mathbf{c} .14 mathrm{km} ) D. ( 15 mathrm{km} ) | 10 |

336 | For a random variable ( boldsymbol{X} . ) If ( boldsymbol{E}(boldsymbol{X})=mathbf{5} ) and ( V(X)=6, ) then ( Eleft(X^{2}right) ) is equal to A . 19 B. 31 c. 61 D. 11 | 11 |

337 | What is the measures of central tendency for the data set ( mathbf{5}, mathbf{5}, mathbf{1 0}, mathbf{1 0}, mathbf{5}, mathbf{2 0}, mathbf{2 5} ? ) | 10 |

338 | Which type of average is most affected by extreme values in the data? A. Mean B. Mode c. Median D. All of the above | 10 |

339 | Find Mean Deviation from Median for the given data ( boldsymbol{x} quad mathbf{1 0} ) ( mathbf{3 0} ) 5 ( mathbf{2 0} ) 40 ( f ) 18 25 27 A. 18.45 в. 16.65 c. 10.5 D. 11.36 | 11 |

340 | If mean and variance of 7 variates are 8 and 16 respectively and five of them are 2,4,10,12,14 then find the product of remaining two variates ( mathbf{A} cdot 49 ) B. 48 c. 45 D. 40 | 11 |

341 | Mean of 100 observations is 50 and standard deviation is ( 10 . ) If 5 is added to each observations, then what will be the new mean and new standard deviation respectively? ( mathbf{A} cdot 50,10 ) B. 50,15 ( mathbf{c} .55,10 ) D. 55,15 | 11 |

342 | If the mean of ( x ) and ( 1 / x ) is ( M ) then the mean of ( x^{2} ) and ( 1 / x^{2} ) is A ( cdot M^{2} ) B . ( M^{2} / 4 ) c. ( 2 M^{2}-1 ) D. ( 2 M^{2}+1 ) | 10 |

343 | The median of 230 observations of the following frequency distribution is 46 Find ( a ) and ( b: ) ( begin{array}{lllll}text { Class } & begin{array}{l}10- \ 20end{array} & begin{array}{l}20- \ 30end{array} & begin{array}{l}text { 30- } \ 40end{array} & begin{array}{l}text { 40- } \ text { 50 }end{array}end{array} ) 12 ( quad ) 30 Frequency a | 10 |

344 | Find the mode of the following data. begin{tabular}{lllll} multirow{2}{*} { Number } & ( mathbf{0}- ) & ( mathbf{3}- ) & ( mathbf{6}- ) & ( mathbf{9}- ) \ & ( mathbf{3} ) & ( mathbf{6} ) & ( mathbf{9} ) & ( mathbf{1 2} ) end{tabular} Frequency ( quad 4 quad 18 ) 9 A . 19 B. 31 c. 26 D. 2 | 10 |

345 | If ( x_{1}, x_{2}, dots . . x_{n} ) are ( n ) values of a variable ( X ) and ( y_{1}, y_{2}, dots . y_{n} ) are ( n ) values of ( a ) variable ( boldsymbol{Y} ) such that ( boldsymbol{y}_{i}= ) ( frac{boldsymbol{x}_{i}-boldsymbol{a}}{boldsymbol{h}} ; quad boldsymbol{i}=mathbf{1}, boldsymbol{2}, ldots . ., boldsymbol{n}, ) then A. ( operatorname{Var}(Y)=operatorname{Var}(X) ) B. ( operatorname{Var}(X)=h^{2} operatorname{Var}(Y) ) C ( . operatorname{Var}(Y)=h^{2} operatorname{Var}(X) ) D. ( operatorname{Var}(X)=h^{2} operatorname{Var}(Y)+a ) | 11 |

346 | The median of the following data is 525 Find the values of ( x ) and ( y ) if the total frequency is 100 begin{tabular}{|c|c|} hline Class Interval & Frequency \ hline ( 0-100 ) & 2 \ hline ( 100-200 ) & 5 \ hline ( 200-300 ) & ( x ) \ hline ( 300-400 ) & 12 \ hline ( 400-500 ) & 17 \ hline ( 500-600 ) & 20 \ hline ( 600-700 ) & ( mathrm{Y} ) \ hline ( 700-800 ) & 9 \ hline ( 800-900 ) & 7 \ hline ( 900-1000 ) & 4 \ hline end{tabular} | 10 |

347 | Which of the following is not changed for the observations ( mathbf{3 1}, mathbf{4 8}, mathbf{5 0}, mathbf{6 0}, mathbf{2 5}, mathbf{8}, mathbf{3 x}, mathbf{2 6}, mathbf{3 2} ? ) (where ( boldsymbol{x} ) lies between ( 10 text { and } 15) ) A . A.M B. Range c. Median D. Q.D | 11 |

348 | To find out the concentration of ( S O_{2} ) in the air (in parts per million, i.e., ( p p m ) ), the data was collected for 30 localities in certain city and is presented below: Concentration of ( S O_{2} ) ( f(operatorname{in} p p m) ) Frequency ( 2^{2} ) reeter ( 0.00-0.04 ) ( 0.04-0.08 ) ( 0.08-0.12 ) 9 ( 0.12-0.16 ) 2 ( 0.16-0.20 ) 4 ( 0.20-0.24 ) 2 Find the mean concentration of ( S O_{2} ) in the air. | 10 |

349 | The rainfall ( in ( mathrm{mm} ) ) in a city on 7 days of a certain week was recorded as follows: Days Mon Tue Wed Thurs Rainfall 2.2 i) Find the range of the rainfall in the above data. | 11 |

350 | Find the median for the following data given below: ( begin{array}{llll}text { class } & 11- & 21- & 31- \ text { interval } & 21 & 31 & 41end{array} ) Frequencies A . 35.28 B . 45.28 c. 55.28 D. 65.28 | 10 |

351 | Which one of the following statements is correct? A. The standard deviation for a given distribution is the square ofthe variance B. The standard deviation for a given distribution is the square root of the variance C. The standard deviation for a given distribution is equal to the variance D. The standard deviation for a given distribution is halfofthe variance | 11 |

352 | 30 children were asked about the number of hours they watched TV programmes last week. The results are recorded as under: ( begin{array}{lllll}begin{array}{l}text { Number } \ text { of }end{array} & mathbf{0}- & mathbf{5}- & mathbf{1 0}- & mathbf{1 5}- \ text { hours } & mathbf{5} & mathbf{1 0} & mathbf{1 5} & mathbf{2 0}end{array} ) frequncy 16 What is the number of children who watched TV for 10 or more hours a week? A . 8 B. 6 c. 10 D. 4 | 10 |

353 | The mean deviation from mean of the observation ( boldsymbol{a}, boldsymbol{a}+boldsymbol{d}, boldsymbol{a}+boldsymbol{2} boldsymbol{d}, ldots, boldsymbol{a}+ ) ( 2 n d ) is | 11 |

354 | Compute the modal class of the scores of the students in a Mathematics VIII test. 21 ( begin{array}{llll}text { class } & 12- & 15- & 1 \ text { score } & 15 & 18 & 2end{array} ) 21 24 frequency 2 A . ( 15-18 ) в. ( 24-27 ) c. ( 27-30 ) D. ( 30-33 ) | 10 |

355 | Coefficient of range 5,2,3,4,6,8,10 is? A ( cdot frac{2}{3} ) B. ( frac{1}{3} ) ( c cdot frac{3}{5} ) D. | 11 |

356 | The S.D. of scores 1,2,3,4,5 is A ( cdot sqrt{2} ) B. ( sqrt{3} ) ( c cdot frac{2}{5} ) D. | 11 |

357 | A shoe shop in Chennai sold hundred pairs of shoes of a particular brand in a certain day with the following distribution. [ begin{array}{lcccc} text { size } & & & & \ text { of } & 4 & 5 & 6 & 7 \ text { shoe } & & & & end{array} ] No [ begin{array}{l} text { of } \ text { pairs } \ text { sold } end{array} ] 23 Find the mode of the following distribution. | 10 |

358 | Calculate the range and coefficient of range from the following data: Number of trees planted in 6 months: ( mathbf{1 8 6}, mathbf{2 3 4}, mathbf{4 6 5}, mathbf{3 6 1}, mathbf{2 9 0}, mathbf{1 4 2} ) | 11 |

359 | Find the standard deviation of 40,42 and ( 48 . ) If each value is multiplied by 3 find the standard deviation of the new data | 11 |

360 | The following table shows the marks obtained by 48 students in a Quiz competition in Mathematics. Calculate the standard deviation. Data x [ begin{array}{cc} mathbf{7} & mathbf{8} end{array} ] Frequency | 11 |

361 | 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: (i) Draw a histogram to depict the given information. (ii) Write the class interval in which the maximum number of surnames lie. begin{tabular}{|c|c|} hline Number of letters & Number of surnames \ hline ( 1-4 ) & 6 \ ( 4-6 ) & 30 \ ( 6-8 ) & 44 \ ( 8-12 ) & 16 \ ( 12-20 ) & 4 \ hline end{tabular} | 9 |

362 | Calculate the standard deviation of the following data. ( mathbf{1 0}, mathbf{2 0}, mathbf{1 5}, mathbf{8}, mathbf{3}, mathbf{4} ) A . 5.97 в. 59.7 c. 4.97 D. None of these | 11 |

363 | Draw a frequency polygon for the following data using histogram. Marks 20 an Number of students | 9 |

364 | Find the mode for the following data: ( begin{array}{llll}text { Farm } & 12 & 13 & 14 \ text { size } & & end{array} ) ( mathbf{1 5} ) Number of animals 4 A . 13 B. 14 c. 19 D. All the above | 10 |

365 | Standard deviation of four observations -1,0,1 and ( k ) is ( sqrt{5} ) then ( k ) will be? A ( cdot 2 sqrt{6} ) B. ( c cdot 2 ) D. ( sqrt{6} ) | 11 |

366 | The following histogram shows the frequency distribution of the ages of 22 teachers in a school: What are the class marks of the classes | 9 |

367 | Find the arithmetic mean of the sales per day in a fair price shop in a week. Rs.10000, Rs.10250, Rs.10790, Rs.986 | 10 |

368 | A group of 100 candidates have their average height ( 163.8 mathrm{cm} ) with coefficient of variation ( 3.2 . ) What is the standard deviation of their heights? A . 5.24 в. 2.24 ( c .7 .24 ) D. None of these | 11 |

369 | In a set of ( 2 n ) observations, half of them are equal to ‘ ( alpha ) ‘ and the remaining half are equal to ‘ – ( boldsymbol{alpha} ) ‘. If the standard deviation of all the observations is 2 then the value of ( |boldsymbol{alpha}| ) is equal to A .2 B. ( sqrt{2} ) ( c cdot 2 sqrt{2} ) D. 4 | 11 |

370 | Consider the following groups ( A ) and B.A ( : 3,4,5, dots dots dots dots ) pto n terms ( B: 15,19,23, dots dots dots ) pto ( n ) terms If means deviations of groups ( A ) and ( B ) about their means are ( alpha ) and ( beta ) respectively then A ( . beta=5 alpha ) в. ( beta=4 alpha+3 ) c. ( beta=4 alpha ) D. None | 11 |

371 | The mean of five observations is 4 and their variance is ( 5.2 . ) If three of them are ( 1,2,6, ) then other two are A .2,9 B. 4,7 ( c cdot 5,6 ) D. 2, 10 | 11 |

372 | What is the difference of frequencies of the intervals ( 30-40 ) and ( 40-50 ? ) A . 5 B. 20 c. 15 D. 25 | 9 |

373 | The mean of 100 observations is 50 and their standard deviation is ( 5 . ) The sum of the squares of all the observations is ( mathbf{A} .50000 ) B. 250000 c. 252500 D. 255000 | 11 |

374 | The marks scored by two students ( M, N ) in a class are given below. Find the mean using direct method. begin{tabular}{|l|l|l|l|l|l|} hline( M ) & 98 & 88 & 87 & 90 & 70 \ hline( N ) & 50 & 65 & 80 & 95 & 100 \ hline end{tabular} A. 65 marks B. 70 marks C. 85 marks D. 90 marks | 10 |

375 | The population of four towns A, B, C and D as on 2011 are as follows: Town Population 6863 B 519 A D 1755 What is the most appropriate diagram to present the above data? (a) Pie chart (b) Bar chart (c) Histogram (d) Line graph | 9 |

376 | Calculate variance for the following data: 2,4,6,8 and 10 | 11 |

377 | state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret, the two measures. A. ( M o d e=43.6 ) and Mean( =21 . ) and ( M e a n=24 . ) B. Mode( =39.6 ) c. Mode( =35.6 ) and Mean ( =27.2 ) D. ( M o d e=30.6 ) and Mean | 10 |

378 | Daleel-1 15 talse, Statement 58. All the students of a class perform students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ? (JEE M 2013] (a) mean (b) median (c) mode (d) variance – ond y = 9(n-1): neN}, | 11 |

379 | The percentage of marks obtained by the students in a class of 50 are given below. Find the mode for the following data. Marks ( begin{array}{lll}mathbf{4 0}- & mathbf{5 0}- & mathbf{6 0}- \ mathbf{5 0} & mathbf{6 0} & mathbf{7 0}end{array} ) ( (%) ) Number of 6 12 14 horses A .62 .5 B. 63.5 c. 64.5 D. 65.5 | 10 |

380 | What proportion of good student are male? A. 0 B. 0.73 ( c cdot 0.4 ) D. 1.0 | 10 |

381 | A box contains 6 pens, 2 of which are defective. Two pens are taken randomly from the box. If r.v. ( X: ) Number of defective pens obtained, then standard deviation of ( boldsymbol{X}= ) ( ^{mathrm{A}}: pm frac{4}{3 sqrt{5}} ) B. ( frac{8}{3} ) ( c cdot frac{16}{45} ) D. ( frac{4}{3 sqrt{5}} ) | 11 |

382 | In two construction companies ( A ) and ( B ) the average weekly wages in rupees and the standard deviations are as follows: ( begin{array}{lll}text { Company } & begin{array}{l}text { Average of } \ text { wages }(text { in } mathrm{Rs})end{array} & begin{array}{l}text { S.D of wages } \ text { in }(mathrm{Rs})end{array} \ A & 3450 & 6.21 \ B & 2850 & 4.56end{array} ) Determine which factory has greater variability in individual wages? | 11 |

383 | In a village, an enumerator has surveyed for 25 households. The size of the family (number of family members) and the number of families is tabulated as follows: Size of [ begin{array}{lcccc} begin{array}{l} text { the family } \ text { (No. of } \ text { members) } end{array} & begin{array}{c} 1- \ 3 end{array} & begin{array}{c} 3- \ 5 end{array} & begin{array}{c} 5- \ 7 end{array} & begin{array}{c} 7- \ 9 end{array} \ begin{array}{l} text { No. of } \ text { families } end{array} & 6 & 7 & 9 & 2 end{array} ] Find the mode of the data. | 10 |

384 | If the coefficient of variation and standard deviation of a distribution are ( 50 % ) and 20 respectively, then its mean is A .40 B. 30 c. 20 D. none of these | 11 |

385 | Laspeyres Price Index ( =? ) begin{tabular}{|c|c|c|c|c|} hline multirow{2}{*} { Items } & multicolumn{2}{|c|} {2005} & multicolumn{2}{|c|} {2010} \ cline { 2 – 5 } & ( mathrm{P}_{0}(₹) ) & ( mathrm{Q}_{0} ) & ( mathrm{P}_{1}(₹) ) & ( mathrm{Q}_{1} ) \ hline ( mathrm{A} ) & 2 & 5 & 3 & 4 \ ( mathrm{B} ) & 1 & 2 & 2 & 3 \ ( mathrm{C} ) & 3 & 1 & 4 & 1 \ hline end{tabular} A. 157.33 B. 153.14 ( mathbf{c} cdot 153.33 ) D. 157.14 | 11 |

386 | Construct a histogram for the marks obtained by 600 students in the VII class annual examinations. ( mathbf{3 6 0} quad mathbf{4 0 0} quad mathbf{4 4 0} ) Marks No. of students 125 140 | 9 |

387 | Compute the mean for the following data: ( begin{array}{ll}text { Marks } & text { No. of students } \ text { Less than 10 } & 0 \ text { Less than 30 } & 10 \ text { Less than 50 } & 25 \ text { Less than 70 } & 43 \ text { Less than 90 } & 65 \ text { Less than 110 } & 87 \ text { Less than 130 } & 96 \ text { Less than 150 } & 100end{array} ) mean is 74.80 f true then enter 1 and if false then enter | 10 |

388 | In any discrete series (when all the value are not same) the relationship between M.D. about mean and S.D. is ( A cdot M cdot D=S cdot D ) в. ( M . D .> ) S.D. c. ( M . D .<S . D ) D. ( M . D . leq S . D . ) | 11 |

389 | 3. Pooja spends different hours of a working day as follows: Activity Number of hours School Coaching Play Sleep Wonwoo Other What is the difference in central angles for sleep and play in the pie chart? 11 TL | 9 |

390 | Observations of a data are ( mathbf{1 6}, mathbf{7 2}, mathbf{0}, mathbf{5 5}, mathbf{6 5}, mathbf{5 5}, mathbf{1 0}, ) and ( mathbf{4 1} ) Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing? | 10 |

391 | The mean and variance of 7 observations are 8 and 16 respectively. If 5 of the observations are ( 2,4,10,12,14, ) find the remaining two observations. ( mathbf{A} cdot 3,6 ) в. 6,8 c. 1,5 D. None of these | 11 |

392 | If the standard deviation of a set of scores is 1.2 and their mean is ( 10, ) then the coefficient of variation of the scores is A . 12 B. 0.12 c. 20 D. 120 | 11 |

393 | Which of the following are measures of central tendency A. Percentile, Quartile, Median B. Median,Mode, Percentile c. Percentile, Quartile, Mode D. Mean,Mode, Median | 11 |

394 | Identify the median class. ( begin{array}{lllll}text { Farm } & mathbf{2 0}- & mathbf{5 0}- & mathbf{8 0}- & mathbf{1 1 0} \ text { size } & mathbf{5 0} & mathbf{8 0} & mathbf{1 1 0} & mathbf{1 4 0}end{array} ) Rooms ( 4 quad 8 quad 12 ) A. ( 20-50 ) B . ( 50-80 ) c. ( 80-110 ) D. ( 110-140 ) | 10 |

395 | To find out the concentration of ( S O_{2} ) in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below: Concentration of ( S O_{2}(text { in ppm }) ) Frequency ( 0.00-0.04 ) ( 0.04-0.08 ) ( 0.08-0.12 ) ( 0.12-0.16 ) ( 0.16-0.20 ) ( 0.20-0.24 ) Find the mean concentration of ( S O_{2} ) in the air. | 10 |

396 | Assertion If ( boldsymbol{x}_{boldsymbol{i}}=(2 boldsymbol{i}-mathbf{1}) ; boldsymbol{i}=mathbf{1}, boldsymbol{2}, boldsymbol{3} ldots . ) Then, the sum of the deviations of ( boldsymbol{x}_{1}, boldsymbol{x}_{2}, dots dots boldsymbol{x}_{boldsymbol{n}} ) from ( boldsymbol{x}=boldsymbol{n} ) is zero Reason The algebraic sum of the deviations of a set of observations about their mean is zero. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion C. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason is correct | 11 |

397 | For the next three (03) items that follow The number of telephone calls received in 245 successive one minute intervals at an exchange is given below in the following frequency distribution. Number of calls 0 2 Frequency ( begin{array}{llll}text { 21 } & text { 25 } & text { 43 } & text { 35 } & text { 43 }end{array} ) What is the median of the distribution ( ? ) A . 3.5 B. 4 c. 4.5 D. 5 | 10 |

398 | If each observation of a dist., whose variance is ( sigma^{2}, ) is multiplied by ( lambda, ) then the ( S . D . ) of the new new observations is A . ( sigma ) B. ( lambda sigma ) c. ( |lambda| sigma ) D. ( lambda^{2} sigma ) | 11 |

399 | The S.D. of the following freq. dist. ( begin{array}{lllll}text { class } & begin{array}{c}0 \ 10end{array} & begin{array}{c}10 \ 20end{array} & begin{array}{c}20 \ 30end{array} & begin{array}{c}30- \ 40end{array}end{array} ) 2 ( f_{i} quad 1 quad 3 ) A . 7.8 B. 9 c. ( 8 . ) D. 0.9 | 11 |

400 | The following table shows the number of workers in a factory and their daily wages. Find the median of the daily wages. ( begin{array}{llll}text { Daily } & mathbf{1 0 0}- & mathbf{1 1 0}- & mathbf{1 2 0}- \ text { wages(Rupees) } & mathbf{1 1 0} & mathbf{1 2 0} & mathbf{1 3 0}end{array} ) No. of workers 37 38 | 10 |

401 | Calculate the number of patients in the hospital using step deviation method. begin{tabular}{|l|l|l|l|l|} hline Rooms & 20 & 30 & 40 & 50 \ hline Nübbrof patients & 7 & 14 & 21 & 28 \ hline end{tabular} A . 30 в. 40 c. 50 D. 60 | 10 |

402 | Find the mean deviation about the median for the data ( mathbf{1 3}, mathbf{1 7}, mathbf{1 6}, mathbf{1 4}, mathbf{1 1}, mathbf{1 3}, mathbf{1 0}, mathbf{1 6}, mathbf{1 1}, mathbf{1 8}, mathbf{1 2}, mathbf{1} ) | 11 |

403 | 58. Out of 30 teachers of a school, a teacher of age 60 years re- tired. In his place another teacher of age 30 years was appointed. As a result, the mean age of the teachers will (1) decrease by 2 years (2) decrease by 6 months (3) decrease by 1 year (4) remain same | 9 |

404 | Find the approximate value of mode for the following data: ( begin{array}{lllll}text { Marks } & 50- & 60- & 70- & 80 \ & 60 & 70 & 80 & 900end{array} ) Students 24 12 ( mathbf{A} cdot 71 ) B. 72 ( c cdot 73 ) D. 74 | 10 |

405 | The modal class of the given frequency distribution is ( begin{array}{llll}text { Marks } & mathbf{1 0}- & mathbf{2 0}- & mathbf{3 0}- \ text { Obtained } & mathbf{2 0} & mathbf{3 0} & mathbf{4 0}end{array} ) 7 35 Cumulative Frequency 27 A . ( 10-20 ) в. ( 30-40 ) ( c cdot 20-30 ) D. ( 40-50 ) | 10 |

406 | The mean deviation about median for the following data is ( 4.4 . ) calculate value of ( x ) ( 2,3, x, 10,17 ) A . 3 B. 5 ( c cdot 7 ) D. 17 | 11 |

407 | Find the upper limit of the median class from the given frequency distribution table ( begin{array}{cccc}mathbf{0}- & mathbf{6}- & mathbf{1 2}- & mathbf{1 8}- \ mathbf{5} & mathbf{1 1} & mathbf{1 7} & mathbf{2 3}end{array} ) Class Frequency 8 ( 03 quad 10 quad 15 ) ( mathbf{A} cdot 17 ) B . 17.5 ( mathbf{c} cdot 18 ) D. 18.5 | 10 |

408 | Identify the mode for the following data: 12 ( mathbf{5 6} ) 67 begin{tabular}{r} 34 \ hline end{tabular} Height(cm) Swimmers 1 1 2 A . 34 B. 56 c. 67 D. 10 | 10 |

409 | The two observations ( A & B ) are given by ( 100,101, ldots ldots .149 ) and ( 200,201, ldots ldots, 249 ) with ( V_{A} ) and ( V_{B} ) are variances of ( A ) and ( B ) than ( V_{A} ) is equal to: A. ( V_{B} ) в. ( 100 V_{B} ) ( mathbf{c} cdot 50 V_{B} ) D. ( 200 V_{B} ) | 11 |

410 | The coefficient of range of the following distribution 10,14,11,9,8,12,6 A . 0.4 B . 2. c. 8 D. 0.9 | 11 |

411 | Find mean of the following for example distribution Marks ( quad begin{array}{cccc}0 & 20- & 40- & 60- \ 20 & 40 & 60 & 80end{array} ) No.of students 10 8 | 10 |

412 | The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. find the mode of the data. | 10 |

413 | Find the variance of the following distribution ( begin{array}{llll}text { Class } & mathbf{3 . 5}- & mathbf{4 . 5}- & mathbf{5 . 5 -} \ text { interval } & mathbf{4 . 5} & mathbf{5 . 5} & mathbf{6 . 5}end{array} ) Frequency 14 | 11 |

414 | Find the mode for the following table. Temperature in ( ^{o} boldsymbol{C} ) [ begin{array}{ll} text { 3) } 3.4 & text { 34.6 } end{array} ] ( mathbf{2 9} ) Number of days 7 6 | 10 |

415 | Find the mean, variance and standard deviation for the following frequency distribution. Classes ( begin{array}{lll}0- & 10- & 2 \ 10 & 20 & 3end{array} ) 30 40 Frequency १५ 16 | 11 |

416 | What is the total number of children entered in to the library between ( 0-30 ) hours? istogran ( A cdot 45 ) в. 55 ( c .100 ) ( D, 11 ) | 9 |

417 | What is the mean deviation about the mean for the data 4,7,8,9,10,12,13,17 ( ? ) A . 2.5 B. 3 ( c .3 .5 ) D. 4 | 11 |

418 | The standard deviation (a) the numbers U NC UI these ndard deviation of 17 numbers is zero. Then (1980) the numbers are in geometric progression with common ratio not equal to one. eight numbers are positive, eight are negative and one is zero. (d) none of these idarany set of 201be (b) (c) either (a) or (b) | 11 |

419 | The mean of ( 7,9, x+3,12,2 x-1 ) and 3 is 9. Find the value of ( x ) | 10 |

420 | Write the marks wise frequencies in the following frequency distribution table. Marks ( begin{array}{cccc}text { Up } & text { Up } & text { Up } & text { Up } \ text { to } & text { to } & text { to } & text { to } \ mathbf{5} & mathbf{6} & mathbf{7} $ & mathbf{8}end{array} ) No of 11 student | 11 |

421 | In Hostel, one day reading hours of 20 students was observed, whose result is mentioned in the table below. Form the table, find the Mode. [ begin{array}{llllll} text { No. of } & 1- & 3- & 5- & 7- & 9- \ text { reading } & 3 & 5 & 7 & 9 & 11 end{array} ] Student’s strength in the nostel | 10 |

422 | The value of median of ( begin{array}{llll}text { Income } & & & & \ & 1000 & 1100 & 1200 & 1300end{array} ) No. of persons ( quad 14 quad 26 quad 21 ) ( A cdot 1300 ) B. 1200 c. 1250 D. 1150 | 10 |

423 | Find the median of the following data. ( begin{array}{lllll}text { class } & 0- & 20- & 40- & 60 \ text { interval } & 20 & 40 & 60 & 800end{array} ) 12 Frequency ( quad 8 quad 10 ) A . 45 B. 40 c. 55 D. 50 | 10 |

424 | The mean of ( frac{1}{3}, frac{3}{4}, frac{5}{6}, frac{1}{2} ) and ( frac{7}{12}, ) is A ( cdot frac{2}{5} ) B. ( frac{3}{5} ) ( c cdot frac{1}{5} ) D. None of these | 10 |

425 | Find the median of the following numbers ( mathbf{1 1}, mathbf{1 3}, mathbf{8}, mathbf{1 0}, mathbf{1 5}, mathbf{1 8}, mathbf{1 2}, mathbf{7}, mathbf{9}, mathbf{1 6} ) A . 12 B. 11 c. 11.5 D. 12.5 | 10 |

426 | The width of a rectangle in a histogram represents of the class. A. frequency B. range c. class limit D. upper limit | 9 |

427 | Find ( operatorname{Var}(2 X+3) ) A ( .5 operatorname{Var}(X)+3 ) в. ( 4 operatorname{Var}(X)+3 ) c. ( 4 operatorname{Var}(X) ) D. None of these | 11 |

428 | The standard deviation of15 terms is 6 and each item is decreased by 1. Then the standard deviation of new data is? A . 5 B. 7 c. ( frac{91}{15} ) D. 6 | 11 |

429 | The following table shows the heights ( (c m) ) of 50 girls of class ( X ) of a school ( begin{array}{ll}text { Height }(mathrm{cm}) & text { Number of girls } \ 120-130 & 2 \ 130-140 & 8 \ 140-150 & 12 \ 150-160 & 20 \ 160-170 & 8 \ & \ text {Total} & 50end{array} ) Find the mean of the above data by step deviation method. | 10 |

430 | The sum of squares of deviation of variates from their A. M. is always: A. zero B. Minimum c. Maximum D. Nothing can be said | 11 |

431 | 3 The following tables gives production yield per hectare wheat of 100 farms of a village. Production yield (in kg/he) Number of farms 50-55 55-60 60-65 65-70 24 70-75 75-80 38 16 Change the distribution to a more than type distribution. | 10 |

432 | Heights of students of class ( X ) are given in the following frequency distribution. Find the modal height. | 10 |

433 | If the median of the distribution (arranged in ascending order) ( 1,3,5,7,9, x, 15,17, ) is ( 8, ) what is the value of ( x ? ) A . 11 B. 13 c. ( 9<x<15 ) D. ( 9 leq x leq 15 ) 5 | 10 |

434 | If mean deviation about Mean of a particular data consisting 10 observations is7, then what will be value of mean deviation when each is multiplied by ( 5 ? ) A . 35 B . 45 c. 55 D. 65 | 11 |

435 | The sum of squares of deviations for 10 observations taken from mean 50 is 250. Then Co-efficient of variation is A . ( 10 % ) B. ( 40 % ) ( c .50 % ) D. None | 11 |

436 | Median of the odd divisors of 360 is A. the mean of 3 rd and 4 th item B. the mean of 4 th and 5 th item c. the mean of 5 th and 6 th item D. none of these | 10 |

437 | What is the standard deviation of the ( 5,5,10,10,10 ? ) A .2 .44 B. 1.44 ( c cdot 5 ) ( D ) | 11 |

438 | A batsman scores runs in 10 innings as ( mathbf{3 8}, mathbf{7 0}, mathbf{4 8}, mathbf{3 4}, mathbf{4 2}, mathbf{5 5}, mathbf{6 3}, mathbf{4 6}, mathbf{5 4}, mathbf{4 4 .} ) The mean deviation about mean is : A. 8.6 B. 6.4 c. 10.6 D. 7.6 | 11 |

439 | Calculate the mean from the following data: | 10 |

440 | Mean deviation of ( mathbf{7}, mathbf{1 0}, mathbf{1 0}, mathbf{1 5}, mathbf{1 0}, mathbf{8}, mathbf{8}, mathbf{7}, mathbf{3}, mathbf{2}, mathbf{1 0} ) through mean is A . 3.14 B. 8 ( c cdot frac{4}{5} ) D. None of these | 11 |

441 | The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate. Literacy ( 55-quad 6 ) [ 75 ] rate (in ( 45- ) 55 ( 65 quad 75 quad 85 ) ( % ) vumbe of cities | 10 |

442 | The following table shows the ages of the patients admitted in a hospital during a year: 25- ( quad 35 ) [ begin{array}{lll} text { Agetin } & text { 5- } & text { 15- } \ text { years ) } & text { 15 } & text { 25 } & text { 35 } end{array} ] Number of patients Find the mode and the mean of the data given above. Compare and interpret the two measure of central tendency. | 10 |

443 | A histrogram consists of A. sectors B. rectangles ( c . ) triangle D. squares | 9 |

444 | Find the median of the following set of values. 1) 83,66,86,30,82 2) 45,49,46,44,38,37,55,51 3) 70,71,70,68,67,69,70 4) 51,55,46,47,53,55,51,46 | 10 |

445 | Draw a Histogram for the following data ( begin{array}{ll}text { Class Interval } & text { Frequency } \ 0-10 & 35 \ 10-20 & 70 \ 20-30 & 20 \ 30-40 & 40 \ 40-50 & 50end{array} ) | 9 |

446 | Find the mean of the following frequency distribution: ( begin{array}{lllll}text { Class } & 0- & 10- & 20- & 30- \ text { interval: } & 10 & 20 & 30 & 40end{array} ) 10 Frequency: ( quad 9 quad 12 quad 15 ) | 10 |

447 | The monthly income (in rupees) of 7 households in village are ( mathbf{1 2 0 0}, mathbf{1 5 0 0}, mathbf{1 4 0 0}, mathbf{1 0 0 0}, mathbf{1 0 0 0}, mathbf{1 6 0 0}, mathbf{1 0 0} ) (i) Find the median income of the house holds. (ii) If one more household with monthly income of Rs. 1500 is added, what will the median income be? ( begin{array}{ll} text { A }. i) 1400 & text { i) } 1450end{array} ) B. ( i ) ) 1450 ii) 1400 c. ( i) 1200 ) ii) 1450 D. ( i ) ) 1000 ii) 1250 | 10 |

448 | For the following grouped frequency distribution find the mode: ( begin{array}{llll}text { Class: } & begin{array}{l}3- \ 6end{array} & begin{array}{l}text { 6- } \ text { 9 }end{array} & begin{array}{l}text { 9- } \ 12end{array}end{array} ) 15 Frequency: : 2 5 10 23 | 10 |

449 | The mean of ( 51,81,42,65, x ) is 75 find ( x ) | 10 |

450 | Calculate the range and coefficient of range with following data Marks ( quad begin{array}{cccc}0- & 10- & 20- & 30- \ 10 & 20 & 30 & 40end{array} ) No. of student O5 , and o7 08 | 11 |

451 | The variance of first 20 natural numbers is ( mathbf{A} cdot 133 / 4 ) B. ( 279 / 2 ) c. ( 133 / 2 ) D. ( 399 / 4 ) | 11 |

452 | The median of the series ( 8,12,15,7, x, 19,22 ) lies in the interval ( mathbf{A} cdot[12,15] ) B . [7,15] c. [15,17] D. [9,12 | 10 |

453 | The marks distribution of 30 students in a mathematics examination are as follows: Class- [ begin{array}{lll} text { interval } & mathbf{1 0}- & mathbf{2 5}- \ text { of } & mathbf{2 5} & mathbf{4 0} end{array} ] marks Number of students Find the mean by assume mean method and find also the mode of given data. | 10 |

454 | Find the range and the coefficient of range of 43,24,38,56,22,39,45 | 11 |

455 | Find the mean and standard deviation using short-cut method 60 ( begin{array}{lll}61 & 62 & 63end{array} ) ( boldsymbol{x}_{i} ) ( f_{i} ) | 11 |

456 | In a series of ( 2 n ) observations, half of them equal ( a ) and remaining half equation ( -a . ) If the standard deviation of the observations is ( 2, ) then ( |a| ) equals: A ( cdot frac{1}{n} ) B. ( sqrt{2} ) ( c cdot 2 ) D. ( frac{sqrt{2}}{n} ) | 11 |

457 | If ( n>1, x>-1, x neq 0, ) then the statement ( (1+x)^{n}>1+n x ) is true for ( mathbf{A} cdot n epsilon N ) в. ( forall n>1 ) c. ( x>-1 ) and ( x neq 0 ) D. None of these | 11 |

458 | The following frequency distribution gives the monthly consumption of 68 consumers of a locality. Find the median. ( begin{array}{llll}text { Monthly } & 65- & 85- & 105- \ text { Consumption } & 85 & 105 & 125end{array} ) No. of 4 | 10 |

459 | The time(s) taken by a group of students to walk across their college is given in the table below. Find the average time using direct method. A. 12.02 sec B. 39.12 sec c. 40.20 sec D. 31.90 sec | 10 |

460 | Find the expected value, variance and standard deviation of a random variable whose ( p . m . f ) is. [ begin{array}{lllll} boldsymbol{X}=boldsymbol{x} & & 1 & 2 & 3 \ p(X=x) & frac{1}{5} & frac{2}{5} & frac{2}{5} & frac{2}{5} end{array} ] | 11 |

461 | The mode of the following series is 36 Find the missing frequency in it ( begin{array}{lllll}text { Class } & 0- & 10- & 20- & 30- \ text { interval } & 10 & 20 & 30 & 40end{array} ) Frequency 1 8 10 ( dots ) A . 10 B. 15 c. 16 D. 12 | 10 |

462 | Find the mode of the data given below: begin{tabular}{|l|c|c|c|c|c|} hline Class & ( 20-29 ) & ( 30-39 ) & ( 40-49 ) & ( 50-59 ) & ( 60-69 ) \ hline Frequency & 15 & 20 & 50 & 30 & 10 \ hline end{tabular} | 10 |

463 | Compare the modal ages of two groups of students appearing for an entrance test: ( begin{array}{llll}text { Age } & mathbf{1 6}- & mathbf{1 8}- & mathbf{2 0}- & mathbf{2 2}- \ text { (in } & mathbf{1 8} & mathbf{2 0} & mathbf{2 2} & mathbf{2 4} \ text { years) } & & & end{array} ) begin{tabular}{lcccc} Group A: & 50 & 78 & 46 & 28 \ Group B: & 54 & 89 & 40 & 25 \ hline end{tabular} | 10 |

464 | Find the mode of the following data 1) 74,81,62,58,77,74 2) 43,36,27,25,36,66,20,25 3) 55,51,62,71,50,32 4) 24,20,27,32,20,28,20 | 10 |

465 | Find the mean, variance and standard deviation for the following frequency distribution. Classes ( begin{array}{lll}0- & 10- & 2 \ 10 & 20 & 3end{array} ) 30 40 Frequency १५ 16 | 11 |

466 | Find the mean deviation about the mean for the data in ( mathbf{1 5} quad mathbf{2 0} ) ( boldsymbol{x}_{i} quad boldsymbol{5} quad mathbf{1 0} ) 3 ( begin{array}{llll}f_{i} & 7 & 4 & 6end{array} ) | 11 |

467 | Find the mean deviation about mean for the following data: Marks 10 11 obtained 12 No. of students 2 3 | 11 |

468 | Find the difference between the mean and the median of the ( operatorname{set} 3,8,10,15 ) A . 0 B. ( c cdot 4 ) ( D ) | 10 |

469 | The standard deviation of 5 items is found to be ( $ $ 15 $ . ) What will be the standard deviation if the values of al the items are increased? A . 15 B . 20 c. 10 D. None of the above | 11 |

470 | The probability distribution of a random variable ( boldsymbol{X} ) is given below: [ boldsymbol{X}=boldsymbol{x} quad 0 quad 1 quad 2 quad 3 ] ( P(X=x) quad frac{1}{10} quad frac{2}{10} quad frac{3}{10} ) [ begin{array}{r} frac{4}{10} \ hline 0 end{array} ] Then the variance of ( boldsymbol{X} ) is ( A ) B. 2 ( c cdot 3 ) D. 4 | 11 |

471 | Calculate the coefficient of variation of the following data: 20,18,32,24,26 A . 20.41 в. 2041 c. 204.1 D. None of these | 11 |

472 | Mean deviation for ( n ) observations ( x_{1}, x_{2}, ldots . . x_{n} ) from their mean ( bar{X} ) is given by: A ( cdot sum_{i=1}^{n}left(x_{i}-bar{X}right) ) B ( cdot frac{1}{n} sum_{i=1}^{n}left|x_{i}-bar{X}right| ) C ( cdot sum_{i=1}^{n}left(x_{i}-bar{X}right)^{2} ) D ( cdot frac{1}{n} sum_{i=1}^{n}left(x_{i}-bar{X}right)^{2} ) | 11 |

473 | Find the correct Standard Deviation: A . 5.24 в. 4.93 ( c .5 .01 ) D. None of the above | 11 |

474 | 67. If the standard deviation of the numbers 2,3, a and 1l is 3. then which of the following is true? [JEE M 2016] (a) 3a2-34a +91=0 (b) 3a- 23a +44=0 (c) 3a2-26a +55=0 (d) 3a²-32a +84=0 | 11 |

475 | If expected value in n Bernoulli trials is 8 and variance is ( 4 . ) If ( P(x leq 2)=frac{k}{2^{16}} ) then value of k is? ( mathbf{A} cdot mathbf{1} ) B. 137 c. 136 D. 120 | 11 |

476 | DIRECTIONS! Give answer in jour 10 jive semono 1. Prepare “Less than” and “More than” frequency distribution table for the following data. Marks Obtained 50-60 60-70 70-80 80-90 90-100 No. of Students (Cumulative I 4 18 | 12 I 6 frequency) TL1.12 .111100 OOO | 10 |

477 | Find the Variance and Standard Deviation of the values 4,4,4,4,4,4 using short-cut method. A .4 B. 0 c. 12 D. None of these | 11 |

478 | Average can be used A. only in unity B. when combined with other average ( c cdot ) Both a & b D. None of the above | 10 |

479 | The standard deviation of some temperature data in ( ^{circ} boldsymbol{C} ) is ( 5 . ) If the data were converted into ( ^{circ} boldsymbol{F} ), the variance would be ( A cdot 81 ) B. 57 ( c . ) 36 D. 25 | 11 |

480 | begin{tabular}{lccccc} Size & ( boldsymbol{6} ) & ( boldsymbol{7} ) & ( boldsymbol{8} ) & ( boldsymbol{9} ) & ( boldsymbol{1 0} ) \ No. of Shoes & 4 & 5 & 1 & 2 & 1 \ hline end{tabular} Find the mode ( mathbf{A} cdot mathbf{7} ) ( B . quad 8 ) ( mathbf{C} cdot mathbf{6} ) D. 10 | 10 |

481 | Find expected value ( (mu) ) variance ( left(6^{-12}right) ) and ( mathrm{S.D}(sim) ) for the following probability distribute. ( x ) 2 3 ( P(x) quad 0.4 quad 0.3 quad 0.2 ) o. | 11 |

482 | Find the arithmetic mean for the table given below using direct method: A. 14.18 B. 12.54 ( c cdot 13.72 ) D. 15.61 | 10 |

483 | The following table gives production yield per hectare wheat of 100 farms of a village. ( begin{array}{llll}text { production } & mathbf{5 0}- & mathbf{5 5}- & mathbf{6 0}- \ text { of fields } & mathbf{5 5} & mathbf{6 0} & mathbf{6 5}end{array} ) Numbers of farms 2 Change the distribution to a more than type distribution and its ogive. | 10 |

484 | Find the mode of the following data in each case: 14,25,14,28,18,17,18,14,23,22,14,18 | 10 |

485 | The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method. ( begin{array}{lllll}text { Time } & mathbf{0}- & mathbf{2}- & mathbf{4}- & mathbf{6}- \ text { (hrs.) } & mathbf{2} & mathbf{4} & mathbf{6} & mathbf{8}end{array} ) No. of 12 students A. 4 hrs B. 5 hrs c. 4.36 hrs D. 5.36 hrs | 10 |

486 | If the mean of ( n ) observations ( x_{1}, x_{2}, ldots ) ( x_{n} ) is ( bar{x} ),then the sum of deviations of observations from mean is A . 0 B. ( n bar{x} ) c. ( bar{x} ) D. none of these | 11 |

487 | Ten students collected the following amounts (in rupees) for an orphanage: 250,450,500,750,300,650,200,350 500,560 Find their mean and median. | 10 |

488 | The sum of absolute deviation is least when taken from A. Mean B. Median c. mode D. None of the above | 11 |

489 | The mean deviation of the data ( mathbf{3}, mathbf{1 0}, mathbf{1 0}, mathbf{4}, mathbf{7}, mathbf{1 0}, mathbf{5} ) from the mean is A . 2 в. 2.57 ( c .3 ) D. 3.75 | 11 |

490 | Below is given distribution of profit (in Rs.) per day of a shop in a certain town. Calculate median profit of shops. Profit 500 ( quad 1000 quad 1500 quad 2000 ) in Rs.) ( quad 1000 quad ) 1500 ( quad 2000 ) [ begin{array}{l} text { No. of } \ text { shops } end{array} ] 18 A. Rs. 1867 B. Rs. 196 c. Rs. 2167 D. Rs.2567 | 10 |

491 | Create a set of 8 observations with mean 14. | 10 |

492 | The mean and the standard devition (s.d) of five observations are 9 and 0 respecively. If one of the observations is changed such that the mean of the new set of five obervatons becomes 10 , then their s.d. is: A. B. ( c cdot 2 ) ( D cdot 4 ) | 11 |

493 | The coefficients of variation of two series are ( 58 % ) and ( 69 % ). If their standard deviations are 21.2 and 15.6 then their A.M’s are A ( .36 .6,22.6 ) в. 34.8,22.6 c. 36.6,24.4 D. None of these | 11 |

494 | If the median of the observation ( frac{x}{5}, x, frac{x}{4}, frac{x}{2} ) and ( frac{x}{3} ) is ( 8, ) then ( x= ) ( boldsymbol{x}>0 ) ( A cdot 2 ) B. 4 c. 24 D. 16 | 10 |

495 | One situation where mean would be appropriate representative value | 10 |

496 | number of runs scored by some top batsmen of the world in one day international cricket matches: begin{tabular}{ll} Runs scored & No. of batsman \ ( 3000-4000 ) & 4 \ ( 4000-5000 ) & 18 \ ( 5000-6000 ) & 9 \ ( 6000-7000 ) & 7 \ ( 7000-8000 ) & 6 \ ( 8000-9000 ) & 3 \ ( 9000-10000 ) & 1 \ ( 10000-11000 ) & 1 \ hline end{tabular} Find the mode of the data A .4608 .695652 B. 4408.695652 c. 4202.695652 D. 4882.69 | 10 |

497 | The mean of a distribution is ( 4 . ) If its coefficient of variation is ( 58 % ). Then the S.D. of the distribution is A . 2.23 B. 3.23 c. 2.32 D. none of these | 11 |

498 | Time alloted for the preparation of an examination by some students is shown in the table. Draw a histogram to show the information. ( begin{array}{llll}operatorname{Time} & mathbf{6 0}- & mathbf{8 0 -} & mathbf{1 0 0}- \ (text { minutes }) & mathbf{8 0} & mathbf{1 0 0} & mathbf{1 2 0}end{array} ) No. of 14 20 24 | 9 |

499 | In a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement. If true then enter 1 and if false then enter 0 A . 1 B. c. can’t determine D. None of these | 9 |

500 | ( X^{2} ) test is equal to A ( cdot sum_{i=1}^{n} A x^{1}=A x^{1}+A x^{2}+ldots+A x^{n} ) B . ( V=(r-1)(e-1) ) ( frac{Sigma(O-E)^{2}}{E} ) D ( r=frac{Sigma_{x y}}{sqrt{Sigma x^{2} y^{2}}} ) | 11 |

501 | For two data sets, each of size 5 , the variances are given to be 4 and 5 and the corresponding means are given to be 2 and ( 4, ) respectively. The variance of the combined data set is A ( cdot frac{11}{2} ) B. 6 c. ( frac{13}{2} ) D. | 11 |

502 | Find the mean variance and standard deviation using short-cut method ( begin{array}{ll}begin{array}{l}text { Height } \ text { in cms }end{array} & text { No. of children } \ text { 70-75 } & 3 \ text { 75-80 } & 4 \ 80-85 & 7 \ text { 85-90 } & text { 7 } \ text { 90-95 } & 15 \ text { 95-100 } & 9 \ text { 100-105 } & 6 \ text { 105-110 } & 6 \ text { 110-115 } & text { 3 }end{array} ) | 11 |

503 | The mean of ten items is 17 and if each item is increased by 5 then the new mean will be A . 22 B. 67 c. 17 D. 85 | 10 |

504 | If two variates ( X ) and ( Y ) are connected by the relation ( boldsymbol{Y}=frac{boldsymbol{a} boldsymbol{X}+boldsymbol{b}}{boldsymbol{c}}, ) where ( a, b, c ) are constants such that ( a c<0 ) then ( ^{mathbf{A}} cdot_{sigma_{Y}}=_{c}^{a} sigma_{X} ) в. ( _{sigma_{Y}}=-frac{a}{c} sigma_{X} ) c. ( _{sigma_{Y}}=frac{a}{c} sigma_{X}+b ) D. none of these | 11 |

505 | The median of 21 observations is 18 If two observations 15 and 24 are included to the observation then the median of new series is A . 15 B . 18 ( c cdot 24 ) D. 16 | 10 |

506 | The mean and variance of eight observation are 9 and ( 9.25, ) respectively. If six of the observation are 6,7,10,12,12 and ( 13, ) find the remaining two observations. | 11 |

507 | Following are the weights (in ( mathrm{kg} ) ) of 10 new born babies in a hospital on a particular day: 3.4,3.6,4.2,4.5,3.9,4.1 ( 3.8,4.5,4.4,3.6 . ) Find the mean ( bar{X} . ) (in kg) | 10 |

508 | Consider the following frequency distribution: ( begin{array}{lllll}text { Class } & 0- & 6- & 12- & 1 \ & 5 & 11 & 17 & 2end{array} ) Frequency 13 10 15 The upper limit of the median class is A. 17 в. 17.5 c. 18 D. 18.5 | 10 |

509 | Given that ( r=0.4 sum(x-bar{x})(y-bar{y})= ) ( mathbf{1 0 8}, boldsymbol{sigma}_{boldsymbol{y}}=mathbf{3} ) and ( sum(boldsymbol{x}-overline{boldsymbol{x}})^{2}=mathbf{9 0 0} . ) Find the number of pairs of observations. | 11 |

510 | 15. In a series of 2 n observations, half of them equal a and remaining half equal -a. If the standard deviation of the observations is 2, then la equals. (2004) (b) 2 – | 11 |

511 | Find mode for given data: ( begin{array}{lllll}text { Class } & 20- & 30- & 40- & 50- \ 29 & 39 & 49 & 59 \ text { Frequency } & 15 & 20 & 50 & 30end{array} ) | 10 |

512 | The mean and variance of 7 observation are 8,16 respectively. If 5 of the observation are ( 2,4,10,12,14, ) then the ( L C M ) of remaining two observation is ( mathbf{A} cdot 16 ) B . 24 c. 20 D. 14 | 11 |

513 | Find the standard deviation of the first 10 natural numbers | 11 |

514 | Find the mean salary of 80 workers of a factory from the following tables: ( begin{array}{ll}text { Salary (in Rs) } & text { Numbers of workers } \ 5000 & 22 \ 6000 & 18 \ 7000 & 15 \ 8000 & 10 \ 9000 & 8 \ 10000 & 7end{array} ) | 10 |

515 | Find the median of the following data. [ begin{array}{lllll} text { Maths } & mathbf{6 0}- & mathbf{6 5}- & mathbf{7 0 -} & mathbf{7} \ text { marks } & mathbf{6 5} & mathbf{7 0} & mathbf{7 5} & mathbf{8} \ begin{array}{l} text { No. of } \ text { students } end{array} & 8 & 12 & 14 & 8 end{array} ] A. 73.05 B. 72.54 c. 63.54 D. 91.09 | 10 |

516 | The height (in ( mathrm{cm} ) ) of 50 students in a particular class are given. Find the median. ( begin{array}{lll}mathbf{1 5 6} & mathbf{1 5 5} & mathbf{1 5 4}end{array} ) Height (in ( mathrm{cm} ) ) Numbe of studen | 10 |

517 | The average of first and second number is 25 more than the average off the second and third number. Find the difference between the first and the third number | 11 |

518 | The median of the following distribution is ( begin{array}{lllll}text { Class } & 35- & 45- & 55- & 65- \ text { interval } & 45 & 55 & 65 & 70end{array} ) Frequency ( quad 8 quad 12 quad ) 20 10 A . 56. B. 57.5 c. 58.7 D. 59 | 10 |

519 | How many ponds had ( 20-39 ) ducks? Ducks per pond A .25 B. 30 ( c cdot 20 ) D. 15 | 9 |

520 | The relative humidity (in %) of a certain city for a September month of 30 days was as follows: ( begin{array}{lllll}98.1 & 98.6 & 99.2 & 90.3 & 86.5 \ 89.2 & 92.3 & 97.1 & 93.5 & 92.7 \ 96.0 & 92.1 & 84.9 & 90.0 & 95.7end{array} ) What is the range of the data? | 11 |

521 | 53. A cricketer has a mean score of 60 runs in 10 innings. Find out how many runs are to be scored in the eleventh innings to raise the mean score to 62? (1) 83 (2) 82 (3) 80 (4) 81 | 10 |

522 | Marks obtained by four students are ( : 25,35,45,55 . ) The average deviations from the mean is A . 10 B. 9 c. 7 D. none of these | 11 |

523 | Find out the range for the following prices of shirts in a shop. Rupees 150 250 100 500 175 450 300 280 A. Rs. 400 B. Rs. 500 C. Rs. 350 D. Rs. 100 | 11 |

524 | Find variance for following data: ( begin{array}{lllll}text { Class } & 0- & 10- & 20- & 30 \ & 10 & 20 & 30 & 40end{array} ) frequency ey 6 8 A. 14.75 в. 15.75 c. 17.75 D. 16.75 | 11 |

525 | The variation of 20 observations is ( 5 . ) If each observation is multiplied by 2 then what is the new variance of the resulting observations? A . 5 B. 10 c. 20 D. 40 | 11 |

526 | Find the mean for the following data using step deviation method. ( A cdot 4 ) B. 5 ( c .6 ) D. | 11 |

527 | Find the average age of the people given below in the tabular column. Use step deviation method. A. 12 years B. 11 years c. 13 years D. 14 years | 10 |

528 | If the sum and sum of squares of 10 observations are 12 and 18 resp., then, The ( S . D ) of observations is : A ( cdot frac{1}{5} ) B. ( frac{2}{5} ) ( c cdot frac{3}{5} ) D. ( frac{4}{5} ) | 11 |

529 | Find the coefficient of range for the data 43,24,38,56,22,39,45 A . 0124 B. 0.212 c. 0.236 D. 0.436 | 11 |

530 | The given distribution shows the number of wickets taken by bowlers in inter-school competitions: Find the median. | 10 |

531 | Find out the coefficient of range for the following prices of shirts in a shop. Rupees 150 250 100 500 175 450 300 280 A. 1.25 B. 0.666 c. 0.333 D. 0.30 | 11 |

532 | If different values of variable ( x ) are ( 9.8,5.4,3.7,1.7,1.8,2.6,2.8,8.6,10.5 a r ) find the mean. A . 5.8 B. 7.8 ( mathrm{c} .9 .8 ) D. None of these | 10 |

533 | If the mean of ( 10,12,18,13, x, 17 ) is 15 find ‘ ( boldsymbol{x}^{prime} ) | 10 |

534 | Let ( x_{1}, x_{2}, ldots . . x_{n} ) be ( n ) observations and ( bar{X} ) be their arithmetic mean. The formula for the standard deviation is given by A ( cdot sum_{i=1}^{n}left(x_{i}-bar{X}right)^{2} ) B ( cdot frac{1}{n} sum_{i=1}^{n}left(x_{i}-bar{X}right)^{2} ) c. ( sqrt{frac{1}{n} sum_{i=1}^{n}left(x_{i}-bar{X}right)^{2}} ) D. ( sqrt{frac{1}{n} sum_{i=1}^{n} x_{i}^{2}+bar{X}^{2}} ) | 11 |

535 | The annual maintenance cost of a machine in a factory over a seven years period is represented in the histogram. In which year the maintenance cost is ( 2500 ? ) A . ( 1998-1999 ) в. ( 2000-2001 ) c. ( 2001-2002 ) D. ( 1995-1996 ) | 9 |

536 | The mode from the following table will be: Term ( quad mathbf{2 5} quad mathbf{3 5} quad mathbf{4 5} ) Frequency ( quad 14 quad 16 quad 24 quad 20 ) A . 24 B. 45 c. 65 ( D ) | 10 |

537 | Find the mean deviation about the mean for the data ( boldsymbol{X}_{i} quad 10 quad ) 30 ( quad ) 50 ( quad ) 70 16 28 ( f_{i} quad 4 quad 24 ) | 10 |

538 | If the coefficient of variation and standard deviation are ( 60 % ) and 21 respectively, the arithmetic mean of distribution is. A . 30 B. 21 ( c cdot 60 ) D. 35 | 11 |

539 | Find the mean derivation from the mean for the following data [ begin{array}{ccccc} x_{1} & 2 & 5 & 6 & 8 \ y_{1} & 2 & 8 & 10 & 7 end{array} ] | 11 |

540 | The marks of a student in 6 tests are 41,45,54,57,43 and ( x ). If the mean marks of these tests is ( 48, ) then standard deviation of these tests is? A ( cdot frac{10}{sqrt{3}} ) B. ( frac{10}{sqrt{2}} ) c. ( frac{10}{3} ) D. ( frac{20}{3} ) | 11 |

541 | The standard deviation of variate ( boldsymbol{x}_{boldsymbol{i}} ) is ( boldsymbol{sigma} ) Then standard deviation of the variate ( frac{a x_{i}+b}{c}, ) where ( a, b, c ) are constants is A ( cdotleft(frac{a}{c}right)^{sigma} ) в. ( left|frac{a}{c}right| sigma ) ( ^{mathrm{c}} cdotleft(frac{a^{2}}{c^{2}}right) sigma ) D. none of these | 11 |

542 | What is the shape of this histogram? A. Symmetrical B. Skewed left c. Skewed right D. Rotational | 9 |

543 | According to above histogram, How many workers earn less than Rs ( 850 ? ) A . 30 B. 20 ( c cdot 10 ) D. 40 | 9 |

544 | The marks scored by two students ( A, B ) in a class are given below. ( begin{array}{llllll}text { A } & 58 & 51 & 60 & 65 & 66end{array} ) В 56 87 88 46 Who is more consistent? | 11 |

545 | Calculate variance for following data: ( begin{array}{llll}text { Length } & mathbf{1 7 0 0}- & mathbf{1 9 0 0}- & mathbf{2 1 0 0}- \ text { of wire } & mathbf{1 9 0 0} & mathbf{2 1 0 0} & mathbf{2 3 0 0}end{array} ) Number 10 16 20 ( mathbf{A} cdot 55,822.22 ) B . 55,238.51 c. 55832.55 D. 56,823.50 | 11 |

546 | The histogram shows the age groups of working women in a city. Find the number of working women in the age group of ( 29-34 ) years ( A cdot 300 ) 3. 230 ( c .320 ) D. 41 | 9 |

547 | A group of 100 candidates attending a physical test for recruitment have their average height as ( 163.8 mathrm{cm} ) with coefficient of variation ( 3.2 . ) What is the standard deviation of their heights? | 11 |

548 | 9. From From the following table, the percentage of the families with less than 3 children is 0 5 2 15 3 I 8 4 4 Number of children Number of families (a) 70% (c) 54% 1 8 I (b) 60% (d) 45% | 9 |

549 | Calculate the standard deviation of the following data ( boldsymbol{x} quad boldsymbol{3} quad boldsymbol{8} quad mathbf{1 3} quad mathbf{1 7} quad boldsymbol{2 3} ) ( begin{array}{llllll}f & 7 & 10 & 15 & 10 & 8end{array} ) | 11 |

550 | If the probability of defective bolts is 0.1 find the mean and standard deviation for the distribution of defective bolts in a total of 500 bolts. | 11 |

551 | = MISLLIUM 49. For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set [2010] is (a) – (6) 6 (c) 27 (d) ? | 11 |

552 | Find the Standard Deviation of the following data: ( mathbf{5}, mathbf{9}, mathbf{8}, mathbf{1 2}, mathbf{6}, mathbf{1 0}, mathbf{6}, mathbf{8} ) A . 2.14 B . 2.16 c. 2.15 D. 2.17 | 11 |

553 | How much did the maintenance cost increased in ( 1996-1997 ) when compared to ( 1997-1998 ? ) A . 1200 B. 1500 ( c .2500 ) D. 4500 | 9 |

554 | How many employees get to work in less than 60 minutes? A . 10 B. 5 ( c .15 ) D. 20 | 9 |

555 | State the following statement is True or False Standard deviation is the measure of dispersion | 11 |

556 | Calculate the approximate value of mode for the following data: ( begin{array}{lllll}mathbf{x} & mathbf{3}- & mathbf{6}- & mathbf{9}- & mathbf{1 2}- \ mathbf{6} & mathbf{9} & mathbf{1 2} & mathbf{1 5}end{array} ) 2 3 A . 14 B. 15 c. 16 D. 17 | 10 |

557 | If the variance of ( 1,2,3,4,5, dots, x ) is 10 then the value of ( x ) is ( mathbf{A} cdot mathbf{9} ) B . 13 c. 12 D. 10 E. 11 | 11 |

558 | The mean deviation of the numbers 1,2 3,4,5 is A. 0 B. 1.2 ( c cdot 2 ) D. 1.4 | 11 |

559 | 70 number of student’s height are measured in cm as shown in the histogram. How many students have heights more than ( 180 mathrm{cm} ) A. 40 B. 63 ( c cdot 38 ) D. 32 | 9 |

560 | If the mean deviation about the median of the numbers ( a, 2 a, ldots ., 50 a ) is ( 50, ) then ( |a| ) equals:- A .4 B. 5 ( c cdot 2 ) D. 3 | 11 |

561 | The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes ( 0- ) ( begin{array}{lll}text { 20- } & text { 40- } & text { 60- }end{array} ) [ text { in } quad 20 quad 40 quad 60 ] hours) Frequency 10 [ 35 ] 52 Determine the modal lifetimes of the components. A. 69.268 hours B. 65.625 hours c. 62.126 hours D. 58.267 hours | 10 |

562 | begin{tabular}{lllll} Mark & ( 25- ) & ( 35- ) & ( 45- ) & ( 55- ) \ obtained & 35 & 45 & 55 & 65 \ Number of students & 7 & 31 & 33 & 17 \ hline end{tabular} Find mean | 10 |

563 | If the two observations are 10 and 0 their arithmetic mean is A . 10 B. 0 c. 5 D. none of the above | 10 |

564 | Forty persons were examined for their Haemoglobin % in blood (in mg per 100 ( mathrm{ml} ) ) and the results were grouped as below: Determine modal value of Haemoglobin ( % ) in blood of persons. Haemoglobins 5 [ %(mathrm{mg} / ] 13. -14 100mI) No. of Persons A. ( 3.71 mathrm{mg} / 100 mathrm{ml} ) B. ( 14.71 mathrm{mg} / 100 mathrm{ml} ) c. ( 15.71 mathrm{mg} / 100 mathrm{ml} ) D. ( 16.71 mathrm{mg} / 100 mathrm{ml} ) | 10 |

565 | An Incomplete rrequency alstrıbution IS given below Median value is ( 46, ) the missing frequency is ( begin{array}{lll}text { Variate } & text { Frequency } \ 10-20 & 12 \ 20-30 & 30 \ 30-40 & ? \ 40-50 & 65 \ 50-60 & 45 \ 60-70 & 25 \ 70-80 & 18 \ text { Total } & 229end{array} ) A . 33 B. 35 ( c cdot 34 ) D. 2 | 10 |

566 | The table shows the number of books on each number of subjects. Find the median. Subject ( quad 2 quad 3 quad 5 quad 6 ) 3 50 begin{tabular}{l|c|c|c|} number f books & 20 & 39 & 10 \ hline end{tabular} 20 ( A cdot 2 ) B. 3 c. 5 ( D ) | 10 |

567 | A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household. [ begin{array}{llllll} text { Family } & 1- & 3- & 5- & 7- & 9- \ text { size } & 3 & 5 & 7 & 9 & 11 end{array} ] Numbe of 7 familie The mode of this data 3.286 A. True B. False | 10 |

568 | Find mode for given data: ( begin{array}{llll}text { Class } & 20- & 30- & 40- \ 29 & 39 & 49end{array} ) 3. 20 Frequency 15 | 10 |

569 | The mean deviation of the following data from mean is : ( begin{array}{llllll}text { Class } & 0- & 5- & 10- & 15- & 20 \ text { interval } & 5 & 10 & 15 & 20 & 25end{array} ) Frequency ( quad 3 quad 4 quad 8 quad 10 ) ( mathbf{A} cdot mathbf{5} ) B. 4 ( c cdot 6 ) D. 3 | 11 |

570 | Find the mean wage of the following distributions ( begin{array}{llllll}text { Category } & text { A } & text { B } & text { c } & text { D } & text { E } \ begin{array}{l}text { Wages } \ text { per day }end{array} & text { 50 } & text { 60 } & text { 70 } & text { 80 } & text { 90 } \ begin{array}{l}text { No. of } \ text { Workers }end{array} & 2 & 4 & 8 & 12 & 10end{array} ) | 10 |

571 | 4. The class size of an interval 10-20 is (b) 5 (a) 10 (c) 20 (d) 15 | 9 |

572 | Range and standard deviation are similar in that each looks A. The difference between the high and the low scores B. The numerical value that occurs the most often c. How spread out the data is. D. The central score | 11 |

573 | If the ( S D ) of a set of observation is 8 and each observation is divided by ( -2, ) then the SD of the new set of observations will be. A . -4 B. -8 ( c cdot 8 ) ( D ) | 11 |

574 | Types of histograms includes A. deviation bar charts B. paired bar charts C . grouped charts D. all of the above | 9 |

575 | Find the sum of deviation of all observations of the data 5,8,10,15 22 from their mean | 11 |

576 | The scores obtained by 50 students in an examination is tabulated as shown below. ( begin{array}{ll}text { Score } & text { Number of students } \ text { below 10 } & 3 \ text { below 20 } & text { 7 } \ text { below 30 } & text { 13 } \ text { below 40 } & text { 22 } \ text { below 50 } & text { 32 } \ text { below 60 } & text { 40 } \ text { below 70 } & text { 46 } \ text { below 80 } & text { 50 }end{array} ) Find the median score | 10 |

577 | The smallest value of a collection of data is 12 and the range is ( 59 . ) Find the largest value of the collection of data. | 11 |

578 | If the sum of mean and variance of ( B . D ) for 5 trials is ( 1.8, ) the binomial distribution is A ( cdot(0.8+0.2)^{5} ) B. ( (0.2+1.8)^{5} ) c. ( (0.8+0.2)^{10} ) D. ( (0.2+1.8)^{10} ) | 11 |

579 | If the mean deviation about the median of the numbers a, ( 2 a, ldots, 50 a ) is 50 then |a| is equal A .2 B. 3 ( c cdot 4 ) D. 5 | 11 |

580 | Calculate the mean deviation for the following data about median. ( begin{array}{lcc}text { Class } & & \ text { interval } & & 2 & 7end{array} ) [ mathbf{1 7} ] 12 ( 11 quad 12 ) Frequency 17 12 A . 5.12 в. 2.12 c. 7.21 D. 7.54 | 11 |

581 | The variance of the first ( n ) natural number is A ( cdot frac{1}{12}left(n^{2}-1right) ) B ( cdot frac{1}{6}left(n^{2}-1right) ) c. ( frac{1}{6}left(n^{2}+1right) ) D. ( frac{1}{12}left(n^{2}+1right) ) | 11 |

582 | The mean of two samples of sizes 200 and 300 were found to be 25 and 10 respectively. Their standard deviations were 3 and 4 respectively. The varience of combined sample size of 500 is ( mathbf{A} cdot 64 ) B. 65.2 c. 67.2 D. 64.2 | 11 |

583 | A survey conducted on 20 household in a locality by a group of statement resulted in the following frequency table for the number of family Members in a house hold. Family size ( begin{array}{ccc}1- & 3- & 5 \ 3 & 5 & 7end{array} ) Number of families Find the mode of the data. | 10 |

584 | The table below classifies 60 students in a class according to their heights. begin{tabular}{ll} Height ( (mathrm{cm}) ) & Number of students \ ( 140-145 ) & 5 \ ( 145-150 ) & 8 \ ( 150-155 ) & 12 \ ( 155-160 ) & 16 \ ( 160-165 ) & 11 \ ( 165-170 ) & 5 \ ( 170-175 ) & 3 \ hline end{tabular} Find the median of the amount paid. | 10 |

585 | The salary of 43 employees are given in the following table. Find the median. Salary (in ( quad 4000 quad 5500 quad 6000 ) Rs Number of employees | 10 |

586 | The following table draws the income of finance of a grape season find the mean of their income. ıncome ( begin{array}{lll}mathbf{2 0}- & mathbf{3 0}- & mathbf{4 0}- \ mathbf{3 0} & mathbf{4 0} & mathbf{5 0}end{array} ) ( – ) (thousand Rs) Farmer 10 | 10 |

587 | Find standard deviation 50,56,59,60 63,67,68 | 11 |

588 | Give the formula for Step up deviation method. | 11 |

589 | The S.D.is not less than the mean deviation. If this is true enter 1 , else enter 0 | 11 |

590 | The following table gives the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers. ( begin{array}{lllll}begin{array}{l}text { Wages } \ text { (Rs) }end{array} & begin{array}{l}text { 125- } \ text { 175 }end{array} & begin{array}{l}text { 175- } \ text { 225 }end{array} & begin{array}{l}text { 225- } \ text { 275 }end{array} & begin{array}{l}text { 275- } \ text { 325 }end{array}end{array} ) of workers ? | 11 |

591 | The variance of first ( n ) natural numbers is A ( cdot frac{n(n+1)}{12} ) B. ( frac{(n+1)(n+5)}{12} ) c. ( frac{(n+1)(n-1)}{12} ) D. ( frac{n(n-5)}{12} ) | 11 |

592 | Find the missing frequencies if the mean of the given data is 53 ( begin{array}{lllll}text { Age in } & 0- & 20- & 40- & 60- \ text { years } & 20 & 40 & 60 & 80end{array} ) Number of 15 ( F_{1} ) People | 10 |

593 | Read the following graph and answer the question given below What is the percentage obtained by the student ? ( A cdot 80 % ) B. ( 63 % ) ( c .57 % ) ( 0.90 % ) | 9 |

594 | Assertion If mean ( & ) median of an asymmetrical distribution are 58 & 61 respectively, then Mode ( =mathbf{6 7} ) Reason For an asymmetrical distribution Mode ( =3 ) Median – 2 Mean A. Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion. B. Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion c. Assertion is true Reason is false D. Assertion is false Reason is true | 10 |

595 | Find the Median from the following table- ( begin{array}{llll}text { Class } & mathbf{0}- & mathbf{2 0 -} & mathbf{4 0 -} \ text { Interval } & mathbf{2 0} & mathbf{4 0} & mathbf{6 0}end{array} ) 17 26 Frequency 10 | 10 |

596 | Calculate the mean deviation about the mean of the set of first ( n ) natural numbers when ( n ) is an odd number | 11 |

597 | The variance and ( S D ) of the following is ( begin{array}{cccccc}boldsymbol{x} & mathbf{4 . 5} & mathbf{1 4 . 5} & mathbf{2 4 . 5} & mathbf{3 4 . 5} & mathbf{4 4 . 5} \ f & 1 & 5 & 12 & 22 & 17end{array} ) ( mathbf{A} cdot 176,13 ) B. 175.9,13.26 ( mathbf{c} .8 .56,13 ) D. 4.1,12.13 | 11 |

598 | The following table gives production yield per hectare of wheat of 100 farms of a village. Production yield (in 50- 55- 60 so- 55 kg/ha) 60 ( begin{array}{ll}65 & 70end{array} ) No. of farms Change the distribution to a more than type distribution and draw its ogive | 10 |

599 | If the S.D. of ( boldsymbol{y}_{1}, boldsymbol{y}_{2}, boldsymbol{y}_{3}, dots . . boldsymbol{y}_{n} ) is ( boldsymbol{6}, ) then the variance of ( boldsymbol{y}_{1}-boldsymbol{3}, boldsymbol{y}_{2}-boldsymbol{3}, boldsymbol{y}_{3}- ) ( mathbf{3}, dots . . y_{n}-3, ) is ( A cdot 6 ) B. 36 ( c .3 ) D. 27 | 11 |

600 | 01 Lese (c) ellu Consider any set of 2016 It is given that r deviation of this ny set of 201 observations X1, X2, ….X200, X01 iven that x, < X2….< X200 X201. Then the mean n of this set of observations about a point k is minimum when k equals (1981 – 2 Marks) (a) (x1 + x2 + … + x200 + x201)/201 (b) X1 (c) x 101 (d) X201 | 11 |

601 | A certain characteristic in a large population has a distribution that is symmetric about the mean ( m ). If 68 percent of the distribution lies within one standard deviation ( d ) of the mean, what percent of the distribution is less ( operatorname{than} boldsymbol{m}+boldsymbol{d} ? ) A . ( 16 % ) B. ( 32 % ) c. ( 48 % ) D. ( 84 % ) E ( .92 % ) | 11 |

602 | Find the mean deviation from the mean of the following data, using step deviation method. ( begin{array}{lllll}text { Marks } & begin{array}{l}0- \ 10end{array} & begin{array}{l}10- \ 20end{array} & begin{array}{l}text { 20- } \ 30end{array} & begin{array}{l}text { 30- } \ 40end{array}end{array} ) No. of students 5 | 11 |

603 | The ages of ten students of a group are given below. The ages have been recorded in years and months: ( 8-6,9-0,8-4,9-3,7-8,8- ) ( mathbf{1 1}, mathbf{8}-mathbf{7}, mathbf{9}-mathbf{2}, mathbf{7}-mathbf{1 0}, mathbf{8}-mathbf{8} ) What is the lowest age? What is the highest age? Determine the range? | 11 |

604 | Construct a frequency distribution table for the data on weights ( (text { in } k g ) ) of 20 students of a class using intervals ( 30-35,35-40 ) and so on ( mathbf{3 9}, mathbf{3 8}, mathbf{4 7}, mathbf{4 4}, mathbf{4 2}, mathbf{6 5}, mathbf{4 9}, mathbf{5 5}, mathbf{4 9}, mathbf{3 6}, mathbf{3 4}, mathbf{4} ) Also, draw histrogram for the above data | 9 |

605 | The table below gives the distribution of villages under different heights from sea level in a certain region. Compute the mean height of the region: Height in ( begin{array}{lll}text { 200 } & text { 600 } & text { 1000 }end{array} ) meters: No. of ( quad 142 quad ) 265 ( quad 560 ) village: | 10 |

606 | For the next three (03) items that follow The number of telephone calls received in 245 successive one minute intervals at an exchange is given below in the following frequency distribution. Number of calls [ 2 ] Frequency ( begin{array}{llll}14 & 21 & 25 & 43end{array} ) What is the mean of the distribution? A . 3.76 B. 3.84 c. 3.96 D. 4.05 | 10 |

607 | If the sum of squares of deviations of 15 observations from their mean 20 is 240 then what is the value of coefficient of variation ( (mathrm{CV}) ? ) A . 20 B . 21 c. 22.36 D. 24.70 | 11 |

608 | Find the mean from the following frequency distribution of marks at a test in class. Maks 10 ; No. of students 76 [ (f) ] | 10 |

609 | The difference between he maximum and the minimum observations in the data is A. class interval B. frequency c. cumulative frequency D. range | 11 |

610 | The median of the following items ( mathbf{2 5}, mathbf{1 5}, mathbf{2 3}, mathbf{4 0}, mathbf{2 7}, mathbf{2 5}, mathbf{2 3}, mathbf{2 5} ) and ( mathbf{2 0} ) is A .27 B . 40 c. 25 D. 23 | 10 |

611 | ff ( x ) follows binomial distribution with mean 4 variance ( 2 . ) Find ( P(|x-4|) leq 2 ) | 11 |

612 | An Egg Seller distributes eggs to the shop in a city. The number of eggs he distributes for each shop has been recorded and the data obtained was grouped into a class shown in the table below. Find the mean using shortcut method. begin{tabular}{|l|l|l|l|l|l|l|} hline Number of eggs & ( 0-30 ) & ( 30-60 ) & ( 60-90 ) & ( 90-120 ) & ( 150- ) 150 & ( 150- ) 180 \ hline Frequency & 40 & 26 & 38 & 12 & 25 & 30 \ hline end{tabular} A. 91.5 B. 83.07 c. 87.34 D. 89.76 | 10 |

613 | Which of the following is not the measure of dispersion. A. Quartile Deviation B. Range c. Mean Deviation D. None of these | 11 |

614 | If ( v ) is the variance and ( sigma ) is the standard deviation, then A ( cdot v^{2}=sigma ) B . ( v^{2}=sigma^{3} ) c. ( v^{2}=frac{1}{sigma} ) D. ( v^{2}=frac{1}{sigma^{2}} ) | 11 |

615 | Find the Arithmetic mean of the following data using direct method. begin{tabular}{|l|l|l|l|l|l|l|} hline Marks obtained & 50 & 60 & 70 & 80 & 90 & 100 \ hline No of students & 3 & 7 & 5 & 2 & 10 & 2 \ hline end{tabular} ( mathbf{A} cdot 75.17 ) B . 67.17 ( mathbf{c} .76 .1 ) D. 57.177 | 10 |

616 | The formula for coefficient of variation (C.V.) is given by | 11 |

617 | Find the mean deviation about the mean for the data 4,7,8,9,10,12,13,17 | 10 |

618 | Find the mean of the following frequency distribution: ( begin{array}{llll}text { Class } & 0- & 8- & 16 \ text { interval: } & 8 & 16 & 2end{array} ) ( 16- ) 24 32 6 4 Frequency: ( quad 5 ) | 10 |

619 | (U DUwgrann a (a) Line graph 8. From the following frequency table, find out how many students failed if the pass marks are 40. Mark 10-1920–39|40-49 50-5960–8990-100 Number of 8 6 1513 students (a) 29 (b) 7 (c) 8 (d) 14 | 9 |

620 | A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data Number ( begin{array}{ll}0- & 10 \ 10 & 2end{array} ) 30 of cars ( begin{array}{ll}10- & 2 \ 20 & 3end{array} ) ( 20- ) 30 40 Frequency 14 | 10 |

621 | Find the mean and variance for the following frequency distrubution ( begin{array}{lllll}text { classes } & begin{array}{l}0- \ 10end{array} & begin{array}{l}10- \ 20end{array} & begin{array}{l}text { 20- } \ text { 30 }end{array} & begin{array}{l}text { 30 } \ 40end{array}end{array} ) Frequencies 5 8 3. 15 | 11 |

622 | Write the relation between mean, median and mode. | 10 |

623 | (Use a graph paper for this question.) The daily pocket expenses of 200 students in a school are given below: [ begin{array}{llll} text { Pocket } & mathbf{0}- & mathbf{5}- & mathbf{1 0} \ text { expenses } & mathbf{5} & mathbf{1 0} & mathbf{1 5} end{array} ] (in Rs) Number of students 28 (frequency) Draw a histogram representing the above distribution and estimate the mode from the graph. | 10 |

624 | The modal class is A ( .60-65 ) В. ( 55-60 ) ( c .50-55 ) D. none of these | 10 |

625 | Calculate the Standard Deviation and coefficient of variation for the given frequency table: ( begin{array}{ll}text { Class-interval } & text { Frequency } \ 1-5 & 1 \ 6-10 & 2 \ 11-15 & 3 \ 16-20 & 4end{array} ) | 11 |

626 | If the median of the distribution given below is ( 28.5, ) find the values of ( x ) and ( y ) ( begin{array}{ll}text { Class interval } & text { Frequency } \ 0-10 & 5 \ 10-20 & x \ 20-30 & 20 \ 30-40 & 15 \ 40-50 & y \ 50-60 & 5 \ text { Total } & 60end{array} ) | 10 |

627 | The distribution of Abhishek’s high school grades by percentage of course credits is given in the circle graph. What is Abhishek’s grade point average | 11 |

628 | If ( sum_{i=1}^{10}left(x_{1}-15right)=12 ) and ( sum_{i=1}^{10}left(x_{i}-right. ) 15)( ^{2}=18, ) then the S.D. of observations ( boldsymbol{x}_{1}, boldsymbol{x}_{2} ldots ldots ldots ldots boldsymbol{x}_{mathbf{1 0}} ) is A ( cdot frac{2}{5} ) B. ( frac{3}{5} ) ( c cdot frac{4}{5} ) D. none of these | 11 |

629 | The difference between the maximum and the minimum observation in the data is A. class interval B. frequency c. cumulative frequency D. range | 11 |

630 | A student noted that the number of cars passing through the spot on the road for 200 periods each of 10 minutes and summarized in a table given below. Find the mode of the data. Number ( begin{array}{ll}5- & 1 \ 10 & 1end{array} ) ( mathbf{n} ) 5 ( 20- ) of cars 15 20 25 frequency 12 1. If 24 ( 15 quad 10 ) A . 15.5 B. 20.50 c. 25.45 D. 19.4 | 10 |

631 | The variance of a constant is A. Constant B. zero c. Number itself D. None | 11 |

632 | Following table gives frequency distribution of amount of bonus paid to the workers in a certain factory. Bonus Below Below Below paid ( 500 quad 600 ) [ 700 ] (in Rs.) No. of 12 24 workers Find median amount of bonus paid to the workers. A. 801.27 Rs. B. 812.27 Rs. c. 846.27 Rs. D. 735.29 Rs. | 10 |

633 | Mode of the following data. begin{tabular}{lllll} Interval & ( 0- ) 20 & ( 20- ) 40 & 40-60 & 60-80 \ Frequency & 6 & 8 & 12 & 10 \ hline end{tabular} | 10 |

634 | The following are the marks of 9 students in a class: 19,26,29,28,31,35,36,37,48 Find the median of these marks. | 10 |

635 | In a final examination in Statistics the mean marks of a group of 150 students were 78 and the ( S . D ) was ( 8.0 . ln ) Economics, however, the mean marks | 11 |

636 | The average of 15 numbers is 18 The average of first 8 is 19 and that last 8 is 17 then the 8 th number is A . 15 B . 16 c. 18 D. 20 | 10 |

637 | Find the median for the data set. 22,45,56,56,45,123,122,56,103,56 A . 103 в. 102 ( c cdot 122 ) D. 56 | 10 |

638 | 14. Consider the following statements: (A) Mode can be computed from histogram (B) Median is not independent of change of scale (C) Variance is independent of change of origin and scale. Which of these is/are correct ? [20041 (a) (A),(B) and (C) (b) only (B) (c) only (A) and (B) (d) only (A) f ula and | 11 |

639 | If the standard deviation of the numbers ( 2,3, a ) and 11 is ( 3.5, ) then which of the following is true? A ( cdot 3 a^{2}-32 a+84=0 ) B . ( 3 a^{2}-34 a+91=0 ) c. ( 3 a^{2}-23 a+44=0 ) D. ( 3 a^{2}-26 a+55=0 ) | 11 |

640 | Variance of the first 11 natural numbers is: A ( cdot sqrt{5} ) B. ( sqrt{10} ) ( c cdot 5 sqrt{2} ) D. 10 | 11 |

641 | The variance of 5 numbers is ( 10 . ) If each number is divided by ( 2, ) then the variance of new numbers is A . 5.5 B . 2. ( c .5 ) D. None of these | 11 |

642 | State the following statement is True or False Mean Deviation is used where the number of values are large A. True B. False | 11 |

643 | If the mean and S.D. of n observation ( x_{1}, x_{2}, dots dots x_{n} ) are ( bar{x} ) and ( sigma ) resp, then the sum of squares of observations is A ( cdot nleft(sigma^{2}+bar{x}^{2}right) ) В ( cdot nleft(sigma^{2}-bar{x}^{2}right) ) c. ( nleft(overline{x^{2}}-sigma^{2}right) ) D. none of these | 11 |

644 | Find the mode of the following distribution begin{tabular}{llllll} Daily & ( 31- ) & ( 37- ) & ( 43- ) & ( 49- ) & 55 \ Wages & 36 & 42 & 48 & 54 & 6 \ No. of workers & 6 & 12 & 20 & 15 & 9 \ hline end{tabular} ( mathbf{A} cdot 48.5 ) B. 47.5 c. 46.2 D. 48.3 | 10 |

645 | The mean deviation of the numbers ( mathbf{3}, mathbf{4}, mathbf{5}, mathbf{6}, mathbf{7} ) from mean is A . 25 B. 5 c. 1.2 ( D ) | 11 |

646 | The median of the observations, arranged in increasing order is ( 26 . ) Find the value of ( boldsymbol{x} . mathbf{1 0}, mathbf{1 7}, mathbf{2 2}, boldsymbol{x}+mathbf{2}, boldsymbol{x}+ ) 4,30,36,40 | 10 |

647 | If the coefficient of variation of some observation is 60 and their standard deviation is 20 , then their mean is A . 35 B. 34 ( c cdot 33 ) D. 33.33(nearly) | 11 |

648 | The SD of the data 6,5,9,13,12,8,10 is A ( cdot sqrt{frac{52}{7}} ) B. ( frac{52}{7} ) c. ( sqrt{6} ) D. 6 | 11 |

649 | Find the mean begin{tabular}{lccccc} Age (yrs) & 7 & 8 & 9 & 10 & 11 \ No. of Students & 5 & 6 & 4 & 12 & 7 \ hline end{tabular} ( A cdot 9.3 ) B. 8.7 C. 11.9 ( D cdot 5.2 ) | 10 |

650 | The difference between the maximum and the minimum obervations in data is called the A. mean of the data B. range of the data c. mode of the data D. median of the data | 11 |

651 | The following table of grouped data represents the weight (in kg) of 100 gas cylinders. Calculate the mode weight of a cylinder. Weight ( begin{array}{cccc}mathbf{3}- & mathbf{5}- & mathbf{7}- & mathbf{9}- \ mathbf{5} & mathbf{7} & mathbf{9} & mathbf{1 1}end{array} ) ( (%) ) Number of gas 16 13 15 cylinders A. 12.96 B. 15.96 ( mathbf{c} .9 .96 ) D. 10.96 | 10 |

652 | Statement-1: The variance of first n even natural numbers is ( frac{n^{2}-1}{4} ) Statement-2: The sum of first n natural numbers is ( frac{n(n+1)}{2} ) and The sum of squares first n natural numbers is ( frac{boldsymbol{n}(boldsymbol{n}+mathbf{1})(boldsymbol{2} boldsymbol{n}+mathbf{1})}{boldsymbol{6}} ) A. Statement-1 is true, Statement-2 is true ;Statement-2 is not a correct explanation for Statement- B. Statement-1 is true, Statement-2 is false c. Statement-1 is false, Statement-2 is true D. Statement-1 is true, Statement-2 is true ;Statement-2 is a correct explanation for Statement- | 11 |

653 | The distribution of sale of shirts sold in a month in a departmental store is as under. Calculate the model size of shirts sold. ( begin{array}{llll}text { 80- } & text { 85- } & text { 90- } & text { 95- }end{array} ) [ begin{array}{lll} text { Size } & text { 80- } & text { 85- } \ text { (in } & text { 85 } & text { 90 } end{array} ] ( 95 quad 100 ) ( mathrm{cm} ) No of 3 85 155 shirts sold | 10 |

654 | The sum of the squares of deviation of 10 observations from their mean 50 is ( 250, ) then coefficient of varition is A . 10% B. 40% c. 50% D. None of these | 11 |

655 | The sum of the deviations of the variates from the arithmetic mean is always. ( A cdot+1 ) B. 0 ( c cdot-1 ) D. Real number | 11 |

656 | If the coefficient of range is 0.18 and the largest value is 7.44 ,then the smallest value is? A . 3.23 в. 4.15 c. 5.17 D. 5.14 | 11 |

657 | The arithmetic mean of following data is 17. find the value of ( P ) ( 10 quad 15 quad 20 ) Term(x) 25 Frequency(f) ( quad ) 7 ( quad 10 quad ) P | 10 |

658 | {9,12,15,18,21} Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set? I. 14,16 Il. 9,21 III. 15,100 A. Il only B. III only c. I and ॥ E . ।, ॥।, and III | 11 |

659 | A group of 10 observations has mean 5 and ( operatorname{s.D.} 2 sqrt{6} . ) Another group of 20 observations has mean 5 and ( mathrm{S.D.} 3 sqrt{2} ) then the S.D. of combined group of 30 observations is A . ( sqrt{5} ) B. ( 2 sqrt{5} ) ( c cdot 3 sqrt{5} ) D. None of these | 11 |

660 | Calculate the standard deviation of the following data: 18 ( quad ) 23 ( begin{array}{lllll}x & 3 & 8 & 13 & 18end{array} ) A a ( f quad ) 7 ( quad 10 quad ) 15 ( quad 10 quad 8 ) | 11 |

661 | 10 san Study the nistoyranli allu auswu 4. How many students have been observed? (a) 20 (b) 55 (c) 40 (d) 80 | 9 |

662 | The number of books bought at a book fair by 200 students from a school are given in the following table. [ x ] ‘s and 4 6 ( mathbf{1 0} ) ( mathbf{2} ) 8 ( f ) 4 15 Calculate the standard deviation. | 11 |

663 | the following cumulative frequency distribution: ( begin{array}{ll}text { Marks } & text { Number of students } \ text { o and above } & 80 \ text { 10 and above } & text { 77 } \ text { 20 and above } & text { 72 } \ text { 30 and above } & 65 \ text { 40 and above } & text { 55 } \ text { 50 and above } & text { 43 } \ text { 60 and above } & 28 \ text { 70 and above } & 16 \ text { 80 and above } & 10 \ text { 90 and above } & 8 \ text { 100 and above } & text { 0 }end{array} ) | 10 |

664 | The variance of the series ( boldsymbol{a}, boldsymbol{a}+boldsymbol{d}, boldsymbol{a}+ ) ( 2 d, ldots ldots a+(2 n-1) d, a+2 n d, ) is ( ^{text {A } cdot} frac{n(n+1)}{2} d^{2} ) ( ^{text {В }} cdot frac{n(n-1)}{6} d^{2} ) c. ( frac{n(n+1)}{6} d^{2} ) D. ( frac{n(n+1)}{3} d^{2} ) | 11 |

665 | Calculate the median for the following [ begin{array}{lcccc} begin{array}{l} text { Weight } \ text { in kg. } end{array} & 20 & 22 & 24 & 27 \ begin{array}{l} text { No. of } \ text { boys } end{array} & 8 & 10 & 11 & 9 end{array} ] A . 23 B . 26 c. 23.5 D . 24 | 10 |

666 | The S.D of a variable ( x ) is ( sigma . ) The S.D of the variate ( frac{boldsymbol{a} boldsymbol{x}+boldsymbol{b}}{boldsymbol{c}} ) where ( boldsymbol{a}, boldsymbol{b}, boldsymbol{c} ) are constant, is A ( cdotleft(frac{a}{c}right) sigma ) В. ( left|frac{a}{c}right| sigma ) ( ^{mathrm{c}} cdotleft(frac{a^{2}}{c^{2}}right) sigma ) D. none of these | 11 |

667 | If a variable ( x ) takes values ( 0,1,2, dots n ) with frequencies proportional to the binomial coefficients ( n_{0},^{n} C_{1},^{n} C_{2}, dots dots^{n} C_{n}, ) then mean of distribution is A ( cdot frac{n(n+1)}{2} ) в. ( frac{n}{2} ) ( c cdot frac{2}{n} ) D. ( frac{n(n-1)}{2} ) | 11 |

668 | Find the range and the coefficient of range of 43,24,38,56,22,39,45 | 11 |

669 | If the difference between the mode and the median is ( 36, ) then find the difference between the median and the mean. A . 16 B. 33 c. 18 D. 32 | 10 |

670 | The S.D. of ( 1,2,3, cdots 23 ) is A ( cdot 2 sqrt{11} ) B. ( sqrt{11} ) c. ( frac{sqrt{11}}{2} ) D. None of these | 11 |

671 | The table below- shows the daily expenditure on food of 25 households in a locality. ( begin{array}{llll}text { Daily } & text { 100- } & text { 150- } & text { 200- } \ text { nenses } & text { 150 } & text { 200 } & text { 250 } \ text { (in Rs.) } & text { 150 } & text { (i) }end{array} ) expenses 250 (in Rs.) No. of households 12 Find the mean daily expenses on food by a suitable method | 10 |

672 | The median and mode of a frequency distribution are 525 and 500 then mean of same frequency distribution is- A . 75 в. 107.5 c . 527.5 D. 537.5 | 10 |

673 | If coefficient of range is 0.092 and the largest value is 71 , the range is? A . 12 B. 13 c. 14 D. 16 | 11 |

674 | The weight(in ( mathrm{kg} ) ) of 13 students in a class are 42.5,47.5,48.6,50.5,49,46.2,49.8,45.8 Find the range and coefficient of range. | 11 |

675 | There are 4 cards numbered 1,3,5 and ( 7, ) one number on one card. Two cards are drawn at random without replacement. Let ( X ) denote the sum of the numbers on the two drawn cards. Find the mean and variance of ( boldsymbol{X} ) | 11 |

676 | State the following statement is True or False The variance of first ( n ) even natural numbers is ( frac{n^{2}-1}{4} ) A . True B. False | 11 |

677 | Find the sum of deviations of all observations of the data 5,8,10,15,22 from their mean | 11 |

678 | TINI [2008] 40. The mean of the numbers a, b, 8, 5, 10 is 6 and the var is 0.80. Then which one of the following gives po values of a and b? (a) a=0,b=7 (b) a=5,b=2 (c) a=1. 6=6 (d) a=3, b=4 1. Let be the statement is an intianal number” a be the | 11 |

679 | Find the mean deviation from the median for the following ungrouped data 20,25,30,18,15,40 ( mathbf{A} cdot mathbf{6} ) B. 4 ( c cdot 7 ) D. 5 | 11 |

680 | Find Mode, if Mean ( =70.4 ) and Median is ( = ) ( 71_{–} ) A . 71.06 в. 72.9 ( c cdot 69.6 ) D. 72.2 | 10 |

681 | The mean of 20 items of a data is 5 and if each item is multiplied by 3 then the mean will be A . 5 B. 10 c. 15 D. 20 | 10 |

682 | Find the mean and variance for the data 6,7,10,12,13,4,8,12 | 11 |

683 | 52. If the mean deviation about the median of the numbers a, 2a……..,50a is 50, then aequals [2011] (a) 3 (6) 4 (c) 5 (d) 2. The negation of the statement | 11 |

684 | Which of the following are dimensionless A. S.D. в. М.D. c. variance D. coefficient of variation | 11 |

685 | state-wise teacher student ratio in higher secondary schools of India. Find the mode and mean of this data. nterpret the two measures. ( A ) Mode( =31.7, ) Mean( =28.2 ) B. Mode( =33.6, ) Mean( =25.3 ) c. Mode( =35.7, ) Mean( =26.3 ) Mean( =29 ) D. Mode( =30.6, ) | 10 |

686 | Which factory has more variation in wages? A . ( A ) в. ( B ) C. Equal Variation D. Cannot be determined. | 11 |

687 | For a Binomial distribution mean and variance is given by A ( . n p, n p q ) B . ( n^{2} p, N^{2} p^{2} q^{2} ) c. ( n^{2} p^{2}, N^{2} p^{2} q^{2} ) D. None of these | 11 |

688 | Suppose a population ( A ) has 100 observations ( 101,102, ldots, 200 ) and another population ( B ) has 100 observations ( 151,152,153, dots, 250 . ) If ( V_{A} ) and ( V_{B} ) represent the variances of the two populations respectively, then ( frac{boldsymbol{V}_{boldsymbol{A}}}{boldsymbol{V}_{boldsymbol{B}}} ) is ( mathbf{A} cdot mathbf{1} ) B. ( frac{9}{4} ) ( c cdot frac{4}{9} ) D. ( frac{2}{3} ) | 11 |

689 | The mean of 10 observation is 20 . if each observation is added by ( ^{prime} 5^{prime} ). Find the mean of new observation. | 10 |

690 | Calculate mode of the following data. ( begin{array}{lllll}text { Marks } & 0- & 20- & 40- & 60- \ & 20 & 40 & 60 & 80end{array} ) Number of students ( quad 8 quad begin{array}{ll}8 & 10 \ text { students }end{array} ) | 10 |

691 | Calculate the mean deviation from the mean for the scores given below: ( mathbf{1 5}, mathbf{1 1}, mathbf{1 3}, mathbf{2 0}, mathbf{2 6}, mathbf{1 8}, mathbf{2 1} ) | 11 |

692 | Mean deviation of ( mathbf{3 9}, mathbf{4 0}, mathbf{4 0}, mathbf{4 1}, mathbf{4 1}, mathbf{4 2}, mathbf{4 2}, mathbf{4 3}, mathbf{4 3}, mathbf{4 4}, mathbf{4 4}, mathbf{4} ) from their median is? A . 15 в. 1.5 c. 42 D. 35 5 | 11 |

693 | Draw the histogram and use it to find the mode for the following frequency distribution. House – [ begin{array}{llll} text { Rent in } & mathbf{4 0 0 0}- & mathbf{6 0 0 0}- & mathbf{8 0 0 0}- \ text { Rs. per } & mathbf{6 0 0 0} & mathbf{8 0 0 0} & mathbf{1 0 0 0 0} end{array} ] month Number of [ 200 ] families A . Rs. 8000 B. Rs. 8350 c. Rs. 8500 D. Rs. 8750 | 9 |

694 | Mean of 5 observation is ( 7 . ) If four of these observation are 6,7,8,10 and one is missing then the variance of of all the five observations is : A . 4 B. 6 ( c cdot 8 ) D. 2 | 10 |

695 | The mode of the following data is 85.7 Find the missing frequency in it. ( begin{array}{ll}text { Size } & text { Frequency } \ text { 45-55 } & text { 7 } \ text { 55-65 } & 12 \ text { 65-75 } & text { 17 } \ text { 75-85 } & text { f } \ text { 85-95 } & text { 32 } \ text { 95-105 } & text { 6 } \ text { 105-115 } & text { 10 }end{array} ) A . 33 B. 31 ( c .30 ) D. 32 | 10 |

696 | Find the mean deviation about the mean for the data in ( begin{array}{lllll}x_{i} & 10 & 30 & 50 & 70end{array} ) ( mathbf{9 0} ) ( f_{i} quad 4 quad 24 quad 28 quad 16 ) | 11 |

697 | Ashok got the following marks in different subjects in a unit test, 20,11,21,25,23 and ( 14 . ) What is arithmetic mean of his marks? | 10 |

698 | If the mean deviation about the median of the numbers ( a, 2 a, 3 a, dots .50 a ) is 50 then ( |a| ) equals A .2 B. 3 ( c cdot 4 ) D. 5 | 11 |

699 | The average of ( 1 frac{1}{6}, 2 frac{1}{3}, 6 frac{2}{3} ) and ( 8 frac{5}{6} ) is A ( cdot 6 frac{3}{4} ) в. ( _{5} frac{3}{4} ) c. ( _{4} frac{3}{4} ) D. ( _{3} frac{3}{4} ) | 10 |

700 | If the coefficient of variation and standard deviation of a distribution are ( 50 % ) and 20 respectively, the its mean is A .40 B. 30 c. 20 D. None of these | 11 |

701 | Find the mean deviation about the mean for the following data: ( mathbf{3}, mathbf{6}, mathbf{1 0}, mathbf{4}, mathbf{9}, mathbf{1 0} ) | 11 |

702 | The weight in ( mathrm{Kg} ) of 13 students in a class are 42.5,47.5,48.6,50.5,49,46.2,49.8,45.8 Find the coefficient of range. A. 0.077 B. 0.213 c. 0.0803 D. 0.093 | 11 |

703 | Find the variance for an ungrouped data ( mathbf{5}, mathbf{1 2}, mathbf{3}, mathbf{1 8}, mathbf{6}, mathbf{8}, mathbf{2}, mathbf{1 0} ) | 11 |

704 | From the prices of shares ( X ) and ( Y ) below find out which is more stable in value: 35 54 52 53 56 ( x ) 108 ( Y ) 107 ( quad 105 ) 105 106 | 11 |

705 | A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. If aschool makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives? Also, find its mean and standard deviation. | 11 |

706 | What is the median for the following data? ( begin{array}{lllll} & 2- & 4- & 6- & 8- \ x & 4 & 6 & 8 & 10end{array} ) 4 frequency ( quad 1 quad 3 quad 2 ) ( mathbf{A} cdot mathbf{6} ) B. 6.5 c. 7 D. 7.5 | 10 |

707 | Consider the following groups ( A ) and ( B ) ( A: 3,4,5, ldots . . ) upto n terms ( mathrm{B}: 15,19,23, ldots ldots ) upto n terms If the mean deviations of groups ( A ) and ( B ) about their means are ( boldsymbol{alpha} ) and ( boldsymbol{beta} ) respectively then A ( . beta=5 alpha ) в. ( beta=4 alpha+3 ) c. ( beta=4 alpha ) D. None | 11 |

708 | The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure: Expenditure (in C) ( quad ) Number of families 4 ( 1000-1500 ) 24 The line 1 1 ( 1500-2000 ) 40 33 ( 2000-2500 ) A 3 ( begin{array}{lll}2500-3000 & 28 \ 3000-3500 & 30 \ 3500-4000 & 22 \ 4000-4500 & 16 \ 4500-5000 & 7end{array} ) | 10 |

709 | Below is given frequency distribution of I.Q. (Intelligent Quotient) of 80 candidates. [ 70 ] 80 [ 90 quad 100 ] I.Q. ( begin{array}{lll}text { 80 } & text { 90 } & text { 100 }end{array} ) No. o 16 20 Candidates Find median I.Q. of candidates A. 100.5 B. 98.5 c. 94.5 D. None of these | 10 |

710 | Find the mean of the following frequency distribution by the assumed mean method: ( begin{array}{lllll}text { No. of } & mathbf{5 0}- & mathbf{5 3 -} & mathbf{5 6 -} & mathbf{5 9 -} \ text { apples } & mathbf{5 3} & mathbf{5 6} & mathbf{5 9} & mathbf{6 2}end{array} ) No of boxes 150 115 | 10 |

711 | Given ( N=10, Sigma x=60 ) and ( Sigma x_{i}= ) 1000. The standard deviation is | 11 |

712 | Find the mean using step deviation method. A . 14 B. 13 c. 12 D. 10 | 10 |

713 | Prove that ( : sum_{i=1}^{n}left(x_{i}-bar{x}right)=0 ) | 11 |

714 | The marks obtained by 60 students in a test are given as follows: ( begin{array}{lllll}text { Marks } & 5- & 15- & 25- & 35 \ 15 & 25 & 35 & 45end{array} ) No. of its 8 12 studen Calculate the mean and standard deviation of the distribution. Also interpret the results. | 11 |

715 | For the given data, ( S D=10, A M=20 ) the coefficient of variation is A . 47 B. 24 c. 44 D. 50 | 11 |

716 | 6. The heights in em of 10 students in a class are 134, 138, 142, 136, 129, 144, 137, 138, 142, 140 The range of the above data is (b) 10 (d) 20 (c) 15 | 9 |

717 | If each observation of the raw data, whose variance is ( sigma^{2}, ) is multiplied by ( k ) then new variance A. raised by ( k ) times B. raised by ( k^{2} ) times c. reduced by ( k ) times D. reduced by ( k^{2} ) times | 11 |

718 | The mean and standard deviation of a random variable ( x ) is given by 5 and 3 respectively. The standard deviation of ( 2-3 x ) is A . -7 B. 81 ( c .34 ) D. 9 | 11 |

719 | The formula to find SD is This question has multiple correct options ( mathbf{A} cdot sqrt{frac{sum(x-bar{x})^{2}}{n}} ) B. ( sqrt{frac{sum x^{2}}{n}-left(frac{sum x}{n}right)} ) ( mathbf{C} cdot sqrt{frac{sum x^{2}}{n}-left(frac{sum x}{n}right)^{2}} ) ( ^{mathrm{D}} cdot frac{sum x}{n}-left(frac{sum x}{2}right)^{2} ) | 11 |

720 | Write two demerits of arithmetic mean. | 10 |

721 | Calculate Mean Deviation about Median ( begin{array}{lllll}text { Class } & 0- & 10- & 20- & 30 \ & 10 & 20 & 30 & 40end{array} ) Frequency ( quad 5 quad 10 quad 20 ) ( A cdot 7 ) B. 8 c. 19 D. | 11 |

722 | The following table shows ages of 300 patients getting medical treatment in a hospital on a particular day. Find the median age of patients Age (in 1 20 30 years) [ text { 20 } quad 30 ] 40 50 No. of ( quad ) 60 ( quad 42 ) Patients ( begin{array}{llll}60 & 42 & 55 & 70end{array} ) ( mathbf{A} cdot 33.73 ) years B. 38.73 years C. 42.37 years D. 44.73 years | 10 |

723 | Find the average weight using direct method. ( mathbf{A} cdot 81.15 k g ) B. ( 82.50 k g ) ( mathbf{c} .86 .26 mathrm{kg} ) D. ( 80.21 k g ) | 10 |

724 | What is the standard deviation of ( 7,9,11,13,15 ? ) A . 2.4 B . 2. c. 2.7 D. 2.8 | 11 |

725 | The is the difference between the greatest and the least value of the variate. A . Range B. Data c. Average D. Variance | 11 |

726 | Find the variance of the following data 6,8,10,12,14,16,18,20,22,24 | 11 |

727 | In a moderately asymmetrical distribution the distance between mean ( & ) median is ‘k’ times the distance between mean ( & ) mode, then ‘k’ equals ( mathbf{A} cdot mathbf{3} ) B. 2 ( c cdot frac{2}{3} ) D. None of these | 11 |

728 | The following data shows the number of visitors to a zoological park every hour. Calculate the average number of visitors to the park during the whole day. Time ( begin{array}{ll}10- & 11-12 \ 11 & text { noon } quad 12-1 \ text { a.m } & text { p.m }end{array} ) Number of 30 40 34 visitors | 10 |

729 | If a random variable ( boldsymbol{X} ) has probability distribution function ( boldsymbol{f}(boldsymbol{x})=frac{boldsymbol{c}}{boldsymbol{x}}, mathbf{1}< ) ( boldsymbol{x}mathbf{0} ) find ( c, E(X) ) and ( operatorname{Var}(X) ) | 11 |

730 | Calculate the median of the farm size for the following data: ( begin{array}{lllll}text { Farm } & 2- & 5- & 8- & 11- \ text { size } & 5 & 8 & 11 & 14end{array} ) 12 Rooms ( quad 4 quad 8 ) A. 9.125 B. 8.125 c. 7.125 D. 6.125 | 10 |

731 | The demand for different shirt sizes is given in the table. 38 39 40 Size 4 No of Persons 26 ( begin{array}{lll}text { 36 } & text { 20 } & text { 15 }end{array} ) Find the modal shirt size. A . 39 B . 40 c. 44 D. 42 | 10 |

732 | The mean of the numbers ( a, b, 8,5,10 ) is 6 and the variance is ( 6.80 . ) Then which one of the following gives possible values of ( a ) and ( b ) A ( . a=1, b=6 ) В. ( a=3, b=4 ) c. ( a=0, b=7 ) D. ( a=5, b=2 ) | 11 |

733 | Which one of the following measures is determined only after the construction of cumulative frequency distribution? A. Arithmetic mean B. Mode c. Median D. Geometric mean | 11 |

734 | 57. The average value of the num- bers 15, 21, 32, 35, 46, X, 59, 65, 72 should be greater than or equal to 43 but less than or equal to 44. Then the value of x should be (1) 42 s x < 51 (2) 43 sxs 50 (3) 42 < x < 49 (4) 43 < x < 50 | 9 |

735 | Which one of the following statements is correct? A. Th Standard deviation for a given distribution is the square of the variance. B. The standard deviation for a given distribution is the square root of the variance. C. The standard deviation for a given distribution is equal to the variance. D. The standard deviation for a given distribution is half of the variance. | 11 |

736 | Calculate the median from the following distribution ( begin{array}{lllll}text { Class } & begin{array}{l}5- \ 10end{array} & begin{array}{l}10 \ 15end{array} & begin{array}{l}15- \ 20end{array} & 2end{array} ) ( 20- ) 25 Frequency ( quad 4 quad ) 7 10 | 10 |

737 | Below is the distribution of money collected by students for flood relief. Money No. of student ( 0-10 ) ( 10-20 ) ( 20-30 ) ( 30-40 ) ( 40-50 ) find mean of money collected by a student using “Direct Method” | 10 |

738 | Find the standard deviation of the numbers 62,58,53,50,63,52,55 | 11 |

739 | The median of the first 100 natural numbers is A . 49.5 B. 22.75 c. 23.75 D. 50.5 | 10 |

740 | If the median of the following frequency distribution is ( 46 . ) find the absolute difference of missing frequencies ( begin{array}{ccc}10- & 20- & 30- \ 20 & 30 & 40end{array} ) variable Frequency 12 30 | 10 |

741 | Variance is independent of change of A . only origin B. only scale c. origin and scale both D. none of these | 11 |

742 | The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set [2003] (a) remains the same as that of the original set (b) is increased by 2 (c) is decreased by 2 (d) is two times the original median. | 9 |

743 | Means of two samles of sizes 50,100 respectivly are 54.1,50.3 and ( $ D ) are 8 and ( 7 . ) The combined ( $ D ) of two samples is A . 7.56 B. 7.00 c. 7.28 ( D ) | 11 |

744 | The variance of the data 6,8,10,12,14,16,18,20,22,24 is A . 15 B . 20 c. 30 D. 33 | 11 |

745 | Find mean deviation from the mean for the given data ( mathbf{8} quad mathbf{1 0} quad mathbf{1 2} quad mathbf{1 4} ) Item Frequency ( quad 10 quad 5 quad 11 ) A .2 .12 в. 3.04 c. 10.45 D. 5.76 | 11 |

746 | A data consists of ( n ) observation: ( boldsymbol{x}_{1}, boldsymbol{x}_{2}, ldots ldots . ., boldsymbol{x}_{n} . ) If ( sum_{i=1}^{n}left(boldsymbol{x}_{i}+mathbf{1}right)^{2}=mathbf{9} boldsymbol{n} ) and ( sum_{i=1}^{n}left(x_{i}-1right)^{2}=5 n, ) then the standard deviation of this data is: A . 5 B. ( sqrt{5} ) c. ( sqrt{7} ) ( D ) | 11 |

747 | Find variance for following data: ( begin{array}{lllll}text { Class } & mathbf{3 0}- & mathbf{4 0}- & mathbf{5 0 -} & mathbf{6} \ text { interval } & mathbf{4 0} & mathbf{5 0} & mathbf{6 0} & mathbf{7}end{array} ) Frequency ( quad 3 ) What is and 12 A. 14.17 B. 18.17 c. 16.17 D. 15.17 | 11 |

748 | Read the following graph and answer the question given below What is the ratio of the highest marks to the lowest marks obtained by the | 9 |

749 | The median of the observations arranged in increasing order is ( 26 . ) Find the value of ( x ) ( mathbf{1 0}, mathbf{1 7}, mathbf{2 2}, boldsymbol{x}+mathbf{2}, boldsymbol{x}+mathbf{4}, mathbf{3 0}, mathbf{3 6}, mathbf{4 0} ) | 10 |

750 | The blood groups of 36 students of ( 1 x ) class are recorded as follows. ( begin{array}{llll}boldsymbol{A} & boldsymbol{O} & boldsymbol{A} & boldsymbol{O}end{array} ) ( boldsymbol{B} ) ( A ) В ( o ) ( o ) ( Omega ) Represent the data in the form of a frequency distribution table. Which is the most common and which is the rarest blood group among these students? | 11 |

751 | The mean deviation about the mean of the set of first ( n ) natural numbers when ( n ) is an odd number. A ( cdot frac{n^{2}-1}{4 n} ) B. ( frac{n}{4} ) c. ( frac{n^{2}+1}{4 n} ) D. ( frac{n^{2}-1}{12} ) | 11 |

752 | Which one of the following statements is not correct with reference to a histogram? A. Frequency curve is obtained by joining the midpoints of the top of the adjacent rectangles with smooth curves B. Histogram is drawn for continuous data C. The height of the bar is proportional to the frequency of that class D. Mode of the distribution can be obtained from the histogram | 9 |

753 | The arithmetic mean and mode of a data are 24 and 12 respectively, Then the median of the data is A . 20 B . 18 ( c cdot 21 ) D. 22 | 10 |

754 | Which measure of dispersion has a different unit other than the unit of measurement of values? A . Range B. Mean deviation c. standard deviation D. Variance | 11 |

755 | 3. How many babies weigh 2.8 kg? (a) 1 (b) 2 (c) 3 (d) 4 | 9 |

756 | ( begin{array}{llll}text { class } & 10- & 25- & 40- \ text { Interval } & 25 & 40 & 55end{array} ) 70 Frequency 3 2 2 How do you find the deviation from the assumed mean for the above data? | 11 |

757 | A survey regarding the heights (in cm) of 51 girls of Class ( X ) of a school was conducted and data was obtained as shown in table. Find their median. ( begin{array}{ll}text { Height (in cm) } & text { Number of girls } \ text { Less than } 140 & 4 \ text { Less than } 145 & 11 \ text { Less than } 150 & 29 \ text { Less than } 155 & 40 \ text { Less than } 160 & 46 \ text { Less than } 165 & 51end{array} ) | 10 |

758 | 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Number ( begin{array}{ccc}mathbf{1 -} & mathbf{4}- & mathbf{7 -} \ mathbf{4} & mathbf{7} & mathbf{1 0}end{array} ) of letters Number of 30 surnames Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames. | 10 |

759 | Calculate Mean deviation from Median for the given data. Wages(Rs) ( quad 20 ) 18 ( mathbf{1 6} ) 14 Frequency ( quad 2 quad 4 quad 9 ) A .6 .84 в. 4.44 c. 2.24 D. 3.21 | 11 |

760 | Attempt the following: The table gives the ages of husbands and wives: Find: a. The marginal frequency distribution of the age of husbands. b. The conditional frequency distribution of the age of husbands when the age of wives lies between 25 35 begin{tabular}{|c|c|c|c|c|} hline Age of wires (in years) & multicolumn{3}{|c|} { Age of husbands (in years) } \ hline ( 15-25 ) & ( 20-30 ) & ( 30-40 ) & ( 40-50 ) & ( 50-60 ) \ hline ( 25-35 ) & ( – ) & 9 & 3 & ( – ) \ hline ( 35-45 ) & ( – ) & 10 & 25 & 2 \ hline ( 45-55 ) & ( – ) & ( – ) & 4 & 2 \ hline ( 55-65 ) & ( – ) & ( – ) & ( – ) & 16 \ hline end{tabular} | 11 |

761 | Calculate the mode of the frequency distribution Mark ( quad begin{array}{ll}text { Above } & text { Above } \ mathbf{2 5} & mathbf{3 5}end{array} quad begin{array}{l}text { Above } \ mathbf{4 5}end{array} ) No. of students 49 42 | 10 |

762 | Find the mode of the following frequency table: ( begin{array}{ll}text { Class Interval } & text { Frequency } \ 140-150 & 4 \ 150-160 & 6 \ 160-170 & 10 \ 170-180 & 12 \ 180-190 & 9 \ 190-200 & 3end{array} ) | 10 |

763 | The mean deviation of the data 2,9,9,3,6,9,4 from the mean is A .2 .23 в. 3.23 c. 2.57 D. 3.57 E . 1.03 | 11 |

764 | ( begin{array}{lll}text { Weight (Kg) } & text { Frequency } \ text { 60 up to 70 } & 13 \ text { 70up to 75 } & 2 \ text { 75 up to 95 } & 45 \ text { 95 up to 100 } & text { 7 }end{array} ) Given the table above, find the modal class. ( A cdot 70 ) up to 75 ( B .75 ) up to 95 ( mathbf{C} cdot 60 ) up to 70 D. 95 up to 100 | 10 |

765 | For the measures of central tendency, of the following is not true. A. ( Z=3 M-2 bar{x} ) в. ( 2 bar{x}+Z=3 M ) c. ( 2 bar{x}-3 M=-Z ) D. ( 2 bar{x}=Z-3 M ) | 10 |

766 | For a group of 200 candidates, the mean and ( S . D . ) were found to be 40 and 15 respectively. Late on it was found that the score 43 was misread as ( 34 . ) Find the correct mean and correct ( S . D . ) | 11 |

767 | The percentage of marks obtained by the students in a class of 50 are given below. Find the mean for the following data. Marks ( begin{array}{lll}mathbf{4 0}- & mathbf{5 0}- & mathbf{6 0}- \ mathbf{5 0} & mathbf{6 0} & mathbf{7 0}end{array} ) ( (%) ) Number of 12 14 students A . ( 64.6 % ) B . ( 65.6 % ) c. ( 66.6 % ) D. ( 67.6 % ) | 10 |

768 | Find the median of the following data ( mathbf{3}, mathbf{1}, mathbf{5}, mathbf{6}, mathbf{3}, mathbf{4}, mathbf{5} ) | 10 |

769 | The standard deviation ( sigma ) of the first ( N ) natural numbers can be obtained using which one of the following formula? ( ^{mathrm{A}} cdot_{sigma}=frac{N^{2}-1}{12} ) B. ( sigma=sqrt{frac{N^{2}-1}{12}} ) c. ( _{sigma}=sqrt{frac{N-1}{12}} ) D. ( _{sigma}=sqrt{frac{N^{2}-1}{6 N}} ) | 11 |

770 | Find the median for the following frequency distribution table : ( begin{array}{lccc}text { Class- } & 0 & 5 & 10 \ text { interval } & 5 & 10 & 15end{array} ) ( – ) frequency ( quad 5 quad 3 ) 9 | 10 |

771 | The following frequency table shows that the demand for a sweet and the number of customers. Find the mode of demand of sweet. weight of ( begin{array}{ll}250- & 500- \ 500 & 750end{array} ) sweet ( begin{array}{ll}0- & 25 \ 250 & 50end{array} ) (gram) No. of 60 25 custome | 10 |

772 | The mean deviation of an ungrouped data is ( 50 . ) If each observation is increased by ( 2 % ), then the new mean deviation is A . 50 B. 51 c. 49 D. 50.5 | 11 |

773 | The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect which were recorded as 21,21 and ( 18 . ) Find the mean and standard deviation if the incorrect observation are omitted | 11 |

774 | Find the range and coefficient of range of the following data. ( mathbf{5 9}, mathbf{4 6}, mathbf{3 0}, mathbf{2 3}, mathbf{2 7}, mathbf{4 0}, mathbf{5 2}, mathbf{3 5}, mathbf{2 9} ) A . 36,0.44 в. 32,0.44 c. 36,0.84 D. None of these | 11 |

775 | In a school the mark distribution of 25 students in a mathematics examination is given below. Calculate it’s mode. ( begin{array}{cccc}30- & 40- & 50- & 6 \ 40 & 50 & 60end{array} ) Marks 2 No. of students A. 65 в. 32 c. 34 D. 31 | 10 |

776 | If the mean of the following frequency distribution is 7.2 find value of ( ^{prime} K^{prime} ) ( boldsymbol{x} ) 2 4 8 ( mathbf{1 0} ) 7 [ K ] ( f quad 4 ) and 10 16 3. | 10 |

777 | The variance is the standard deviation. A. Square B. Cube c. square root D. cube root | 11 |

778 | Draw the histogram to represent the following data, hence find the mode. Daily [ begin{array}{llll} text { sales of } & 0- & 1000- & 2000- \ text { a store } & 1000 & 2000 & 3000 \ text { in (Rs.) } & & & end{array} ] Number of days 12 in a month ( mathbf{A} cdot ) Rs. 1500 B. Rs. 1600 c. Rs. 1700 D. Rs. 1800 | 9 |

779 | Which of the following can be used as measures of dispersions? A. Range B. Percentiles c. standard Deviation D. All | 11 |

780 | The following is the frequency distribution of time (in minutes) a worker takes to complete the work. Find mean time taken by a worker to complete the work by using ‘Assumed Mean Method’. begin{tabular}{ll} Time (in minutes) & No. of Workers \ ( 20-24 ) & 2 \ ( 25-29 ) & 10 \ ( 30-34 ) & 20 \ ( 35-39 ) & 28 \ ( 40-44 ) & 25 \ ( 45-49 ) & 15 \ hline end{tabular} | 10 |

781 | dentify the shape of histogram. Height A. Skewed left B. Skewed right c. Symmetric D. Rotational | 9 |

782 | Q Type your question shooting competition. Use a graph sheet and draw an ogive for the distribution. ( begin{array}{ll}text { Scores } & text { No. of shooters } \ 0-10 & 9 \ 10-20 & 13 \ 20-30 & 20 \ 30-40 & 26 \ 40-50 & 30 \ 50-60 & 22 \ 60-70 & 15 \ 70-80 & 10 \ 80-90 & 8 \ 90-100 & 7end{array} ) Use your graph to estimate the median. | 10 |

783 | Let ( bar{x}, M ) and ( sigma^{2} ) be respectively the mean mode and variance of ( n ) observations ( boldsymbol{x}_{1}, boldsymbol{x}_{2}, ldots . ., boldsymbol{x}_{boldsymbol{n}} ) and ( boldsymbol{d}_{boldsymbol{i}}= ) ( -boldsymbol{x}_{1}-boldsymbol{a}, boldsymbol{i}=1,2, ldots . ., boldsymbol{n}, ) where a is any number. Statement I : Variance of ( boldsymbol{d}_{1}, boldsymbol{d}_{1}, ldots . ., boldsymbol{d}_{n} ) is ( sigma^{2} ) Statement II : Mean and mode of ( boldsymbol{d}_{1}, boldsymbol{d}_{2}, dots, boldsymbol{d}_{n} ) are ( -overline{boldsymbol{x}}-boldsymbol{a} ) and ( -boldsymbol{M}-boldsymbol{a} ) respectively A. Statement I and Statement II are both false B. Statement I and Statement II are both true c. Statement I is true and Statement II is false D. Statement I is false and Statement II is true | 11 |

784 | The mean and the standard deviation of a group of 20 items was found to be 40 and 15 respectively. While checking it was found that an item 43 was wrongly written as ( 53 . ) Calculate the correct mean and standard deviation. | 11 |

785 | Mean deviation of the observations 70 42,63,34,44,54,55,46,38,48 from median is A . 7.8 B. 8.6 ( c .7 .6 ) D. 8.8 | 11 |

786 | The number of books bought by 200 students in a book exhibition is given below. No. of [ text { books } quad 0 quad 1 quad 2 ] No. of ( quad 35 ) ( 64 quad 68 quad 18 ) uder Find the variance and standard variation | 11 |

787 | How many employees get to work in less than 20 minutes? ( A cdot 4 ) B. 6 c. 10 D. 15 | 9 |

788 | If the standard deviation of 5,7,9 and 11 is ( 2, ) then the coefficient of variation is? A . 15 B . 25 c. 17 D. 19 | 11 |

789 | The median of given observations arranged in ascending order in ( 25 . ) Find the value of ( p ) ( mathbf{1 1}, mathbf{1 3}, mathbf{1 5}, mathbf{1 9}, boldsymbol{p}+mathbf{2}, boldsymbol{p}+mathbf{4}, mathbf{3 0}, mathbf{3 5}, mathbf{3 9}, mathbf{4 6} ) A . 22 B . 24 ( c cdot 21 ) D. 26 | 10 |

790 | The mean is A. The statistical or arithmetic average B. The middlemost score C. The most frequently occurring score D. The best representation for every set of data | 10 |

791 | The standard deviation of 1,2,3,4,5,6,7 is? ( A cdot 4 ) B . 2 ( c cdot sqrt{7} ) D. None of the above | 11 |

792 | What is the modal class for the following distributions? ( begin{array}{llll}text { Class } & mathbf{2 2}- & mathbf{3 3}- & mathbf{4 4}- \ text { interval } & mathbf{3 3} & mathbf{4 4} & mathbf{5 5}end{array} ) Frequency 23 45 67 A ( .55-66 ) в. ( 66-77 ) c. ( 77-88 ) D. ( 88-99 ) | 10 |

793 | If the mode of a distribution is 18 and the mean is 24 , then median is A . 18 B. 24 c. 22 D. 21 | 10 |

794 | The difference between the maximum and the minimum observations in the data is A. class interval B. frequency c. cumulative frequency D. range | 11 |

795 | The variance of first 50 even natural numbers is | 11 |

796 | Find the variance of first 10 multiples of 3 ( mathbf{A} cdot 72.65 ) B. 74.05 c. 74.25 D. 73.85 | 11 |

797 | Solve the following: f ( boldsymbol{L}=mathbf{1 0}, boldsymbol{f}_{1}=mathbf{7} mathbf{0}, boldsymbol{f}_{0}=mathbf{5 8}, boldsymbol{f}_{2}= ) ( 42, h=2, ) then find the mode by using formula. | 10 |

798 | If the standard deviation of the numbers ( -1,0,1, k ) is ( sqrt{5} ) where ( k>0, ) then ( k ) is equal to? A ( cdot 2 sqrt{frac{10}{3}} ) в. ( 2 sqrt{6} ) c. ( 4 sqrt{frac{5}{3}} ) D. ( sqrt{6} ) | 11 |

799 | Given that ( bar{X} ) is the mean and ( sigma^{2} ) is the variance of ( n ) observations ( X_{1}, X_{2} dots X_{n} ) Prove that the mean and variance of the observations ( a X_{1}, a X_{2}, a X_{3} ldots a X_{n} ) are ( a^{-} x ) and ( a^{2} sigma^{2} ) respectively ( (a neq 0) ) | 11 |

800 | The following table shows the distribution of weights of 100 candidates appearing for a competition Determine the model weight. ( begin{array}{llll}text { Weight } & mathbf{5 0}- & mathbf{5 5}- & mathbf{6 0}- \ (mathbf{i n k g}) & mathbf{5 5} & mathbf{6 0} & mathbf{6 5}end{array} ) Number of 13 candida 18 | 10 |

801 | The standard deviation of the data 6,5,9,13,12,8,10 is A ( cdot sqrt{frac{52}{7}} ) в. ( frac{52}{7} ) ( c cdot sqrt{6} ) D. 6 | 11 |

802 | Solve: ( log _{5} frac{(25)^{4}}{sqrt{625}} ) ( mathbf{A} cdot mathbf{4} ) B. 5 ( c cdot 6 ) D. | 11 |

803 | Find the mean deviation about the median for the data ( mathbf{3 6}, mathbf{7 2}, mathbf{4 6}, mathbf{4 2}, mathbf{6 0}, mathbf{4 5}, mathbf{5 3}, mathbf{4 6}, mathbf{5 1}, mathbf{4 9} ) | 11 |

804 | Find the mode for the following data: ( begin{array}{lllll}text { class } & 0- & 2- & 4- & 6- \ text { interval } & 2 & 4 & 6 & 8end{array} ) 6 Frequency A . 5.2 в. 5.3 ( c .5 . ) D. 5.5 | 10 |

805 | If ( a, b ) are constants then, ( V a r(a+b X) ) is A. ( operatorname{Var}(a)+operatorname{Var}(X) ) B. ( operatorname{Var}(a)-operatorname{Var}(X) ) ( mathbf{c} cdot b^{2} operatorname{Var}(X) ) D. None of these | 11 |

806 | Find the mode for the following frequency table ( mathbf{1 0} ) ( mathbf{1 5} ) [ x ] and ( mathbf{2 0} ) 25 ( f ) 25 14 [ 37 ] and 16 | 10 |

807 | How many distinct sets of three positive integers have a mean of ( 6, ) a median of 7 and no mode? A . 1 B . 2 ( c .3 ) D. | 10 |

808 | The heights of trees in a forest are given as follows. Draw a histogram to represent the data. ( begin{array}{llll}text { Heights } & mathbf{1 6}- & mathbf{2 1}- & mathbf{2 6}- \ text { in } & mathbf{2 0} & mathbf{2 5} & mathbf{3 0} \ text { metre } & & & end{array} ) Number of trees 10 15 25 | 9 |

809 | Find the mean deviation about the mean as well as the coefficient of Mean Deviation about mean of the following ( operatorname{set} ) data: 4,7,14,11,9 A . 2.8 and 0.311 B. 2.1 and 0.211 c. 24.8 and 0.411 D. 21.3 and0.566 | 11 |

810 | Draw the necessary table to find the Standard Deviation for the data ( mathbf{2 0}, mathbf{1 4}, mathbf{1 6}, mathbf{3 0}, mathbf{2 1}, mathbf{a n d} mathbf{2 5} ) | 11 |

811 | The S.D. of the following frequency distribution is ( begin{array}{lllll}text { Class } & 0- & 10 & 20- & 30- \ & 10 & 20 & 30 & 40end{array} ) ( f_{i} ) A . 7.8 B. 9 c. 8.1 D. 0.9 | 11 |

812 | Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards Find mean variance and standard deviation of the number of kings. | 11 |

813 | If the standard deviation of a population is ( 9, ) the population variance is: ( mathbf{A} cdot mathbf{9} ) B. 3 c. 21 D. 81 | 11 |

814 | Calculate the median for the following data ( begin{array}{lllll}text { class } & 1- & 6- & 11- & 16- \ text { interval } & 5 & 10 & 15 & 20end{array} ) Frequency 1 18 25 | 10 |

815 | A simple formula to calculate the standard error is A ( . S_{y x}=sigma_{y} sqrt{1-r^{2}} ) B . ( S_{x y}=sigma_{x} sqrt{1-r^{2}} ) ( mathbf{c} cdot S_{y x}=mathrm{S.E.} ) D. Both (A) and (B) | 11 |

816 | If the mean deviation of number ( 1,1+ ) ( boldsymbol{d}, mathbf{1}+mathbf{2} boldsymbol{d}, dots, mathbf{1}+mathbf{1 0 0} boldsymbol{d} ) from their mean is 255 then ( d ) is equal to A . 10.0 B. 20.0 c. ( 10 . ) D. 20.2 | 11 |

817 | Let the observations ( x_{i}(1 leq i leq 10) ) satisfy the equations, ( sum_{i=1}^{10}left(x_{i}-5right)=10 ) and ( sum_{i=1}^{10}left(x_{i}-5right)^{2}=40 . ) If ( mu ) and ( lambda ) are the mean and the variance of the observations, ( x_{1}-3, x_{2}-3, dots ., x_{10} ) 3, then the ordered pair ( (mu, lambda) ) is equal to? A . (6,6) в. (3,6) ( c .(3,3) ) D. (6,3) | 11 |

818 | If both the mean and the standard deviation of 50 observations ( x_{1}, x_{2}, dots dots, x_{50} ) are equal to ( 16, ) then the mean of ( left(x_{1}-4right)^{2},left(x_{2}-4right)^{2}, dots . .left(x_{50}-4right)^{2} ) is A . 525 в. 380 ( c .480 ) D. 400 | 11 |

819 | The largest value in a collection of data is ( 7.44 . ) If the range is ( 2.26, ) then find the smallest value in the collection. | 11 |

820 | Let ( a, b, c, d ) and ( e ) be the observations with mean ( m ) and standard deviation ( S ) The standard deviation of the observations ( a+k, b+k, c+k, d+ ) ( k ) and ( e+k ) is | 11 |

821 | f mean of given data is 21 then value of p is ( begin{array}{llllll}mathrm{x} & 10 & 15 & 20 & 25 & 36 \ mathrm{f} & 6 & 10 & mathrm{p} & 10 & 8end{array} ) A . 24 B . 10 c. 26 D. none of the above | 10 |

822 | Consider the following statements in respect of histogram: 1. Histogram is an equivalent graphical representation of the frequency distribution. 2. Histogram is suitable for continuous random variables, where the total frequency of an interval is evenly distributed over the interval. Which of the statements given above is/are correct? A. 1 only B. 2 only c. Both 1 and 2 D. Neither 1 nor 2 | 9 |

823 | 1. The range is (a) 2.1 kg (c) 1.0kg (b) 0.5 kg (d) 1.5 kg | 9 |

824 | The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret, the two measures. ( begin{array}{llll}text { Number } & & text { Number } & \ text { of } & text { Number } & text { of } & text { Numb } \ text { students } & text { of } & text { students } & text { of } \ text { per } & text { States/U.T } & text { per } & text { states } \ text { teacher } & & text { Teacher } & \ text { 15-20 } & 3 & text { 35-40 } & 3 \ text { 20-25 } & 8 & 40-45 & 0 \ text { 25-30 } & 9 & text { 45-50 } & 0 \ text { 30-35 } & 10 & text { 50-55 } & 2end{array} ) | 10 |

825 | Find the mode of the following frequency distribution of marks obtained by 50 students. ( begin{array}{llll}text { Marks } & 0- & 10- & 20- \ text { obtained } & 10 & 20 & 30end{array} ) No. of students 12 20 | 10 |

826 | The mean sand standard deviation of marks obtained by 50 students of a class in three subjects Mathematics, Physics and chemistry are given below: Subject Mathematics Fhysics Mean ( quad 42 ) Standard 12 deviation Which of the three subjects shows the highest variability in marks and which shows the lowest? | 11 |

827 | Calculate the standard deviation for the following data: ( begin{array}{ll}text { Class – internal } & text { Frequency } \ & \ 1-5 & 4 \ 6-10 & 3 \ 11-15 & 2 \ 16-20 & 1 \ & \ & N=10end{array} ) | 11 |

828 | If the mean deviation of the numbers 1 ( mathbf{1}+mathbf{d}, mathbf{1}+mathbf{2} mathbf{d}, ldots, mathbf{1}+mathbf{1 0 0} mathbf{d} ) from their mean is ( 255, ) then the dis equal to A . 10.0 в. 20.0 c. ( 10 . ) D. 20.2 | 11 |

829 | The mean of 30 scores is 18 and their standard deviation is ( 3 . ) Find the sum of all the scores and also the sum of the squares of all the scores | 11 |

830 | If coefficient of variation is 60 and standard deviation is ( 24, ) then Arithmetic mean is A . 40 B. ( frac{1}{40} ) c. ( frac{7}{20} ) D. ( frac{20}{7} ) | 11 |

831 | The range of the data 25.7,16.3,2.8,21.7 24.3,22.7,24.9 is A . 22 в. 22.9 c. 21.7 D. 20.5 | 11 |

832 | Mean deviation from the mean for the observation -1,0,4 is A. ( sqrt{frac{14}{3}} ) B. ( frac{2}{3} ) ( c cdot 2 ) D. none of these | 11 |

833 | In an experiment with 15 observations on ( x, ) then following results were available: ( sum x^{2}=2830, sum x=170 ) One observation that was 20 was found to be wrong and was replaced by the correct value ( 30 . ) Then the corrected variance is: A . 78 B . 188.6666 c. 177.3333 D. 8.3333 | 11 |

834 | If total sum of square is 20 and sample variance is 5 then total number of observations are A . 15 B. 35 c. 25 D. 4 | 11 |

835 | Calculate the standard deviation for the given frequency distribution: C.I. [ begin{array}{cc} 1-5 & 1 \ 6-10 & 2 \ 11-15 & 3 \ 16-20 & 4 \ hline N=10 & end{array} ] | 11 |

836 | Write the relation between standard deviation of a set of scores and its variance | 11 |

837 | Calculate the mean deviation for the following data about median. ( begin{array}{lllll}text { Class } & mathbf{0}- & mathbf{5}- & mathbf{1 0}- & mathbf{1 5}- \ text { interval } & mathbf{4} & mathbf{9} & mathbf{1 4} & mathbf{1 9}end{array} ) Frequency ( quad 11 quad 12 ) 17 A. 10.22 в. 7.57 c. 5.55 D. 8.45 | 11 |

838 | The coefficient of variations of two series are 58 and ( 69 . ) Their standard deviations are 21.2 and ( 51.6 . ) What are their arithmetic means? | 11 |

839 | The mean and variance of 20 observations are found to be 10 and 4 respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was ( 11 . ) Then the correct variabce is: A . 3.98 в. 4.02 c. 4.01 D. 3.99 | 11 |

840 | Find the mean ( S . D ) of 1,2,3,4,5,6 | 11 |

841 | The algebraic sum of the deviations of a set of ( n ) values from their mean is ( mathbf{A} cdot mathbf{0} ) B. ( n-1 ) ( c cdot 1 ) D. | 11 |

842 | The daily sale of milk (in litres) in a ration shop for eight days is as follows( mathbf{6 0}, mathbf{4 0}, mathbf{1 0}, mathbf{4 0}, mathbf{4}, mathbf{7 0}, mathbf{3 0} ) and ( mathbf{1 0} . ) The average daily sale is- A . 40 B. 33 ( c .64 ) D. 24 | 10 |

843 | Which one of the following is not central tendency? A. Mean deviation B. Arithmetic mean c. Median D. Mode | 10 |

844 | The variance of the following data is : [ begin{array}{llll} text { Length } & mathbf{7 2 . 0 -} & mathbf{7 4 . 0 -} & mathbf{7 6 . 0 -} \ text { of rod } & mathbf{7 3 . 9} & mathbf{7 5 . 9} & mathbf{7 7 . 9} end{array} ] No. of Rods A .2 B. 13.45 c. 13.54 D. 13.40 | 11 |

845 | If ( A ) and ( B ) are the variances of the 1 st ( n ) even numbers and 1st ( n ) odd numbers respectively then A ( . A=B ) в. ( A>B ) c. ( A<B ) D. ( A=B+1 ) | 11 |

846 | The most common form of diagrammatic representation of a grouped frequency distribution is – A . Ogive B. Histogram C. Frequency polygon D. None of these | 9 |

847 | The sum of square of deviations for 10 observations taken from mean 50 is 250. The coefficient of variation is A . 10 B. 20 ( c . ) 30 D. 40 | 11 |

848 | The mode of the distribution begin{tabular}{lccccc} Marks & 4 & 5 & 6 & 7 & 8 \ No. of students & 6 & 7 & 10 & 8 & 3 \ hline end{tabular} A. 5 B. 6 ( c cdot 8 ) D. 10 | 10 |

849 | Electricity used by some families is shown in the following table. Find the mode for use of electricity. use of electricity 0 20- ( quad 40 ) 20 40 60 (unit) No. of ( begin{array}{ll}text { 13 } & text { 50 }end{array} ) families | 10 |

850 | 58. On a journey across Mumbai, a taxi averages 20 m.p.h. for 70% of the distance, 25 m.p.h. for 10% of the distance and 8 m.p.h. for the remainder. Then the av- erage speed of the whole journey is – (1) 15.925 m.p.h (2) 15.25 m.p.h (3) 15 m.p.h (4) 15.625 m.p.h | 10 |

851 | Calculate the mean deviation for the data given here: ( begin{array}{llll}text { class } & 0- & 10- & 20- \ text { interval } & 10 & 20 & 30end{array} ) 3 3 5 Frequency | 11 |

852 | In the following distribution calculate mean ( bar{x} ) from assumed mean Class- interval ( begin{array}{lll}10- & 25- & 4 \ 25 & 40 & 5end{array} ) 7. 7 7 55 70 Frequency 2 If ( bar{x}=a b, ) then ( a+b ) is : | 10 |

853 | Suppose for 40 observations, the variance is ( 50 . ) If all the observations are increased by ( 20, ) the variance of these increased observation will be A . 20 B. 50 c. 30 D. None of these | 11 |

854 | Find the mean deviation about median for the following data. begin{tabular}{lllll} multirow{2}{*} {( boldsymbol{C I} )} & ( boldsymbol{8}- ) & ( mathbf{1 3}- ) & ( mathbf{1 8}- ) & ( mathbf{2 3}- ) \ & ( mathbf{1 2} ) & ( mathbf{1 7} ) & ( mathbf{2 2} ) & ( mathbf{2 7} ) end{tabular} 14 20 | 11 |

855 | Find the mean deviation about the mean for the data. ( begin{array}{cccccc}x_{i} & 5 & 10 & 15 & 20 & 25 \ f_{i} & 7 & 4 & 6 & 3 & 5end{array} ) | 11 |

856 | 70. If Ž (x;-5) = 9 and (x,-5) = 45, then the standard i=1 deviation of the 9 items x,,X, …, x, is: [JEEM 2018] (a) 4 (6) 2 (c) 3 (d) 9 The Pool | 11 |

857 | Variance of the distribution ( mathbf{7 3}, mathbf{7 7}, mathbf{8 1}, mathbf{8 5}, dots, mathbf{1 1 3} ) is A . 10 в. 160 ( c cdot 161 ) D. None of these | 11 |

858 | 5 students of a class have an average height ( 150 mathrm{cm} ) and variance ( 18 mathrm{cm}^{2} . ) A new student, whose height is ( 156 mathrm{cm} ) joined them. The variance ( left(operatorname{in} c m^{2}right) ) of the height of these six students is A . 22 B. 20 c. 16 D. 18 | 11 |

859 | The average of 7 consecutive numbers is n. If the next two numbers are included, the average will be…. | 10 |

860 | 10. The lower limit of 45 – 50 is (a) 45 (b) 50 (d) 47.5 (c) 5 | 9 |

861 | The following data gives the information on the life – time (in hours) of 75 electrical instruments. ( begin{array}{ll}text { Lifetime } & text { o- } \ text { (in } & text { 20 } \ text { hours) }end{array} ) 46 ( 20- ) 40 60 Frequency 10 15 find the mean lifetime of the instruments. | 10 |

862 | What are the objectives of measure of dispersion? A. Helpful in use of further statistical analysis as in regression, correlation etc. B. Reliability of measure of central tendency C. Control of variability D. All of the above | 11 |

863 | Find the mode of given data. ( begin{array}{llll}text { Marks } & begin{array}{l}0- \ 10end{array} & begin{array}{l}10- \ 20end{array} & begin{array}{l}20- \ 30end{array}end{array} ) Frequency ( 20 quad 24 ) In | 10 |

864 | Find the median if total students are 40 Weight ( quad mathbf{4 5} quad mathbf{4 6} quad mathbf{4 7} ) and 48 3 Median ( quad 6 quad 2 ) 4 | 10 |

865 | S.D.of the first ( (boldsymbol{n}+mathbf{1}) ) natural number is A. ( sqrt{frac{n^{2}-1}{12}} ) в. ( sqrt{frac{n^{2}+1}{12}} ) c. ( sqrt{frac{n(n+2)}{12}} ) D. None of these | 11 |

866 | Which of the following is correct about measure of dispersion? A. It does not measure direction of the variation B. Dispersion measures the extent to which the items vary from some central value c. Measures only degree of variation D. All of the above | 11 |

867 | Find the coefficient of range for the following data. size ( quad begin{array}{lll}mathbf{1 0}- & mathbf{1 5}- & mathbf{2 0}- \ mathbf{1 5} & mathbf{2 0} & mathbf{2 5}end{array} ) Frequency | 11 |

868 | The mean of ( x_{1}, x_{2} dots x_{50} ) is ( M, ) if every ( boldsymbol{x}_{i},=1,2 ldots 50 ) is replaced by ( boldsymbol{x}_{i} / mathbf{5 0} ) then the mean is A. в. ( _{M+frac{1}{50}} ) c. ( frac{50}{M} ) D. ( frac{M}{50} ) | 10 |

869 | For how many hours did the maximum number of students watch TV? A ( .7-8 ) B . ( 8-9 ) ( mathbf{c} cdot 4-5 ) D. ( 9-10 ) | 9 |

870 | Calculate the coefficient of range for the following data. begin{tabular}{lll} No. of wards & 1 & 2 \ hline end{tabular} 3 begin{tabular}{r} 4 \ hline end{tabular} No. of [ 32 quad 57 ] ( 28 quad 96 ) nouses | 11 |

871 | The following distribution gives the mass of 48 objects measured to the nearest gram. Draw a histogram to illustrate the data. ( begin{array}{llll}text { Mass } & mathbf{1 0}- & mathbf{2 0}- & mathbf{2 5}- \ text { in } & mathbf{1 9} & mathbf{2 4} & mathbf{3 4}end{array} ) ( (g m s) ) No. o objects | 9 |

872 | Find the median for the following data. ( begin{array}{lllll}text { Height } & mathbf{5}- & mathbf{1 0}- & mathbf{1 5}- & mathbf{2 0}- \ (mathrm{ft}) & mathbf{1 0} & mathbf{1 5} & mathbf{2 0} & mathbf{2 5}end{array} ) No. of trees | 10 |

873 | If the variable takes values ( mathbf{0}, mathbf{1}, mathbf{2}, mathbf{3}, cdots, boldsymbol{n} ) with frequencies proportional to ( ^{n} c_{0},^{n} c_{1},^{n} c_{2}, cdots,^{n} c_{n} ) respectively, the variance is A ( cdot frac{n}{4} ) в. ( frac{n}{3} ) ( c cdot frac{2 n}{5} ) D. none of these | 11 |

874 | The model class for the following frequency distribution is begin{tabular}{lllll} Marks & ( 0- ) 10 & ( 10- ) 20 & ( 20- ) 40 & ( 40- ) 50 \ Number of students & 4 & 6 & 14 & 16 \ hline end{tabular} A. ( 20-40 ) B . ( 40-50 ) ( mathbf{c} .50-60 ) D. ( 70-90 ) | 10 |

875 | Calculate mean deviation about for the following data. ( begin{array}{lllll}text { Class } & begin{array}{l}0- \ 10end{array} & begin{array}{l}10 \ 20end{array} & begin{array}{l}text { 20- } \ 30end{array} & begin{array}{l}text { 30- } \ 40end{array}end{array} ) Frequence 6.7 15 16 | 11 |

876 | The mean of given data is ( begin{array}{cccccc}mathbf{x} & 2 & 4 & 6 & 8 & 10 \ f & 7 & 4 & 5 & 5 & 4end{array} ) ( mathbf{A} cdot 5.6 ) B . 6.4 ( c cdot 6 ) D. None of these | 10 |

877 | The following table gives the distribution of IQ of 60 pupils of class X in a school. ( begin{array}{ll}text { IQ } & text { No. of pupils } \ text { 60-70 } & text { 2 } \ text { 70-80 } & text { 3 } \ text { 80-90 } & text { 5 } \ text { 90-100 } & text { 16 } \ text { 100-110 } & text { 14 } \ text { 110-120 } & text { 13 } \ text { 120-130 } & text { 7 }end{array} ) Convert the above distribution to a more than type cumulative frequency distribution and draw its ogive | 10 |

878 | Which peak is second highest? ( A cdot B ) ( mathbf{B} cdot A ) ( c cdot C ) ( D . E ) | 9 |

879 | 38. The average marks of boys in class is 52 and that of 8 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is [2007] (a) 80 (6) 60 (c) 40 (d) 20. Ahody weighing 13 kg is suspended by two strings 5m and 39 | 9 |

880 | Which one of the following is a measure of dispersion? A. Mean B. Median c. mode D. standard deviation | 11 |

881 | The maximum bowling speed ( (k m / h r) ) of 33 players at a cricket coaching centre is given below: [ begin{array}{llll} begin{array}{l} text { Bowling } \ text { Speed } \ (boldsymbol{k m} / boldsymbol{h r}) end{array} & mathbf{8 5}- & mathbf{1 0 0}- & mathbf{1 1 5}- \ mathbf{1 0 0} & & mathbf{1 1 5} & mathbf{1 3 0} end{array} ] Number of players Find the modal bowling speed (in ( k m / h r) ) of players | 10 |

882 | For the given data, ( S D=10, A M=20, ) the coefficient of variation is A . 47 B. 24 ( c cdot 44 ) D. 50 | 11 |

883 | If the mean deviation about the median of the numbers ( a, 2 a, 3 a, dots . ., 50 a ) is 50 then ( |a| ) is equal to? A .2 B. 3 ( c cdot 4 ) D. 5 | 11 |

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