Statistics Questions

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
above
begin{tabular}{|c|c|}
hline Age (in years) & Number of children \
hline ( 1-2 ) & 5 \
( 2-3 ) & 3 \
( 3-5 ) & 6 \
( 5-7 ) & 12 \
( 7-10 ) & 9 \
( 10-15 ) & 10 \
( 15-17 ) & 4 \
hline
end{tabular}

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
12
A. Maths
B. English
c. science
D. French

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
7

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
A. True
B. False

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
if each ( A ) is worth 4 points; each ( B, 3 )
points; and each ( C, 2 ) points?
A . 3.0
B. 3.4
( c .3 .6 )
D. 3.7
E. Cannot be determined from the given information

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
were 73 and the S.S was ( 7.6 . ) The
variability in the two subjects
respectively is
A. ( 10.3 %, 10.4 % )
( % )
B. ( 95 %, 7.9 % )
c. ( 11.2 %, 10.1 % )
D. none of these

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
student ?
( mathbf{A} cdot 2: 11 )
B. 9: 2
( c cdot 2: 9 )
D. 11: 2

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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