# 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 NoQuestionsClass
1The variance of the scores 2,4,6,8,10
is
( A cdot 2 )
B. 4
( c .6 )
( D )
11
2If ( 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
3If 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
4Given 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
5Suppose 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
6If 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
7For 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
8Find 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
9If 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
10The 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
12Identify the mode for the following data:
Number ( mathbf{0} ) 12 ( mathbf{6} ) ( mathbf{9} )
A . 18
B. 12
c. Both A and B
D. 6
10
13A 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
14Calculate 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
1546. 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
16If 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
17If 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
18Find the mode for the following frequency table.
Number of
workers 15 16
10
19For 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
20If 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
21Find 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
22The 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
23Find 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
24Which 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
25Find the Coefficient of Variation for
Factory ( boldsymbol{B} )
A ( .0 .15555 % )
B. ( 0.25714 % )
c. ( 0.36934 % )
D. ( 0.42548 % )
11
26By 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
27Median is independent of change of
A . only origin
B. only scale
c. origin and scale
D. neither origin nor scale
10
28Find 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
29Consider 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
30Mean deviation can be calculated from
A. mean
B. median
c. mode
D. any of the above
11
31The 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
32The 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} )
10
33If 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
34Mean 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
35Mode 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
36A 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
37The 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
3872. Which of the following graphical
representations of data repre-
sents cumulative frequencies ?
(1) Pie-chart
(2) Histogram
(3) Frequency polygon
(4) Ogive
9
39Incomes 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
40T-distribution is symmetrical like
normal distribution and its mean value
is
A. zero
B. – –
( c )
D.
11
41If 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
4212.
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
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
43Find the mode for the following data:
A . 22
B . 30
( c cdot 34 )
D. None of these
10
44The 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
45Find median:
is Cumulative
10
46Assertion
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
47The 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
48The 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
49The sum of 12 observations is ( 600, ) then
their mean is
A . 20
B. 30
c. 40
D. 50
10
50How many employees get to work in
more than 100 minutes?
A . 20
B. 15
( c cdot 4 )
D. 58
9
51Range of data 7,8,2,1,3,13,18 is?
A . 10
B. 15
c. 17
D. None of the above
11
52Find 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
53Find the mean of first six natural
numbers.
A . 3.6
B. 7
( c .3 .5 )
D. None of these
10
541,2,3,6,8 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
55NIVE, 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
56Mode 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
57The 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
58Represent 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
59Find 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
60In 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
62If ( 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
63How to derive the Mode formula for
grouped data?
10
64Constructing 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
65Determine 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
66The 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
67The 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
68Find 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
69For ( 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
70Find the value of ( z ) using shortcut
method whose arithmetic mean is 2.5
A . 14
B . 15
c. 16
D. 17
10
71Find 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
72The 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
73Find 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
74Find 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
7554.
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
76Find 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
77The 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
78The 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
79Find the mean deviation about the
median for the following data:
[
]
11
8075. 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
81Which 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
82Find 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
83Find 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
84Calculate the coefficient of variation
(C.V.) of the following data:
40,36,64,48,52
11
85A 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
86Per 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
87If 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
88In 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
891.
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
90The 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
91The 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
92Variance of first 20 natural number is
A ( frac{133}{4} )
в. ( frac{379}{12} )
( ^{c} cdot frac{133}{2} )
D. ( frac{399}{4} )
11
9364.
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
94Calculate 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
95The 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
96Now, 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
97A 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
98The 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
From the given distribution, calculate
A .1 .021
B. 11.231
c. 10.256
D. 12.214
11
100The 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
101If 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
102The 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
103Find 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
104Following 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
105The 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
curve and determine the median.
10
107Calculate 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
108A 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
109The mode of the following discrete series is:
( mathbf{A} cdot mathbf{3} )
B. 12
c. 8
D. 6
10
110Test 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
111Find 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
112The contents of 100 match boxes were
checked to determine the number of
matches they contained.
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
113If ( 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
114The 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
115The 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
116The 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
117The 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
118Find the mean deviation about the
mean for the following data.
11
119The sum of the squares of deviations of
a set of values is minimum when taken
A . ( A M )
в. ( G M )
с. ( H M )
D. median
11
120The 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
12171. A line graph
(1) shows trend over time
(2) compares structures
(3) makes comparisons
(4) None of the above
9
122If ( 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
123Find the mean of the following frequency distribution:
( begin{array}{lllll}text { Class } & 10- & 30- & 50- & 70- \ text { interval: } & 30 & 50 & 70 & 90end{array} )
10
124A 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
125The 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
126The 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
127Find 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
128If ( 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
129If 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
13052. 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
( f_{i} )
mean
( mathbf{A} cdot 2.1 )
B . 2.25
c. 2.09
D. 2.71
11
132If 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
133Find 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
13428. 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
135The S.D. of 1,2,3,4,5,6,7 is
A .4
B. 2
( c cdot sqrt{7} )
D. none of these
11
136The weight of coffee (in gms) in 70 packets is given below. Determine the modal weight of coffee in packets
Packe
A . ( 201 mathrm{gms} )
в. ( 201.70 mathrm{gms} )
( c cdot 202 g m s )
D. 202.70 gms
10
137If 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
138Find 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
139Find the median of the following data:
2,7,3,15,12,17 and 5
10
140Calculate the mean deviation about the
mean of the set of first ( n ) natural
numbers when ( n ) is an even number
11
141Find the average of 2,3,4,5,10,1310
142Find 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
143Lowest value of variance can be:
( A cdot 1 )
B. –
c. 0
D. None of these
11
144The 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
145Calculate 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
14654. 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
147The 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
148If sum of the 20 deviations from the
mean is 100 , then find the mean deviation
11
149Find 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
150There 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
151The 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
15259. 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
153The 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
154Find the mode for the following data:
Students ( begin{array}{lll}mathbf{1 0} & mathbf{1 4} & mathbf{2 0}end{array} ) ( mathbf{3 0} )
A . 10
B . 20
c. 60
D. 30
10
155Weight 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
156Standard deviation is calculated from
the Harmonic Mean (HM)
A . Always
B. Sometimes
c. Never
D. None of these
11
157In 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
158Sum of all components in normalized histogram is equal to
A . 0
B.
c. 100
( D )
9
159Find the mean deviation about mean for
the following data:
[
]
18
Frequen
[
2
]
11
( (f) )
11
160The 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
161The 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
162The 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
163Length 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
11
164If 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} )
( A cdot 3 )
B.
c. 8
D. None of these
10
165The 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
166he variance of first 50 even natural numbers is
(JEE M 2014]
(2) 437
(6 437
(0) 833
(d) 833
11
167The 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
168Compute 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
169The 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
170The 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
171Draw 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
172On 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
173If 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
174If 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
175How many students weight less than 35 kg?
(a) 38
(b) 24
(c) 16
(d) 18
9
176loss 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
177The 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
178Find 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
179The 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
180Find 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
181Which of the following is not a measure of central location?
A. Mean
B. Median
c. mode
D. Variance
11
182Find 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
10
183Mean 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
184Calculate 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
185Calculate 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
186The 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
187The 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
188The 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
189The 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
190The 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} )
A . 10
B. 30
c. 20
D. 50
10
191The demand of different shirt sizes, as
obtained by a survey, is given. Calculate
the Mode.
Size
Number of
persons(wearin it)
10
192The 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
193Find the mode when median is 12 and
mean is 16 of a data.
10
194If 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
195Calculate 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
19657. 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
197The 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
198Let ( 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
199The 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
200Consider 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
201The 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
202The formula of students t-distribution
is
A ( cdot t=frac{s}{sqrt{n}} )
в. ( t=frac{|bar{X}-mu|}{s} )
11
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} )
( mathbf{A} cdot 10.2 )
B. 10.4
c. 10.5
D. 11.4
11
204Class ( begin{array}{cccc}2- & 4- & 6- & 8- \ 4 & 6 & 8 & 10end{array} ) ( 10- )
12 interval
What is the mode for the grouped data?
A .10 .5
B. 12.5
c. 13.7
D. 9.1
10
205Find the variance for the following data:
6,4,8,5,2,17
11
206Find ( bar{x} ) using shortcut method.
A . 37
B . 38
c. 39
D. 40
10
207Calculate 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
208The 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
209The 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
210Find 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
211If 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
212Histogram are a great way to show results of
A . categories
B. continuous data
c. both ( A ) and ( B )
D. None of these
9
213Find the least number of children in the
interval ( 20-30 ) hours?
4.1
в. 15
( c .25 )
D. 45
9
214The 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
215The 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
216Find the arithmetic mean of the
following data.
A . 59.35
B . 57.35
c. 61.35
D . 52.35
10
217In 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
218Calculate mean deviation from the
median of the following data:
( begin{array}{llll}text { Class } & 0- & 6- & 1 \ text { interval: } & 6 & 12 & 1end{array} )
8

5
11
219Khilona 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
220The 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
221How many students watched TV for less
than 4 hours?
( A, 34 )
В. 32
( c, 24 )
( D, 30 )
9
222toppr
( 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
223What is the arithmetic mean of the
squares of first five natural numbers?
( mathbf{A} cdot mathbf{9} )
B. 11
c. 13
D. 15
10
224Probability density functions are always
A. decreasing
B. increasing
c. positive
D. negative
9
225MATHEMATICS
begin{tabular}{lcccc}
Classes & ( 0- ) 10 & ( 10- ) 20 & ( 20- ) 30 & ( 30- ) 40 \
Frequencies & 5 & 8 & 15 & 16 \
hline
end{tabular}
9
226Let ( 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
227Find the median of the following values:
37,31,42,43,46,25,39,45,32
10
228Find 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
229Find 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
230The 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
231Compute Mean deviation about median for the following Frequency distribution.
Variable(
( x )
( mathbf{1 0} )
Frequency
[
f)
]
A . 10.5
в. 10.1
c. 13.2
D. 12.1
11
232Mean 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
233Arithmetic 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
234The 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
235begin{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
236The 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
237The variance of ( 10,10,10,10,10, ) is
A . 10
B. ( sqrt{10} )
( c .0 )
D. 5
11
238The 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
239The 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
240In 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
241Find the coefficient of variation.
A. 72.66
B. 81.24
( c cdot 264 )
D. 330
E. None
11
242The 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
243If 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
244The 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
245The 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
246The 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
247The 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
248The 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
249If 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
250Heights of the pupils of a particular school are given. Draw greater than cumulative curve and find the median
height from it.
( begin{array}{ll}90- & 100- \ 100 & 110end{array} ) Height
(in ( mathrm{cm} ) ) 120 13.
Number of pupils
10
251For 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
252The 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
253A 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
254Find 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
255The 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
256Find the mean deviation about the
mean for data.
11
257The 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
258Find 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
259Assertion
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
260Which 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
261Coefficient 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
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
263Let ( 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
264The 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
265Find 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
266The 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
267The mean and S.D of 100 observations
are 50 and 4 respectively. Find the sum of squares of observation.
11
268The 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
269The 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
270According to above histogram, Which group has the maximum number of
workers?
4.810
B. 820
( c cdot 830 )
( D cdot 840 )
9
271The 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
272Find 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
273The 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
274If 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
275Find 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} )
( A cdot 7 )
в. 55
c. 64
D. 78
11
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
277If 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
27862. 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
279Find 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
280Draw 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
281The 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
282What 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
283Find 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
284The 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
285The 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
286Find 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
287Following table gives frequency distribution of time (in minutes) taken
by a person in watching T.V. on a day.
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
for the given data.
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
289Find 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
290The 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
291Represent 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
292If 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
293The 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
294Let ( 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
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
296The 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
297Let ( 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
298Find 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
299Following 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
[
15
]
acres
No. of
2
25
farms
A . 33.60 Acres
B. 37.60 Acres
c. 38.60 Acres
D. 40.60 Acres
10
300Calculate M.D about Mean for the given
data
begin{tabular}{lcccc}
Size of item & 4 & 6 & 8 & 10 \
hline
end{tabular}
[
]
6
A . 6.12
в. 5.12
c. 2.44
D. 3.44
11
301If 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
302Median of the following freq. dist.
( boldsymbol{x}_{i} quad boldsymbol{3} quad boldsymbol{6} ) ( mathbf{1 2} ) ( mathbf{1 0} )
( A cdot 7 )
B. 10
c. 8.5
D. None of these
10
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
304On 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
305From 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
306If 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
307Find the standard deviation of the
numbers 62,58,53,50,63,52,55
11
308Coefficients 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
309For 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
310The 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
311Find 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
312Given mean ( =12, ) mode ( =3 . ) Find
median.
A ( cdot 12 )
B. 2
( c cdot 9 )
D.
10
313For 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
314Variance remains unchanged by change
of
A. scale
B. origin
c. both
D. none of these
11
315Assertion
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
316If ‘ ( 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
317The 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
318The 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
319The 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
320Find 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
321Wurks)
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
322A 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
323Consider 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
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
324Find 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
325Let ( 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
326Mean proportion of 64 and 225 will be –
A ( cdot 120 )
B. 90
( c cdot 60 )
D. 30
10
327Find 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
328The 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
329The variance of observations
112,116,120,125,132 is
A . 58.8
B. 48.8
c. 61.8
D. None of these
11
330The one which is the measure of the
central tendency is
A. mode
B. mean deviation
c. standard deviation
D. coefficient of correlation
10
331The 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
332The 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
333Identify the shape of this histogram.
A. Symmetric
B. Skewed right
C. Skewed left
D. Rotational
9
334Batsman ( 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
335Find 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
336For 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
337What 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
338Which type of average is most affected by extreme values in the data?
A. Mean
B. Mode
c. Median
D. All of the above
10
339Find 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
340If 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
341Mean 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
342If 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
343The 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
344Find 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}
A . 19
B. 31
c. 26
D. 2
10
345If ( 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
346The 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
347Which 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
348To 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
349The 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
350Find 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
351Which 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
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
353The 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
354Compute 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
355Coefficient 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
356The S.D. of scores 1,2,3,4,5 is
A ( cdot sqrt{2} )
B. ( sqrt{3} )
( c cdot frac{2}{5} )
D.
11
357A 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
358Calculate 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
359Find the standard deviation of 40,42
and ( 48 . ) If each value is multiplied by 3 find the standard deviation of the new
data
11
360The 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
361100 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
362Calculate 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
363Draw a frequency polygon for the following data using histogram.
Marks
20
an
Number
of
students
9
364Find 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
365Standard 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
366The 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
367Find 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
368A 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
369In 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
370Consider 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
371The 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
372What is the difference of frequencies of
the intervals ( 30-40 ) and ( 40-50 ? )
A . 5
B. 20
c. 15
D. 25
9
373The 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
374The 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
375The 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
376Calculate variance for the following
data: 2,4,6,8 and 10
11
377state-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
378Daleel-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
379The 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
380What proportion of good student are male?
A. 0
B. 0.73
( c cdot 0.4 )
D. 1.0
10
381A 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
382In 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
383In 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
384If 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
385Laspeyres 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
386Construct 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
387Compute 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
388In 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
3893.
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
390Observations 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
391The 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
392If 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
393Which 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
394Identify 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} )
A. ( 20-50 )
B . ( 50-80 )
c. ( 80-110 )
D. ( 110-140 )
10
395To 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
396Assertion
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
397For 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
398If 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
399The 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} )
A . 7.8
B. 9
c. ( 8 . )
D. 0.9
11
400The 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
401Calculate 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
402Find 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
40358. 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
404Find 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
405The 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
406The 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
407Find 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
( mathbf{A} cdot 17 )
B . 17.5
( mathbf{c} cdot 18 )
D. 18.5
10
408Identify 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
409The 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
410The 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
411Find 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
412The 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
413Find 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
414Find 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
415Find 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
416What 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
417What 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
418The 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
419The mean of ( 7,9, x+3,12,2 x-1 ) and 3
is
9. Find the value of ( x )
10
420Write 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
421In 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
422The value of median of
( begin{array}{llll}text { Income } & & & & \ & 1000 & 1100 & 1200 & 1300end{array} ) No. of
( A cdot 1300 )
B. 1200
c. 1250
D. 1150
10
423Find the median of the following data.
( begin{array}{lllll}text { class } & 0- & 20- & 40- & 60 \ text { interval } & 20 & 40 & 60 & 800end{array} )
A . 45
B. 40
c. 55
D. 50
10
424The 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
425Find 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
426The width of a rectangle in a histogram
represents of the
class.
A. frequency
B. range
c. class limit
D. upper limit
9
427Find ( 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
428The 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
429The 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
430The 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
4313
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
432Heights of students of class ( X ) are given in the following frequency distribution. Find the modal height.10
433If 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
434If 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
435The 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
436Median 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
437What is the standard deviation of the
( 5,5,10,10,10 ? )
A .2 .44
B. 1.44
( c cdot 5 )
( D )
11
438A 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
439Calculate the mean from the following
data:
10
440Mean 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
441The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy
[
75
]
rate (in ( 45- )
55
( % )
vumbe
of cities
10
442The following table shows the ages of the patients admitted in a hospital during a year:
[
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
443A histrogram consists of
A. sectors
B. rectangles
( c . ) triangle
D. squares
9
444Find 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
445Draw 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
446Find 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
447The 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
448For 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
449The mean of ( 51,81,42,65, x ) is 75 find ( x )10
450Calculate 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
451The variance of first 20 natural
numbers is
( mathbf{A} cdot 133 / 4 )
B. ( 279 / 2 )
c. ( 133 / 2 )
D. ( 399 / 4 )
11
452The 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
453The 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
454Find the range and the coefficient of
range of 43,24,38,56,22,39,45
11
455Find the mean and standard deviation
using short-cut method
60
( begin{array}{lll}61 & 62 & 63end{array} )
( boldsymbol{x}_{i} )
( f_{i} )
11
456In 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
457If ( 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
458The 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
459The 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
460Find 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
461The 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
462Find 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
463Compare 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
464Find 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
465Find 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
466Find the mean deviation about the
mean for the data in
3 ( begin{array}{llll}f_{i} & 7 & 4 & 6end{array} )
11
467Find the mean deviation about mean for
the following data:
Marks 10 11 obtained
12
No. of students 2
3
11
468Find the difference between the mean
and the median of the ( operatorname{set} 3,8,10,15 )
A . 0
B.
( c cdot 4 )
( D )
10
469The 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
470The probability distribution of a random
variable ( boldsymbol{X} ) is given below:
[
]
[
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
471Calculate 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
472Mean 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
473Find the correct Standard Deviation:
A . 5.24
в. 4.93
( c .5 .01 )
D. None of the above
11
47467.
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
475If 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
476DIRECTIONS! 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
477Find 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
478Average can be used
A. only in unity
B. when combined with other average
( c cdot ) Both a & b
D. None of the above
10
479The 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
480begin{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
481Find expected value ( (mu) ) variance ( left(6^{-12}right) )
and ( mathrm{S.D}(sim) ) for the following probability
distribute.
( x ) 2 3
11
482Find 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
483The 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
484Find the mode of the following data in
each case:
14,25,14,28,18,17,18,14,23,22,14,18
10
485The 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
486If 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
487Ten 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
488The sum of absolute deviation is least
when taken from
A. Mean
B. Median
c. mode
D. None of the above
11
489The 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
490Below is given distribution of profit (in
Rs.) per day of a shop in a certain town. Calculate median profit of shops.
in
[
begin{array}{l}
text { No. of } \
text { shops }
end{array}
]
18
A. Rs. 1867
B. Rs. 196
c. Rs. 2167
D. Rs.2567
10
491Create a set of 8 observations with
mean 14.
10
492The 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
493The 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
494If 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
495One situation where mean would be
appropriate representative value
10
496number 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
497The 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
498Time 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
499In 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
501For 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
502Find 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
503The 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
504If 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
505The 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
506The 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
507Following 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
508Consider 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
509Given 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
51015. 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
511Find 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
512The 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
513Find the standard deviation of the first
10 natural numbers
11
514Find 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
515Find 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
516The 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
517The 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
518The 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
519How many ponds had ( 20-39 ) ducks?
Ducks per pond
A .25
B. 30
( c cdot 20 )
D. 15
9
520The 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
52153. 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
522Marks 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
523Find 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
524Find 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
525The 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
526Find the mean for the following data using step deviation method.
( A cdot 4 )
B. 5
( c .6 )
D.
11
527Find 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
528If 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
529Find 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
530The given distribution shows the number of wickets taken by bowlers in inter-school competitions:
Find the median.
10
531Find 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
532If 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
533If the mean of ( 10,12,18,13, x, 17 ) is 15
find ‘ ( boldsymbol{x}^{prime} )
10
534Let ( 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
535The 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
536The mode from the following table will
be:
A . 24
B. 45
c. 65
( D )
10
537Find the mean deviation about the
mean for the data
10
538If 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
539Find 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
540The 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
541The 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
542What is the shape of this histogram?
A. Symmetrical
B. Skewed left
c. Skewed right
D. Rotational
9
543According to above histogram, How
many workers earn less than Rs ( 850 ? )
A . 30
B. 20
( c cdot 10 )
D. 40
9
544The 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
545Calculate 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
546The 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
547A 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
5489.
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
549Calculate the standard deviation of the
following data
( begin{array}{llllll}f & 7 & 10 & 15 & 10 & 8end{array} )
11
550If 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
552Find 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
553How much did the maintenance cost
increased in ( 1996-1997 ) when
compared to ( 1997-1998 ? )
A . 1200
B. 1500
( c .2500 )
D. 4500
9
554How many employees get to work in less
than 60 minutes?
A . 10
B. 5
( c .15 )
D. 20
9
555State the following statement is True or
False

Standard deviation is the measure of dispersion
A. True
B. False

11
556Calculate 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
557If 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
558The mean deviation of the numbers 1,2
3,4,5 is
A. 0
B. 1.2
( c cdot 2 )
D. 1.4
11
55970 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
560If 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
561The following data gives the information on the observed lifetimes (in hours) of
225 electrical components:
( 0- )
( begin{array}{lll}text { 20- } & text { 40- } & text { 60- }end{array} )
[
]
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
562begin{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
563If the two observations are 10 and 0
their arithmetic mean is
A . 10
B. 0
c. 5
D. none of the above
10
564Forty 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
565An 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
566The table shows the number of books on
each number of subjects. Find the
median.
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
567A 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
568Find mode for given data:
( begin{array}{llll}text { Class } & 20- & 30- & 40- \ 29 & 39 & 49end{array} )
3. 20 Frequency 15
10
569The 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
570Find 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
5714.
The class size of an interval 10-20 is
(b) 5
(a) 10
(c) 20
(d)
15
9
572Range 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
573If 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
574Types of histograms includes
A. deviation bar charts
B. paired bar charts
C . grouped charts
D. all of the above
9
575Find the sum of deviation of all
observations of the data 5,8,10,15
22 from their mean
11
576The 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
577The smallest value of a collection of
data is 12 and the range is ( 59 . ) Find the largest value of the collection of data.
11
578If 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
579If 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
580Calculate the mean deviation for the
( 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
581The 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
582The 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
583A 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
584The 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
585The salary of 43 employees are given in the following table. Find the median.
Rs
Number of employees
10
586The 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
587Find standard deviation 50,56,59,60
63,67,68
11
588Give the formula for Step up deviation
method.
11
589The S.D.is not less than the mean
deviation. If this is true enter 1 , else
enter 0
11
590The 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
591The 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
592Find 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
What is the percentage obtained by the
student ?
( A cdot 80 % )
B. ( 63 % )
( c .57 % )
( 0.90 % )
9
594Assertion
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
595Find 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
596Calculate the mean deviation about the
mean of the set of first ( n ) natural
numbers when ( n ) is an odd number
11
597The 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
598The 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
599If 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
60001 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
601A 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
602Find 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
603The 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
604Construct 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
605The 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:

10
606For 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
607If 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
608Find the mean from the following frequency distribution of marks at a test in class.
Maks
10
;
No. of students
76
[
(f)
]
10
609The difference between he maximum
and the minimum observations in the
data is
A. class interval
B. frequency
c. cumulative frequency
D. range
11
610The 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
611ff ( x ) follows binomial distribution with
mean 4 variance ( 2 . ) Find ( P(|x-4|) leq 2 )
11
612An 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
613Which of the following is not the measure of dispersion.
A. Quartile Deviation
B. Range
c. Mean Deviation
D. None of these
11
614If ( 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
615Find 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
616The formula for coefficient of variation
(C.V.) is given by
11
617Find the mean deviation about the
mean for the data
4,7,8,9,10,12,13,17
10
618Find 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
620A 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
621Find 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
622Write 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
624The modal class is
A ( .60-65 )
В. ( 55-60 )
( c .50-55 )
D. none of these
10
625Calculate 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
626If 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
627The 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
628If ( 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
629The difference between the maximum
and the minimum observation in the
data is
A. class interval
B. frequency
c. cumulative frequency
D. range
11
630A 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
631The variance of a constant is
A. Constant
B. zero
c. Number itself
D. None
11
632Following 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
633Mode 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
634The 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
635In 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
636The 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
637Find 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
63814.
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
639If 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
640Variance of the first 11 natural numbers
is:
A ( cdot sqrt{5} )
B. ( sqrt{10} )
( c cdot 5 sqrt{2} )
D. 10
11
641The 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
642State the following statement is True or False
Mean Deviation is used where the
number of values are large
A. True
B. False
11
643If 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
644Find 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
645The 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
646The 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
647If 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
648The 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
649Find 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
650The 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
651The 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
652Statement-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
653The 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}
]
( mathrm{cm} )
No
of 3
85
155
shirts sold
10
654The 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
655The 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
656If 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
657The arithmetic mean of following data
is
17. find the value of ( 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
659A 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
660Calculate 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
66110
san
Study the nistoyranli allu auswu
4. How many students have been observed?
(a) 20
(b) 55
(c) 40
(d) 80
9
662The 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
663the 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
664The 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
665Calculate 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
666The 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
667If 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
668Find the range and the coefficient of
range of 43,24,38,56,22,39,45
11
669If 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
670The 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
671The 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
672The 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
673If coefficient of range is 0.092 and the largest value is 71 , the range is?
A . 12
B. 13
c. 14
D. 16
11
674The 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
675There 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
676State 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
677Find the sum of deviations of all
observations of the data 5,8,10,15,22 from their mean
11
678TINI
[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
679Find 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
680Find Mode, if Mean ( =70.4 ) and Median is ( = )
( 71_{–} )
A . 71.06
в. 72.9
( c cdot 69.6 )
D. 72.2
10
681The 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
682Find the mean and variance for the data
6,7,10,12,13,4,8,12
11
68352. 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
684Which of the following are dimensionless
A. S.D.
в. М.D.
c. variance
D. coefficient of variation
11
685state-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
686Which factory has more variation in wages?
A . ( A )
в. ( B )
C. Equal Variation
D. Cannot be determined.
11
687For 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
688Suppose 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
689The mean of 10 observation is 20 . if
each observation is added by ( ^{prime} 5^{prime} ). Find the mean of new observation.
10
690Calculate 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
691Calculate 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
692Mean 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
693Draw 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
694Mean 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
695The 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
696Find the mean deviation about the
mean for the data in
( begin{array}{lllll}x_{i} & 10 & 30 & 50 & 70end{array} ) ( mathbf{9 0} )
11
697Ashok 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
698If 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
699The 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
700If 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
701Find 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
702The 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
703Find 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
704From 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
705A 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
706What is the median for the following
data?
( begin{array}{lllll} & 2- & 4- & 6- & 8- \ x & 4 & 6 & 8 & 10end{array} )
( mathbf{A} cdot mathbf{6} )
B. 6.5
c. 7
D. 7.5
10
707Consider 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
708The 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
709Below is given frequency distribution of
I.Q. (Intelligent Quotient) of 80
candidates.
[
70
]
80
[
]
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
710Find 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
711Given ( N=10, Sigma x=60 ) and ( Sigma x_{i}= )
1000. The standard deviation is
11
712Find the mean using step deviation
method.
A . 14
B. 13
c. 12
D. 10
10
713Prove that ( : sum_{i=1}^{n}left(x_{i}-bar{x}right)=0 )11
714The 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
715For the given data, ( S D=10, A M=20 )
the coefficient of variation is
A . 47
B. 24
c. 44
D. 50
11
7166.
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
717If 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
718The 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
719The 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
720Write two demerits of arithmetic mean.10
Median
( begin{array}{lllll}text { Class } & 0- & 10- & 20- & 30 \ & 10 & 20 & 30 & 40end{array} )
( A cdot 7 )
B. 8
c. 19
D.
11
722The 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
723Find 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
724What is the standard deviation of
( 7,9,11,13,15 ? )
A . 2.4
B . 2.
c. 2.7
D. 2.8
11
725The is the difference
between the greatest and the least
value of the variate.
A . Range
B. Data
c. Average
D. Variance
11
726Find the variance of the following data 6,8,10,12,14,16,18,20,22,2411
727In 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
728The 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
729If 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
730Calculate 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} )
A. 9.125
B. 8.125
c. 7.125
D. 6.125
10
731The 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
732The 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
733Which 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
73457. 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
735Which 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
736Calculate 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
10
10
737Below 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
738Find the standard deviation of the
numbers 62,58,53,50,63,52,55
11
739The median of the first 100 natural
numbers is
A . 49.5
B. 22.75
c. 23.75
D. 50.5
10
740If 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
741Variance is independent of change of
A . only origin
B. only scale
c. origin and scale both
D. none of these
11
742The 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
743Means 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
744The variance of the data
6,8,10,12,14,16,18,20,22,24 is
A . 15
B . 20
c. 30
D. 33
11
745Find mean deviation from the mean for
the given data
A .2 .12
в. 3.04
c. 10.45
D. 5.76
11
746A 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
747Find 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
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
749The 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
750The 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
751The 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
752Which 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
753The 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
754Which 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
7553.
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
757A 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
758100 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
759Calculate Mean deviation from Median
for the given data.
Wages(Rs) ( quad 20 ) 18 ( mathbf{1 6} ) 14
A .6 .84
в. 4.44
c. 2.24
D. 3.21
11
760Attempt 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
761Calculate 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
762Find 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
763The 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
765For 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
766For 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
767The 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
768Find the median of the following data
( mathbf{3}, mathbf{1}, mathbf{5}, mathbf{6}, mathbf{3}, mathbf{4}, mathbf{5} )
10
769The 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
770Find the median for the following frequency distribution table :
( begin{array}{lccc}text { Class- } & 0 & 5 & 10 \ text { interval } & 5 & 10 & 15end{array} ) ( – )
10
771The 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
772The 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
773The 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
774Find 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
775In 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
776If 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
777The variance is the
standard deviation.
A. Square
B. Cube
c. square root
D. cube root
11
778Draw 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
779Which of the following can be used as measures of dispersions?
A. Range
B. Percentiles
c. standard Deviation
D. All
11
780The 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
781dentify the shape of histogram.
Height
A. Skewed left
B. Skewed right
c. Symmetric
D. Rotational
9
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
783Let ( 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
784The 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
785Mean 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
786The number of books bought by 200 students in a book exhibition is given
below.
No. of
[
]
No. of ( quad 35 )
uder
Find the variance and standard
variation
11
787How many employees get to work in less
than 20 minutes?
( A cdot 4 )
B. 6
c. 10
D. 15
9
788If 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
789The 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
790The 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
791The 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
792What 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
793If the mode of a distribution is 18 and
the mean is 24 , then median is
A . 18
B. 24
c. 22
D. 21
10
794The difference between the maximum
and the minimum observations in the
data is
A. class interval
B. frequency
c. cumulative frequency
D. range
11
795The variance of first 50 even natural
numbers is
11
796Find the variance of first 10 multiples of
3
( mathbf{A} cdot 72.65 )
B. 74.05
c. 74.25
D. 73.85
11
797Solve 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
798If 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
799Given 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
800The 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
801The 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
802Solve:
( log _{5} frac{(25)^{4}}{sqrt{625}} )
( mathbf{A} cdot mathbf{4} )
B. 5
( c cdot 6 )
D.
11
803Find 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
804Find 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
805If ( 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
806Find 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
807How 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
808The 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
809Find 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
810Draw 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
811The 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
812Two 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
813If the standard deviation of a population is ( 9, ) the population variance is:
( mathbf{A} cdot mathbf{9} )
B. 3
c. 21
D. 81
11
814Calculate 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
815A 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
816If 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
817Let 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
818If 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
819The 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
820Let ( 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
821f 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
822Consider 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
8231.
The range is
(a) 2.1 kg
(c) 1.0kg
(b) 0.5 kg
(d) 1.5 kg
9
824The 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
825Find 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
826The 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
Standard 12 deviation
Which of the three subjects shows the highest variability in marks and which shows the
lowest?
11
827Calculate 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
828If 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
829The 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
830If 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
831The 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
832Mean 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
833In 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
834If 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
835Calculate 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
836Write the relation between standard
deviation of a set of scores and
its variance
11
837Calculate the mean deviation for the
( 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} )
A. 10.22
в. 7.57
c. 5.55
D. 8.45
11
838The 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
839The 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
840Find the mean ( S . D ) of 1,2,3,4,5,611
841The 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
842The 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
843Which one of the following is not central tendency?
A. Mean deviation
B. Arithmetic mean
c. Median
D. Mode
10
844The 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
845If ( 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
846The most common form of
diagrammatic representation of a grouped frequency distribution is –
A . Ogive
B. Histogram
C. Frequency polygon
D. None of these
9
847The 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
848The 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
849Electricity 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
85058. 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
851Calculate 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
852In 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
853Suppose 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
854Find 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
855Find 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
85670. 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
857Variance 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
8585 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
859The average of 7 consecutive numbers
is n. If the next two numbers are
included, the average will be….
10
86010. The lower limit of 45 – 50 is
(a) 45
(b) 50
(d) 47.5
(c) 5
9
861The 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
862What 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
863Find 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
864Find the median if total students are 40
10
865S.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
866Which 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
867Find 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
868The 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
869For 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
870Calculate 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
[
]
nouses
11
871The 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
872Find 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
873If 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
874The 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
875Calculate 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
876The 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
877The 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
878Which peak is second highest?
( A cdot B )
( mathbf{B} cdot A )
( c cdot C )
( D . E )
9
87938.
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
880Which one of the following is a measure of dispersion?
A. Mean
B. Median
c. mode
D. standard deviation
11
881The 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
882For the given data, ( S D=10, A M=20, ) the coefficient
of variation is
A . 47
B. 24
( c cdot 44 )
D. 50
11
883If 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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