1. 56 Measures of Central Tendency
1. If the mean of 3, 4, x, 7, 10 is 6, then the value of x is
(a) 4 (b) 5 (c) 6 (d) 7
2. The mean of a set of numbers is x . If each number is multiplied by , then the mean of new set is
(a) x (b) x

 (c) x
 (d) None of these
3. The mean of discrete observations n
y
y
y ......,
,
, 2
1 is given by
(a)
n
y
n
i
i

1
(b)




n
i
n
i
i
i
y
1
1
(c)
n
f
y
n
i
i
i

1
(d)




n
i
i
n
i
i
i
f
f
y
1
1
4. If the mean of numbers 27, 31, 89, 107, 156 is 82, then the mean of 130, 126, 68, 50, 1 is
(a) 75 (b) 157 (c) 82 (d) 80
5. i
d is the deviation of a class mark i
y from ‘a’ the assumed mean and i
f is the frequency, if )
(
1
i
i
i
g d
f
f
x
M 


 , then x is
(a) Lower limit (b) Assumed mean (c) Number of observations (d) Class size
6. The mean of a set of observation is x . If each observation is divided by ,   0 and then is increased by 10, then the mean of the new
set is
(a)

x
(b)

10

x
(c)


10

x
(d) 10

x

7. If the mean of the numbers x

27 , x

31 , x

89 , x
x 
 156
,
107 is 82, then the mean of x
x
x
x
x 



 1
,
50
,
68
,
126
,
130 is
(a) 75 (b) 157 (c) 82 (d) 80
8. Consider the frequency distribution of the given numbers
Value : 1 2 3 4
Frequency : 5 4 6 f
If the mean is known to be 3, then the value of f is
(a) 3 (b) 7 (c) 10 (d) 14
9. If the arithmetic mean of the numbers n
x
x
x
x ......,
,
,
, 3
2
1 is x , then the arithmetic mean of numbers
b
ax
b
ax
b
ax
b
ax n 


 ........
,
,
, 3
2
1 , where a, b are two constants would be
(a) x (b) nb
x
a
n  (c) x
a (d) b
x
a 
10. The mean of n items is x . If the first term is increased by 1, second by 2 and so on, then new mean is
(a) n
x  (b)
2
n
x  (c)
2
1


n
x (d) None of these
11. The G.M. of the numbers n
3
......,
,
3
,
3
,
3 3
2
is
(a) n
/
2
3 (b) 2
/
)
1
(
3 
n
(c) 2
/
3n
(d) 2
/
)
1
(
3 
n
12. The reciprocal of the mean of the reciprocals of n observations is their
B
Ba
as
si
ic
c L
Le
ev
ve
el
l
Mean
56

2. Measures of Central Tendency 57
(a) A.M. (b) G.M. (c) H.M. (d) None of these
13. The harmonic mean of 3, 7, 8, 10, 14 is
(a)
5
14
10
8
7
3 



(b)
14
1
10
1
8
1
7
1
3
1



 (c)
4
14
1
10
1
8
1
7
1
3
1




(d)
14
1
10
1
8
1
7
1
3
1
5




14. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is
(a) 30 (b) 30.1 (c) 29 (d) 31
15. The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is
(a)
2
1

n
(b)
)
1
2
(
2
)
1
(
3


n
n
n
(c)
6
)
1
2
)(
1
( 
 n
n
(d)
2
)
1
( 
n
n
16. The mean of the values 0, 1, 2,......,n having corresponding weight n
n
n
n
n
c
c
c
c ,
,........
,
, 2
1
0 respectively is
(a)
1
2

n
n
(b)
)
1
(
2 1


n
n
n
(c)
2
1

n
(d)
2
n
17. If the values
n
1
.....
,
5
1
,
4
1
,
3
1
,
2
1
,
1 occur at frequencies 1, 2, 3, 4, 5, …. n in a distribution, then the mean is
(a) 1 (b) n (c)
n
1
(d)
1
2

n
18. The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the
whole group is
(a)
5
1
(b)
4
15
(c) 4 (d) 8
19. A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than
(a) 60% (b) 65% (c) 80% (d) 90%
20. The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and
27, then the percentage of women in the group is
(a) 30 (b) 40 (c) 50 (d) 60
21. The mean monthly salary of the employees in a certain factory is Rs. 500. The mean monthly salary of male and female employees are
respectively Rs. 510 and Rs. 460. The percentage of male employees in the factory is
(a) 60 (b) 70 (c) 80 (d) 90
22. The A.M. of a 50 set of numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the A.M. of the remaining set of
numbers is
(a) 38.5 (b) 37.5 (c) 36.5 (d) 36
23. Mean of 100 observations is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The
correct mean is
(a) 44.0 (b) 44.46 (c) 45.00 (d) 45.54
24. A car completes the first half of its journey with a velocity 1
v and the rest half with a velocity 2
v . Then the average velocity of the car
for the whole journey is
(a)
2
2
1 v
v 
(b) 2
1v
v (c)
2
1
2
1
2
v
v
v
v

(d) None of these
25. An automobile driver travels from plane to a hill station 120 km distant at an average speed of 30 km per hour. He then makes the
return trip at an average speed of 25 km per hour. He covers another 120 km distance on plane at an average speed of 50 km per
hour. His average speed over the entire distance of 300 km will be
(a)
3
50
25
30 

km/hr (b) 3
1
)
50
,
25
,
30
( (c)
50
1
25
1
30
1
3


km/hr (d) None of these

3. 58 Measures of Central Tendency
26. The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by
2
1
kg;
the weight of the teacher is
(a) 40.5 kg (b) 50 kg (c) 41 kg (d) 58 kg
27. If 1
X and 2
X are the means of two distributions such that 2
1 X
X  and X is the mean of the combined distribution, then
(a) 1
X
X  (b) 2
X
X  (c)
2
2
1 X
X
X

 (d) 2
1 X
X
X 

28. If a variable takes values 0, 1, 2, ….., n with frequencies n
n
n
n
p
p
q
n
n
p
q
n
q ......,
,
2
.
1
)
1
(
,
1
, 2
2
1 
 
, where p + q = 1, then the mean is
(a) np (b) nq (c) n(p + q) (d) None of these
29. The A.M. of n observations is M. If the sum of n – 4 observations is a, then the mean of remaining 4 observations is
(a)
4
a
M
n 
(b)
2
a
M
n 
(c)
2
A
M
n 
(d) n M + a
30. Which one of the following measures of marks is the most suitable one of central location for computing intelligence of students
(a) Mode (b) Arithmetic mean (c) Geometric mean (d) Median
31. The central value of the set of observations is called
(a) Mean (b) Median (c) Mode (d) G.M.
32. For a frequency distribution 7th decile is computed by the formula
(a) i
f
C
N
l
D 









7
7 (b) i
f
C
N
l
D 









10
7 (c) i
f
C
N
l
D 









10
7
7 (d) i
f
C
N
l
D 









7
10
7
33. Which of the following, in case of a discrete data, is not equal to the median
(a) 50th percentile (b) 5th decile (c) 2nd quartile (d) Lower quartile
34. The median of 10, 14, 11, 9, 8, 12, 6 is
(a) 10 (b) 12 (c) 14 (d) 11
35. The relation between the median M, the second quartile 2
Q , the fifth decile 5
D and the 50th percentile 50
P , of a set of observations is
(a) 50
5
2 P
D
Q
M 

 (b) 50
5
2 P
D
Q
M 

 (c) 50
5
2 P
D
Q
M 

 (d) None of these
36. For a symmetrical distribution 25
1 
Q and 45
3 
Q , the median is
(a) 20 (b) 25 (c) 35 (d) None of these
37. If a variable takes the discrete values )
0
(
5
,
2
1
,
2
1
,
2
,
3
,
2
5
,
2
7
,
4 







 







 , then the median is
(a)
4
5

 (b)
2
1

 (c) 2

 (d)
4
5


38. The upper quartile for the following distribution
B
Ba
as
si
ic
c L
Le
ev
ve
el
l
Median
A
Ad
dv
va
an
nc
ce
e Level

4. Measures of Central Tendency 59
Size of items 1 2 3 4 5 6 7
Frequency 2 4 5 8 7 3 2
is given by the size of
(a) 




 
4
1
31
th item (b) 










 
4
1
31
2 th item (c) 










 
4
1
31
3 th item (d) 










 
4
1
31
4 th item
39. For a continuous series the mode is computed by the formula
(a) C
f
f
f
f
l
m
m
m
m







1
1
1
or i
f
f
f
f
l
m












2
1
1
(b) C
f
f
f
f
f
l
m
m
m
m
m








1
1
1
or i
f
f
f
f
f
l
m
m





2
1
1
(c) C
f
f
f
f
f
l
m
m
m
m
m








1
1
1
2
or i
f
f
f
f
f
l
m
m





2
1
1
2
(d) C
f
f
f
f
f
l
m
m
m
m
m








1
1
1
2
or i
f
f
f
f
f
l
m
m





2
1
1
2
40. A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is
(a) 6 (b) 7 (c) 8 (d) 10
41. The mode of the following items is 0, 1, 6, 7, 2, 3, 7, 6, 6, 2, 6, 0, 5, 6, 0
(a) 0 (b) 5 (c) 6 (d) 2
42. If mean = (3 median – mode) k, then the value of k is
(a) 1 (b) 2 (c)
2
1
(d)
2
3
43. In a moderately asymmetrical distribution the mode and mean are 7 and 4 respectively. The median is
(a) 4 (b) 5 (c) 6 (d) 7
44. If in a moderately asymmetrical distribution mode and mean of the data are 6 and 9 respectively, then median is
(a) 8 (b) 7 (c) 6 (d) 5
45. Which of the following is not a measure of central tendency
(a) Mean (b) Median (c) Mode (d) Range
46. The most stable measure of central tendency is
(a) Mean (b) Median (c) Mode (d) None of these
47. Which of the following average is most affected of extreme observations
(a) Mode (b) Median (c) Arithmetic mean (d) Geometric mean
48. The following data was collected from the newspaper : (percentage distribution)
Country Agriculture Industr
y
Services Others
India 45 19 28 8
U.K. 3 40 44 13
Japan 6 48 43 3
U.S.A. 3 35 61 1
It is an example of
(a) Data given in text form (b) Data given in diagrammatic form
(c) Primary data (d) Secondary data
49. The mortality in a town during 4 quarters of a year due to various causes is given below :
B
Ba
as
si
ic
c L
Le
ev
ve
el
l
Mode
B
Ba
as
si
ic
c L
Le
ev
ve
el
l
Relation between mean, median and mode
Y
400

5. 60 Measures of Central Tendency
Based on this data, the percentage increase in mortality in the third quarter is
(a) 40
(b) 50
(c) 60
(d) 75
50. A market with 3900 operating firms has the following distribution for firms arranged according to various income groups of workers
Income group No. of firms
150-300 300
300-500 500
500-800 900
800-1200 1000
1200-1800 1200
If a histogram for the above distributionisconstructedthe highestbar in the histogram wouldcorrespondtothe class
(a) 500-800 (b) 1200-1800 (c) 800-1200 (d) 150-300
51. The total expenditure incurred by an industry under different heads is best presented as a
(a) Bar diagram (b) Pie diagram (c) Histogram (d) Frequency polygon
52. The expenditure of a family for a certain month were as follows :
Food – Rs.560, Rent – Rs.420, Clothes – Rs.180, Education – Rs.160, Other items – Rs.120
A pie graph representing this data would show the expenditure for clothes by a sector whose angle equals
(a) 180° (b) 90° (c) 45° (d) 64°
53. Section-wise expenditure of a State Govt. is shown in the given figure. The expenditure incurred on transport is
(a) 25% (b) 30% (c) 32% (d) 35%
54. The measure of dispersion is
(a) Mean deviation (b) S.D. (c) Quartile deviation (d) All of these
55. The mean deviation from the median is
(a) Greater than that measured from any other value (b) Less than that measured from any other value
(c) Equal to that measured from any other value (d) Maximum if all observations are positive
56. The S.D. of 5 scores 1 2 3 4 5 is
(a)
5
2
(b)
5
3
(c) 2 (d) 3
57. The variance of the data 2, 4, 6, 8, 10 is
(a) 6 (b) 7 (c) 8 (d) None of these
B
Ba
as
si
ic
c L
Le
ev
ve
el
l
Measures of dispersion

6. Measures of Central Tendency 61
58. The mean deviation of the numbers 3, 4, 5, 6, 7 is
(a) 0 (b) 1.2 (c) 5 (d) 25
59. If the standard deviation of 0, 1, 2, 3, …..,9 is K, then the standard deviation of 10, 11, 12, 13 …..19 is
(a) K (b) K + 10 (c) 10

K (d) 10K
60. For a normal distribution if the mean is M, mode is 0
M and median is d
M , then
(a) 0
M
M
M d 
 (b) 0
M
M
M d 
 (c) 0
M
M
M d
 (d) 0
M
M
M d 

61. For a frequency distribution mean deviation from mean is computed by
(a) M.D.
f
d


 (b) M.D.
f
fd


 (c) M.D.
f
d
f



|
|
(d) M.D.
|
| d
f
f



62. Let s be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation
of the resulting numbers is
(a) s (b) cs (c) c
s (d) None of these
63. The S.D. of the first n natural numbers is
(a)
2
1

n
(b)
2
)
1
( 
n
n
(c)
12
1
2

n
(d) None of these
64. Quartile deviation for a frequency distribution
(a) 1
3 Q
Q
Q 
 (b) )
(
2
1
1
3 Q
Q
Q 
 (c) )
(
3
1
1
3 Q
Q
Q 
 (d) )
(
4
1
1
2 Q
Q
Q 

65. The variance of the first n natural numbers is
(a)
12
1
2

n
(b)
6
1
2

n
(c)
6
1
2

n
(d)
12
1
2

n
66. For a moderately skewed distribution, quartile deviation and the standard deviation are related by
(a) S.D.
3
2
 Q.D. (b) S.D.
2
3
 Q.D. (c) S.D.
4
3
 Q.D. (d) S.D.
3
4
 Q.D.
67. For a frequency distribution standard deviation is computed by applying the formula
(a)
f
fd
f
fd














2
 (b)
2
2
2














f
fd
f
fd
 (c)
f
fd
f
fd














2
2
 (d)
2
2














f
fd
f
fd

68. For a frequency distribution standard deviation is computed by
(a)
f
x
x
f




)
(
 (b)
f
x
x
f




2
)
(
 (c)
f
x
x
f




2
)
(
 (d)
f
x
x
f




)
(

69. If Q.D is 16, the most likely value of S.D. will be
(a) 24 (b) 42 (c) 10 (d) None of these
70. If M.D. is 12, the value of S.D. will be
(a) 15 (b) 12 (c) 24 (d) None of these
71. The range of following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
(a) 11 (b) 7 (c) 5.5 (d) 6
72. If v is the variance and  is the standard deviation, then
(a) 

2
v (b) 2


v (c)

1

v (d) 2
1


v
73. If each observation of a raw data whose variance is 2
 , is increased by , then the variance of the new set is
(a) 2
 (b) 2
2

 (c) 2

  (d) 2
2

 
74. If each observation of a raw data whose variance is 2
 , is multiplied by , then the variance of the new set is
(a) 2
 (b) 2
2

 (c) 2

  (d) 2
2

 

7. 62 Measures of Central Tendency
75. The standard deviation for the set of numbers 1, 4, 5, 7, 8 is 2.45 nearly. If 10 are added to each number, then the new standard
deviation will be
(a) 2.45 nearly (b) 24.45 nearly (c) 0.245 nearly (d) 12.45 nearly
76. For a given distribution of marks mean is 35.16 and its standard deviation is 19.76. The co-efficient of variation is
(a)
76
.
19
16
.
35
(b)
16
.
35
76
.
19
(c) 100
76
.
19
16
.
35
 (d) 100
16
.
35
76
.
19

77. If 25% of the item are less than 20 and 25% are more than 40, the quartile deviation is
(a) 20 (b) 30 (c) 40 (d) 10
78. For a normal curve, the greatest ordinate is
(a) 2  (b) 
 2 (c)

2
1
(d)

 2
1
79. If the variance of observations n
x
x
x ......
,
, 2
1 is 2
 , then the variance of n
ax
ax
ax .......,
, 2
1 ,   0 is
(a) 2
 (b) 2

a (c) 2
2

a (d) 2
2
a

80. The mean deviation from the mean for the set of observations –1, 0, 4 is
(a)
3
14
(b) 2 (c)
3
2
(d) None of these
81. The mean and S.D. of 1, 2, 3, 4, 5, 6 is
(a)
12
35
,
2
7
(b) 3, 3 (c) 3
,
2
7
(d)
12
35
,
3
82. The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be
(a) 40 (b) 45 (c)
25
21
40  (d) None of these
83. The S.D of 15 items is 6 and if each item is decreased by 1, then standard deviation will be
(a) 5 (b) 7 (c)
15
91
(d) 6
84. The quartile deviation for the data
x : 2 3 4 5 6
f : 3 4 8 4 1
is
(a) 0 (b)
4
1
(c)
2
1
(d) 1
85. The sum of squares of deviations for 10 observations taken from mean 50 is 250. The co-efficient of variation is
(a) 50% (b) 10% (c) 40% (d) None of these
86. One set containing five numbers has mean 8 and variance 18 and the second set containing 3 numbers has mean 8 and variance 24.
Then the variance of the combined set of numbers is
(a) 42 (b) 20.25 (c) 18 (d) None of these
87. The means of five observations is 4 and their variance is 5.2. If three of these observations 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
88. The mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1, 2 and 6, the other two observations are
(a) 4 and 8 (b) 4 and 9 (c) 5 and 7 (d) 5 and 9
89. Consider any set of observations 101
3
2
1 ...,
,.
.
,
, x
x
x
x ; it being given that 101
100
3
2
1 .... x
x
x
x
x 



 ; then the mean deviation of
this set of observations about a point k is minimum when k equals

8. Measures of Central Tendency 63
(a) 1
x (b) 51
x (c)
101
... 101
2
1 x
x
x 


(d) 50
x
90. The mean and S.D of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score of 40
was wrongly read as 50. The correct mean and S.D respectively are
(a) 14.98, 39.95 (b) 39.95, 14.98 (c) 39.95, 224.5 (d) None of these
91. Let r be the range and 




n
i
i x
x
n
S
1
2
2
)
(
1
1
be the S.D. of a set of observations n
x
x
x .....
,
, 2
1 , then
(a)
1


n
n
r
S (b)
1


n
n
r
S
(c)
1


n
n
r
S (d) None of these
92. In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is
(a) M.D. = S.D. (b) M.D. ≥ S.D. (c) M.D. < S.D. (d) M.D. ≤ S.D.
93. For (2n +1) observations n
n x
x
x
x
x
x 

 ,
.....
,
,
,
, 2
2
1
1 and 0 where x’s are all distinct. Let S.D. and M.D. denote the standard deviation
and median respectively. Then which of the following is always true
(a) S.D. < M.D.
(b) S.D. > M.D.
(c) S.D. = M.D.
(d) Nothing can be said in general about the relationship of S.D. and M.D.
94. Suppose values taken by a variable X are such that b
x
a i 
 where i
x denotes the value of X in the ith case for i = 1, 2, …. n. Then
(a) b
X
a 
 )
(
Var (b) 

 b
X
a )
(
Var
2
(c) )
(
Var
4
2
X
a
 (d) )
(
Var
)
( 2
X
a
b 

95. The variance of ,  and  is 9, then variance of 5, 5 and 5 is
(a) 45 (b)
5
9
(c)
9
5
(d) 225