CBSE Class 10 Mathematics Statistics Worksheet Set B

Question. Find the class marks of classes 10–20 and 35–55.
(a) 10, 35
(b) 20, 55
(c) 15, 45
(d) 17.5, 45

Answer: C

Question. If d_i = x_i – 13, ∑f_id_i = 30 and ∑f_i = 120 , then mean, x is equal to
(a) 13
(b) 12.75
(c) 13.25
(d) 14.25

Answer: C

Question. The mean of first ten odd natural numbers is
(a) 5
(b) 10
(c) 20
(d) 19

Answer: B

Question. If the mean of first n natural numbers is 5n/9, then n is equal to
(a) 5
(b) 9
(c) 10
(d) 11

Answer: B

Question. If the mean of x, x + 3, x + 6, x + 9 and x + 12 is 10, then x equals
(a) 1
(b) 2
(c) 4
(d) 6

Answer: C

Question. Four observations are 2, 4, 6 and 8. The frequencies of the first three observations are 3, 2 and 1 respectively. If the mean of the observations is 4, then find the frequency of the fourth observation.
(a) 8
(b) 4
(c) 1
(d) 2

Answer: C

Question. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is ₹ 18. Find the missing frequency f.

(a) 18
(b) 20
(c) 22
(d) 19

Answer: B

Question. The mean of the following data is

(a) 20
(b) 24
(c) 22
(d) 25

Answer: D

Question. The mean of n observations x₁, x₂, x₃, ..., xn is x̄ . If each observation is multiplied by p, then the mean of the new observations is
(a) x̄/p
(b) p x̄
(c) x̄
(d) p + x̄

Answer: B

Question. The algebraic sum of all the deviations of all the observations from their mean is always
(a) 0
(b) +ve
(c) –ve
(d) equal to the number of observations.

Answer: A

Question. Consider the following frequency distribution.

The modal class is
(a) 10-20
(b) 20-30
(c) 30-40
(d) 40-50

Answer: C

Question. Life time of electric bulbs are given in the following frequency distribution.

Find the class mark of the modal class.
(a) 350
(b) 375
(c) 400
(d) 150

Answer: B

Question. The frequency of the class succeeding the modal class in the following frequency distribution is

(a) 3
(b) 6
(c) 9
(d) 12

Answer: D

Question. The modal class of data given below is 10–15, then

(a) f < 9
(b) f ≥ 9
(c) f > 9 only
(d) f < 3

Answer: B

Question. The mode for the following distribution is

(a) 36
(b) 35.5
(c) 36.25
(d) 35

Answer: C

Question. Consider the following table:

The mode of the above data is
(a) 23.5
(b) 24
(c) 24.4
(d) 25

Answer: C

Question. If the median of the data: 6, 7, x – 2, x, 17, 20 written in ascending order, is 16. Then x is equal to
(a) 15
(b) 16
(c) 17
(d) 18

Answer: C

Question. Find the class mark of the modal class in the following distribution.

(a) 45
(b) 55
(c) 65
(d) 63

Answer: C

Question. The median class for the following data is

(a) 20–40
(b) 40–60
(c) 60–80
(d) 80–100

Answer: C

Question. For a frequency distribution, mean, median and mode are connected by the relation
(a) Mode = 3 Mean – 2 Median
(b) Mode = 2 Median – 3 Mean
(c) Mode = 3 Median – 2 Mean
(d) Mode = 3 Median + 2 Mean

Answer: C

Question. The mean and mode of a frequency distribution are 28 and 16 respectively. The median is
(a) 22
(b) 23.5
(c) 24
(d) 24.5

Answer: C

Question. If mode of a series exceeds its mean by 12, then mode exceeds the median by
(a) 4
(b) 8
(c) 6
(d) 10

Answer: B

Question. The mean of 1, 2, 3, 4, ........, n is given by
(a) n(n +1)/2
(b) (n +1)/4
(c) n/2
(d) (n +1)/2

Answer: D

Question. The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is
(a) 60
(b) 100
(c) 10
(d) none of these

Answer: B

Question. Consider the following frequency distribution.

The upper limit of the median class is
(a) 14.5
(b) 14.5
(c) 28
(d) 28.5

Answer: D

Question. Extreme value of a given data
(a) affect the median
(b) do not affect the median
(c) nothing can be said
(d) none of the options

Answer: B

Question. One of the properties of mode is
(a) Not easy to calculate
(b) It is not affected by greatest and least values
(c) Algebraic
(d) Difference of greatest and least values

Answer: B

Question. The mean of n observations is x̄. If the first item is increased by 1, second by 2 and so on, then the new mean is
(a) x̄ + n
(b) x̄ n + 2
(c) x̄ + (n + 1/2)
(d) None of the options

Answer: C

Question. Look at the frequency distribution table given below.

The median of the above distribution is
(a) 56.5
(b) 57.5
(c) 58.5
(d) 59

Answer: B

Question. The mean, mode and median of the observations, 7, 7, 5, 7 and x are the same. Then the observation x is
(a) 10
(b) 9
(c) 8
(d) 7

Answer: B

Question. Mean of 20 observations is 15. If each observation is multiplied by 2/3, then the mean of new observations is
(a) 10
(b) 30
(c) 45
(d) 15

Answer: A

Question. The mean of six numbers : x – 5, x – 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.
(a) 11
(b) 12
(c) 13
(d) 14

Answer: B

Question. The numbers are arranged in the descending order : 108, 94, 88, 82, x + 7, x – 7, 60, 58, 42, 39. If the median is 73, the value of x is
(a) 72
(b) 73
(c) 76
(d) 75

Answer: B

Question. If the mean of the following distribution is 2.6, then the value of y is

(a) 3
(b) 8
(c) 13
(d) 24

Answer: B

Question. The mean of x₁, x₂,.......,x_n is M. If x_i, i = 1,2,......, n is replaced by 5xi, the mean becomes M₁, then M₁ is equal to
(a) 5M
(b) M + 5
(c) M + 100
(d) 10 M

Answer: A

Question. If mean of ten consecutive odd numbers is 120, then the mean of first five odd numbers among them is
(a) 113
(b) 115
(c) 114
(d) 116

Answer: B

Question. The numbers 3, 5, 7 and 9 have their respectively frequencies x – 2, x + 2, and x – 3, x + 3. If the mean is 6.5, then the value of x is
(a) 3
(b) 4
(c) 5
(d) 6

Answer: C

Short Answer Type Questions

Question. Write down less than type cumulative frequency and greater than type cumulative frequency.

Answer: We have