CBSE Class 10 Mathematics Statistics MCQs Set 05

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 \(d_i = x_i - 13\), \(\sum f_i d_i = 30\) and \(\sum f_i = 120\), then mean, \(\bar{x}\) 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 \(\frac{5n}{9}\), 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 \(f\).
Daily pocket allowance (in ₹): 11-13, 13-15, 15-17, 17-19, 19-21, 21-23, 23-25
Frequency:                             ​​​​​​​       ​​​​​​​7,        6,        9,        13,     \(f\),      5,        4
(a) 18
(b) 20
(c) 22
(d) 19
Answer: B

Question. The mean of the following data is
Class interval: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency:         3,       5,         9,        5,        3
(a) 20
(b) 24
(c) 22
(d) 25
Answer: D

Question. The mean of \(n\) observations \(x_1, x_2, x_3, ..., x_n\) is \(\bar{x}\). If each observation is multiplied by \(p\), then the mean of the new observations is
(a) \(\frac{\bar{x}}{p}\)
(b) \(p\bar{x}\)
(c) \(\bar{x}\)
(d) \(p + \bar{x}\)
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.
Class interval: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequency:        3,       9,       15,       30,       18,       5
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.
Life time (in hours): 250-300, 300-350, 350-400, 400-450, 450-500
Number of bulbs:           5,           14,          21,          12,          10
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
Class interval: 10–15, 15–20, 20–25, 25–30, 30–35, 35–40, 40–45
Frequency:          3,          7,        16,       12,       9,         5,         3
(a) 3
(b) 6
(c) 9
(d) 12
Answer: D

Question. The modal class of data given below is 10–15, then
Class interval: 0-5, 5-10, 10-15, 15-20, 20–25
Frequency:        8,    6,       \(f\),       4,       3
(a) \(f < 9\)
(b) \(f \ge 9\)
(c) \(f > 9\) only
(d) \(f < 3\)
Answer: B

Question. The mode for the following distribution is
Marks:                         0–10, 10–20, 20–30, 30–40, 40–50
Number of students:    6,       10,       12,       32,       20
(a) 36
(b) 35.5
(c) 36.25
(d) 35
Answer: C

Question. Consider the following table:
Class interval: 10-14, 14-18, 18-22, 22-26, 26-30
Frequency:         5,         11,      16,       25,     19
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.
Class interval: 40–50, 50–60, 60–70, 70–80, 80–90, 90–100
Frequency:         10,       25,       28,       12,       10,       15
(a) 45
(b) 55
(c) 65
(d) 63
Answer: C

Assertion & Reasoning Based MCQs

Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given.
Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : If for a certain frequency distribution, \(l = 24.5, h = 4, f_0 = 14, f_1 = 14, f_2 = 15\), then the value of mode is 25.
Reason : Mode of a frequency distribution is given by : \(Mode = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h\)
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: D

Question. Assertion : If the median and mode of a frequency distribution are 8.9 and 9.2 respectively, then its mean is 9.
Reason : Mean, median and mode of a frequency distribution are related as: \(mode = 3 median – 2 mean\)
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: D