Maths · Statistics and probability · chapter 13 of 14

Class 11 Maths Chapter 13: Statistics MCQs with answers

10 multiple-choice questions on Statistics, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
The minimum temperatures (in °C) recorded at Shimla on six days were 12, 9, 15, 7, 18 and 11. The range of the data is
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Answer: (b) 11 °C

Range = maximum value − minimum value = 18 − 7 = 11 °C.

Question 2
Which of the following is not a measure of dispersion?
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Answer: (d) median

Range, mean deviation and standard deviation measure scatter; the median is a measure of central tendency.

Question 3
The sum of the deviations of the observations 3, 8, 10 and 15 from their mean is
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Answer: (a) 0

The mean is 36/4 = 9; the deviations are −6, −1, 1, 6, and their sum is 0, as it is for every data about its mean.

Question 4
The mean deviation of 4, 8, 12, 16, 20 about the number 10 is
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Answer: (c) 5.2

The absolute deviations from 10 are 6, 2, 2, 6, 10; their sum is 26, and M.D.(10) = 26/5 = 5.2.

Question 5
The five observations 2, 5, 7, 9 and k have mean 7. Their mean deviation about the mean is
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Answer: (b) 2.8

2 + 5 + 7 + 9 + k = 35 gives k = 12. The absolute deviations from 7 are 5, 2, 0, 2, 5, sum 14; M.D.(x̄) = 14/5 = 2.8. Leaving k out and dividing 9 by 4 gives 2.25; 0 is the mean of the signed deviations.

Question 6
The mean deviation about the median of the six observations 11, 3, 8, 15, 6, 20 is (correct to two decimal places)
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Answer: (a) 4.83

In order: 3, 6, 8, 11, 15, 20. n is even, so M = (8 + 11)/2 = 9.5. The absolute deviations are 6.5, 3.5, 1.5, 1.5, 5.5, 10.5, sum 29; M.D.(M) = 29/6 = 4.83. Dividing by 5 gives the slip 5.80.

Question 7
The variance of the observations 1, 3, 5, 7, 9 is
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Answer: (c) 8

x̄ = 25/5 = 5; the squared deviations are 16, 4, 0, 4, 16, sum 40; σ² = 40/5 = 8. (2√2 is the standard deviation; 40 is the sum, not the mean, of the squares.)

Question 8
The variance of a data set is 6.25. Its standard deviation is
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Answer: (d) 2.5

The standard deviation is the positive square root of the variance: √6.25 = 2.5.

Question 9
The variance of a set of observations is 16. If each observation is halved, the standard deviation of the new observations is
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Answer: (b) 2

Multiplying each observation by k = 1/2 multiplies the variance by k² = 1/4: new variance 4, so the new standard deviation is √4 = 2.

Question 10
A data set has mean 12 and variance 9. If 7 is added to each observation, the new mean and the new variance are
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Answer: (c) 19 and 9

Adding a number to each observation shifts the mean by that number (12 + 7 = 19) and leaves the variance unchanged (9).

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