Maths · Statistics and probability · chapter 13 of 14

Class 11 Maths Chapter 13: Statistics Assertion-reason questions with answers

2 assertion-reason 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. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): The standard deviation of 15, 15, 15, 15, 15 is 0. Reason (R): The standard deviation is the positive square root of the mean of the squares of the deviations from the mean.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Here x̄ = 15 and every deviation is 0, so the mean of the squared deviations is 0 and its square root is 0. R is the definition that gives A.

Question 2
Assertion (A): The range of 7, 2, 19, 11 is 17. Reason (R): The sum of the deviations of a set of observations from their mean is zero.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A: 19 − 2 = 17, true. R is true for every data set, but the range uses only the maximum and minimum and has nothing to do with deviations from the mean.

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