Maths · Statistics and probability · chapter 13 of 14

Class 10 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. 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): For classes written 50-59, 60-69, 70-79, rewriting them as 49.5-59.5, 59.5-69.5, 69.5-79.5 does not change the mean of the data. Reason (R): Closing the gaps between the classes leaves every class mark unchanged.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Both are true: 50-59 and 49.5-59.5 both have class mark 54.5. The mean uses only the class marks and frequencies, so an unchanged class mark is exactly why the mean is unchanged.

Question 2
Assertion (A): Two students find the mean of the same grouped data by the assumed mean method, one taking a = 35 and the other a = 45. They get the same mean. Reason (R): The class mark of a class is the average of its upper and lower limits.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A is true: the mean does not depend on the choice of a. R is true as a definition, but it does not explain why the choice of a does not matter.

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