Question

Assertion (A): If the classes of a frequency distribution are 1–9, 10–18, 19–27, ..., etc., then the class size is 9.

Reason (R): The frequency of each class interval is centred around its midpoint.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. In the continuous form, the first class becomes $$0.5\text{ – }9.5$$, so its size is $$9.5 - 0.5 = 9$$.

Step 2 – Reason: R is true. The class mark is the midpoint of a class interval, around which the class frequency is represented.

Step 3 – Link: The midpoint statement does not establish the class width; the width is found from the class boundaries. Thus, R does not explain A.