Question

Assertion (A): In the following frequency distribution,

Height (in cm)	Number of students
110–115	15
115–130	13
130–145	11
145–160	10
160–175	11

the sum of the lower limit of the modal class and the upper limit of the median class is 240.

Reason (R): The median class of the given frequency distribution is 130–145.

विकल्प

• 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

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

Explanation:

Step 1 – Assertion: A is false. The modal class is 110–115, whose lower limit is 110. The upper limit of the median class is 145, so their sum is $$110 + 145 = 255$$, not 240.

Step 2 – Reason: R is true. The total frequency is $$N = 60$$, so $$\frac{N}{2} = 30$$. The cumulative frequency just greater than 30 is 39, corresponding to the class 130–145.