Question

Assertion (A): For the following frequency distribution,

Class	Frequency
20–40	10
40–60	12
60–80	14
80–100	13
100–120	17

the median class is 60–80.

Reason (R): If the sum of frequencies in a continuous distribution is n then the class interval whose cumulative frequency is just greater than $$\dfrac{n}{2}$$ is called the median class.

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

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

Explanation:

Step 1 – Assertion: A is true. The total frequency is $$N = 66$$, so $$\frac{N}{2} = 33$$. The cumulative frequency just greater than 33 is 36, which corresponds to the class 60–80.

Step 2 – Reason: R is true. It gives the criterion for identifying the median class from the cumulative frequencies.

Step 3 – Link: Applying R to the given distribution identifies 60–80 as the median class, so R correctly explains A.