Question

Assertion (A): If the mean and median of a distribution are 169 and 170 respectively then its mode is 172.

Reason (R): The empirical relation between mean, median and mode is mode = 3 median – 2 mean.

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

Explanation:

Step 1 – Assertion: A is true. Substituting the given mean and median into the stated relation gives $$\text{mode} = 3\times 170 - 2 \times 169 = 510 - 338 = 172$$.

Step 2 – Reason: R is true. It states the empirical relation between the mean, median and mode.

Step 3 – Link: Applying R to the given mean and median yields the mode stated in A, so R correctly explains A.