Question

Assertion (A): If the mean of 6, 7, p, 8, q and 14 is 9 then p + q = 19.

Reason (R): $$\text{Mean} = \dfrac{\text{sum of observations}}{\text{number of observations}}.$$

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. Applying the mean formula gives $$\frac{6 + 7 + p + 8 + q + 14}{6} = 9$$, so $$35 + p + q = 54$$ and $$p + q = 19$$.

Step 2 – Reason: R is true. It states that the mean equals the sum of observations divided by the number of observations.

Step 3 – Link: The mean formula in R is used to obtain $$p + q = 19$$, so R correctly explains A.