Question

Assertion (A): The median of the first eight prime number is 9.

Reason (R): For a data having n observations, if n is odd then the median is the $$\left(\dfrac{n + 1}{2}\right)\text{th}$$ observation.

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. The first eight primes are 2, 3, 5, 7, 11, 13, 17 and 19. Since there are an even number of observations, the median is $$\frac{7 + 11}{2} = 9$$.

Step 2 – Reason: R is true. It correctly states the median rule for an odd number of observations.

Step 3 – Link: There are eight observations, so the even-number median rule is needed; R gives the rule for odd numbers and therefore does not explain A.