Question

Assertion: Median of the given data $34,31,42,43,46,25,39,45,32$, is $39$.
Reason: When the number of observations $\left(n\right)$ is even, then median is the mean of the ${\left(\frac{n}{2}\right)}^{th}$ and ${(\frac{n}{2}+1)}^{th}$ observations.
Which of the following is correct?

• A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation for the Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B

Both Assertion and Reason are correct, but Reason is not the correct explanation for the Assertion

There are 9 observations and the ordered data is 25, 31, 32, 34, 39, 42, 43, 45, 46.

When the number of observations $n$ is odd the median is the $(\frac{n+1}{2}{)}^{th}$ observation.

Here, $n=9$ $\therefore$ the observation at the 5th position is 39.

The reason is not the correct explanation for the Assertion as the number of observations (n) is odd and not even.