Question

Assertion: Median of 51, 70, 65, 82, 60, 68, 62, 95, 55, 64, 58, 75, 80, 85, 90 is 68.
Reason: When n observations are arranged in an ascending order and n is odd, then $\mathrm{median}=\mathrm{value}\mathrm{of}\frac{1}{2}(n+1)$th observation.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

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

Assertion:

We will arrange the numbers in ascending order as:
51, 55, 58, 60, 62, 64, 65, 68, 70, 75, 80, 82, 85, 90, 95

$$\begin{gathered} \mathrm{Here},\mathit{}n\mathrm{is}15,\mathrm{which}\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{number}. \\ \mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{\mathrm{n}+1}{2}\right)\mathrm{th}\mathrm{observation} \\ =\mathrm{Value}\mathrm{of}8\mathrm{th}\mathrm{observation} \\ =68 \\ \mathrm{This}\mathrm{means}\mathrm{that}\mathrm{Assertion}\mathrm{is}\mathrm{correct}. \end{gathered}$$

Reason is true. It is also the correct explanation of Assertion.