MCQ
Statement A (Assertion) : Consider the following frequency distribution:
Class interval0-44-88-1212-1616-20
Frequency6352010

The median class is 12-16.
Statement R (Reason): Let $n=\sum f_i$. Then, the class whose cumulative frequency is just lesser than $\left(\frac{n}{2}\right)$ is the median class.
  • Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
  • B
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion $(A)$ is true but reason $(R)$ is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.

Answer

Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
(a) : Clearly, Reason is correct. Now, the frequency distribution table from the given data can be drawn as :
Class intervalFrequency $\left(f_i\right)$$x_i$$f_i x_i$
0-105525
10-201815270
20-301525375
30-401635560
40-50645270
 $\sum f_i=60$ $\sum f_i x_i=1500$

$\therefore \quad$ Mean $=\frac{\Sigma f_i x_i}{\Sigma f_i}=\frac{1500}{60}=25$, which is true.
$\therefore \quad$ Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

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