Statement A (Assertion) : Consider the following frequency distri… - Vidyadip

MCQ

Statement A (Assertion) : Consider the following frequency distribution:

Class interval	0-4	4-8	8-12	12-16	16-20
Frequency	6	3	5	20	10

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.

A
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).
✓
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

Correct option: C.

Assertion $(A)$ is true but reason $(R)$ is false.

(c) : We know that, if $n=\Sigma f i$, then the class whose cumulative frequency is just greater than $\left(\frac{n}{2}\right)$ is the median class. So, Reason is false.
The cumulative frequency distribution table from the given data can be drawn as :

Class interval	Frequency	Cumalative frequency
0-4	6	6
4-8	3	9
8-12	5	14
12-16	20	34
16-20	10	44

Here, $n=44 \Rightarrow \frac{n}{2}=22$. So, the class whose cumulative frequency is just greater than 22 is 34 , which lies in the interval 12 - 16.
So, the median class is 12-16.
$\therefore$ Assertion is true but Reason is false.

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