Assertion (A) : Consider the following frequency distribution:" C… - Vidyadip

MCQ

Assertion $(A)$ : Consider the following frequency distribution:"

Class interval	$3-6$	$6-9$	$9-12$	$12-15$	$15-18$	$18-21$
Frequency	$2$	$5$	$21$	$23$	$10$	$12$

The mode of the above data is $12.4$.
Reason $(R)$ : The value of the variable which occurs most often is the mode.

A
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 a not a correct explanation of Assertion $(A)$.
C
Assertion $(A)$ is true and Reason $(R)$ is false.
D
Assertion $(A)$ is false and Reason $(R)$ is true

✓

Answer

Correct option: B.

Both Assertion $(A)$ and Reason $(R)$ are true but Reason $(R)$ is a not a correct explanation of Assertion $(A)$.

Reason $(R)$ is true.
Maxximum frequency $= 23$
Hence, modakl class is $12-15$
Now, mode $=\text{x}_\text{k}+\text{h}\Big\{\frac{(\text{f}_\text{k}-\text{f}_{\text{k}-1})}{(2\text{f}_\text{k}-\text{f}_{\text{k}-1}-\text{f}_{\text{k}+1})}\Big\}$
$=12+3\Big\{\frac{(23-21)}{(2(23)-21-10)}\Big\}$
$=12+3\times\frac{2}{15}$
$=12+0.4$
$=12.4$
Thus, Assertion $(A)$ and Reason $(R)$ are both true but Reason $(R)$ rs nor !he eereee explananoon of Assertion $(A)$.

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