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

MCQ

Statement $A ($Assertion$)$ : 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 $12.4 .$
Statement $R ($Reason$):$ 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 the correct explanation of assertion $(A)$.
✓
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: B.

Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A).$

Clearly, Reason is true.
The maximum frequency is $23$ and the modal class is $12-15.$
$\therefore l=12, f_1=23, f_0=21, f_2=10$ and $h=3$
$\therefore \text { Mode }=12+\left(\frac{23-21}{2 \times 23-21-10}\right) \times 3$
$=\left(12+3 \times \frac{2}{15}\right)$
$=12.4$
$\therefore$ Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Class	Class marks $\left(x_i\right)$	Frequency $\left(f_i\right)$	$f_i x_i$
$1-3$	$2$	$12$	$24$
$3-5$	$4$	$22$	$88$
$5-7$	$6$	$27$	$165$
$7-9$	$8$	$19$	$152$
		$\Sigma f_i=80$	$\Sigma f_i x_i=426$

$\therefore$ Mean $=\frac{\sum f_i x_i}{\sum f_i}=\frac{426}{80}=5.325$

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