Question

For the following distribution : Class: $0-05,5-10,10-15,15-20,20-25$ Frequency :$10,15,12,20,9$ the sum of lower limits of the median class and modal class is

• A. $15$
• B. $25$
• C. $30$
• D. $35$

Answer 1

The correct option is B

$25$

Step 1: Create the table

Class	Frequency	Cumulative Frequency
$0-5$	$10$	$10$
$5-10$	$15$	$25$
$10-15$	$12$	$37$
$15-20$	$20$	$57$
$20-25$	$9$	$66$

Step 2: Calculate lower limit of median

From the table, we can see that the total count is $n=66$.

Therefore, median

$N=\frac{n}{2}$

$=\frac{66}{2}$

$=33$

This lies in the interval $10-15$.

Therefore, the lower limit of the median class is $10$.

Step 3: Calculate lower limit of mode

The highest frequency is $20$.

This lies in between the interval $15-20$.

Hence, the lower limit of the modal class is $15$.

Step 4: Total of the limits

$\therefore$the sum of lower limits of the median class and modal class $=10+15$

$=25$

Hence, option $\left(B\right)$ is the correct answer.