Question

Find the median of the following distribution$:$

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Number of students	$12$	$35$	$45$	$25$	$13$

• A. $23$
• B. $22$
• C. $24$
• D. $21$

Answer 1

The correct option is C $24$

Marks	Students(f)	Cumulative frequency(cf)
$10-20$	$12$	$12$
$20-30$	$35$	$12+35=47$
$30-40$	$45$	$47+45=92$
$40-50$	$25$	$92+25=117$
$50-60$	$13$	$117+13=130$
	$n=\Sigma f=130$ $\frac{n}{2}=\frac{130}{2}=65$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$n=\Sigma f=$ Total number of frequency $=130$
$\frac{n}{2}=\frac{20}{2}=65$
So, the median class is $30-40$
L$=$ Lower limit of the median class $=30$
cf$=$ Cumulative frequency of the class preceding the median class $=92$
f$=$ Frequency of the median class $=45$
h$=$ class width$=10$
Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=30+\left(\frac{\frac{130}{2}-92}{45}\right)\times 10$
$=30+\left(\frac{65-92}{45}\right)\times 10$
$=30-6$
$=24$
Hence, the median is $24$.