Question

Find the median for the following data.

Marks	$11-15$	$16-20$	$21-25$	$26-30$	$31-35$	$36-40$
Frequency	$7$	$10$	$13$	$26$	$9$	$5$

Answer 1

Since the table is given in terms of inclusive type we convert it into exclusive type.

Marks	$f$	$cf$
$10.5-15.5$	$7$	$7$
$15.5-20.5$	$10$	$17$
$20.5-25.5$	$13$	$30$
$25.5-30.5$	$26$	$56$
$30.5-35.5$	$9$	$65$
$35.5-40.5$	$5$	$70$
	$N=70$

$N=70$, $\frac{N}{2}=\frac{70}{2}=35$
Median class is $25.5-30.5$
Lower limit of the median class $l=25.5$
Frequency of the median class $f=26$
Cumulative frequency of the preceding median class $m=30$
Width of the median class $c=30.5-25.5=5$
Median $=l+\frac{\frac{N}{2}-m}{f}\times c$
$=25.5+\frac{35-30}{26}\times 5=25.5+\frac{25}{26}=26.46$