Question

The following table gives the marks obtained by 50 students in a class test :

Marks	No. of students
11-15	2
16-20	3
21-25	6
26-30	7
31-35	14
36-40	12
41-45	4
46-50	2

Find the median

Answer 1

$ci$	$f_i$	$cf$
$10.5-15.5$	$2$	$2$
$15.5-20.5$	$3$	$2+3=5$
$20.5-25.5$	$6$	$5+6=11$
$25.5-30.5$	$7$	$11+7=18$
$30.5-35.5$	$14$	$18+14=32$
$35.5-40.5$	$12$	$32+12=44$
$40.5-45.5$	$4$	$44+4=48$
$45.5-50.5$	$2$	$48+2=50$

Median $=l+\frac{(\frac{N}{2}-cf)}{f_m}\times c$

Here,

Class Interval $c=5$

$N=\Sigma f_i=50$

$\frac{N}{2}=25$

$\Rightarrow$ Median class $=30.5-35.5$

$\Rightarrow$Frequency of median class$f_m=14$

Lower boundary of median class $l=30.5$

previous cumulative frequency of median class $cf=18$

$\therefore$ Median $=30.5+\frac{(\frac{50}{2}-18)}{14}\times 5$

$\therefore$ Median $=30.5+\frac{\left(7\right)}{14}\times 5$

$\therefore$ Median $=33$