Question

Find the median from the following table.

Marks scored	below 20	below 40	below 60	below 80	below 100
Number students	6	10	20	36	50

• A. $56$ marks
• B. $60$ marks
• C. $66$ marks
• D. $70$ marks

Answer 1

Answer: (C)

$66$ marks

Frequency distribution table:

$ci$	$f_i$	$cf$
$0-20$	$6$	$6$
$20-40$	$10-6=4$	$10$
$40-60$	$20-10=10$	$20$
$60-80$	$36-20=16$	$36$
$80-100$	$50-36=14$	$50$

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

Here,

Class Interval $c=20$

$N=\Sigma f_i=50$

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

$\Rightarrow$ Median class $=60-80$

$\Rightarrow$Frequency of median class$f_m=16$

Lower boundary of median class $l=60$

previous cumulative frequency of median class $cf=20$

$\therefore$ Median $=60+\frac{(\frac{50}{2}-20)}{16}\times 20$

$\therefore$ Median $=60+\frac{\left(5\right)}{16}\times 20$

$\therefore$ Median $=66.25\approx 66$

Hence. option $C$ is correct.