Question

The following frequency distribution showing the marks obtained by $100$ students in Maths. Find the median.

Marks	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$10$	$15$	$25$	$50$

• A. $40$
• B. $50$
• C. $60$
• D. $70$

Answer 1

The correct option is A $40$

Marks	Frequencies$\left(f\right)$	Cumulative frequency$\left(cf\right)$
$10-20$	$10$	$0$
$20-30$	$15$	$10+15=25$
$30-40$	$25$	$25+25=50$
$40-50$	$50$	$50+50=100$
	$n=\Sigma f=100$ $\frac{n}{2}=\frac{100}{2}=50$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$n=\Sigma f=$ Total number of frequency $=100$
$\frac{n}{2}=\frac{100}{2}=50$
So, the median class is $40-50$
$l=$ Lower limit of the median class $=40$

$cf$= Cumulative frequency of the class preceding the median class = $50$

$f=$ Frequency of the median class $=50$
$h=$ class width$=10$
Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=40+\left(\frac{\frac{100}{2}-50}{50}\right)\times 10$
$=40+\left(\frac{50-50}{50}\right)\times 10$
$=40+0$
$=40$
Hence, the median is $40$. (option $A$)