Question

The distribution below gives the weight of $30$ students in a class. Find the median weight of students:

Weight (in kg)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$
No. of students	$2$	$3$	$8$	$6$	$6$	$3$	$2$

Answer 1

Weight ( in kg )	Frequency	Cumulative frequency
$40-45$	$2$	$2$
$45-50$	$3$	$5$
$50-55$	$8$	$13$
$55-60$	$6$	$19$
$60-65$	$6$	$25$
$65-70$	$3$	$28$
$70-75$	$2$	$30$
	$N=30$

We have $N=30$ and $\frac{N}{2}=15$.

Median class $=55-60$, so $l=55,f=6,cf=13$ and $h=60-55=5$

$Median=l+\frac{\frac{N}{2}-cf}{f}\times h$

$\Rightarrow$ $Median=55+\frac{15-13}{6}\times 5$

$\Rightarrow$ $Median=55+1.67=56.67kg$