Question

Find the median of the following frequency distribution:

Class	0-100	100-200	200-300	300-400	400-500	500-600
Frequency	$64$	$62$	$84$	$72$	$66$	$52$

Answer 1

Here $n=400$. $\therefore$ $\frac{n}{2}=200$

Class	Frequency	Cumulative frequency($c.f.$)
0-100	64	64
100-200	62	64+62=126
200-300	84	126+84=210
300-400	72	210+72=282
400-500	66	282+66=348
500-600	52	348+52=400

Cumulative frequency greater than $200$ is $210$, corresponds to the class $200-300$.
Class $200-300$ is the median class
$l=200,\frac{n}{2}=200,cf=126,f=84$ and $c=100$
Substituting the values in

$M=l+\frac{(\frac{n}{2}-cf)}{f}\times c$
$=200+\frac{200-126}{84}\times 100$
$=200+\frac{74\times 100}{84}$
$=200+88.10$
$=288.10$