Question

Find the median of the following data:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	Total
Frequency	$8$	$16$	$36$	$34$	$6$	$100$

Answer 1

To find the median let us put the data in the table given below:

Class interval	Frequency (fi)	Cumulative frequency (cf)
$0-10$	$8$	$8$
$10-20$	$16$	$24$
$20-30$	$36$	$60$
$30-40$	$34$	$94$
$40-50$	$6$	$100$
Total	$N=\sum f_i=100$

Now,

$N=100$

$\Rightarrow \frac{N}{2}=50.$

The cumulative frequency just greater than $50$ is $60,$ and the corresponding class is $20-30.$

Thus, the median class is $20-30$.

$\therefore l=20,h=10,N=100,f=36$ and $cf=24.$

Now,

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

$=20+\frac{50-24}{36}\times 10$

$=20+\frac{260}{36}$

$=27.22$

Thus, the median is $\mathrm{27.22.}$