Question

Calculate the median from the following distribution

Class	5-10	10-15	15-20	20-25	25-30
Frequency	4	7	10	9	4

Answer 1

Class	Frequency	Cumulative Frequency
5-10	4
10-15	7	11
15-20	10	21 $\text{(Median Class)}$
20-25	9	30
25-30	4	34
	34

$N=34,\frac{N}{2}=17$
The cumulative frequency greater than $17$ is $21$ and corresponding class is $15-20$
Thus, $15-20$ is the median class, such that
$l=15,\frac{N}{2}=17,c\overline{f}=11,f=10,h=5$
Using,
$Median=l+\left(\frac{\frac{N}{2}-c\overline{f}}{f}\right)\times h=15+\left(\frac{17-11}{10}\right)\times 5=15+\frac{6\times 5}{10}$
$Median=18$