Question

Calculate the median from the following data:

Marks:	0-10	10-30	30-60	60-80	80-90
No. of students:	5	15	30	8	2

Answer 1

Here, the class intervals are of unequal width. If the class intervals are of unequal width the frequencies need not be adjusted to make the class intervals equal.
Calculation of Median

Marks	No. of students (frequency)	Cumulative frequency
0-10	5	5
10-30	15	20
30-60	30	50
60-80	8	58
80-90	2	60
		$N=\sum f_i=60$

Here, $N=60\therefore N/2=30$
The cumulative frequency just greater than $N/2=30$ is $50$ and the corresponding class is $30-60$ . Hence, $30-60$ is the median class.
$\therefore l=30,f=30,F=20,h=30$
Now, Median $=l+\frac{\frac{N}{2}-F}{f}\times h$
$\Rightarrow Median=30+\frac{30-20}{30}\times 30=40$