Question

The marks obtained by 68 students in an examination are given below. Compute the median.

Marks	Below 20	20-40	40-60	60-80	Above 80
No of students	0	5	22	25	16

Answer 1

Marks	Students (f)	c.f
Below 20	0	0
20 – 40	5	5
40 – 60	22	27
60 –80	25	52
Above 80	16	68

Median class is given by the size of the ${\left(\frac{N}{2}\right)}^{\mathrm{th}}$ item, i.e. the ${\left(\frac{68}{2}\right)}^{\mathrm{th}}$ item, which is the 34^th item. This corresponds to the class interval 60−80, so this is the median class.

$$\begin{gathered} \mathrm{Median}=l_1+\frac{\left({\displaystyle \frac{N}{2}}\right)-c.f}{f}\times i \\ =60+\frac{34-27}{25}\times 20 \\ =60+\frac{140}{25} \\ =60+5.6 \\ =65.6 \end{gathered}$$

Thus, median is 65.6.