Question

From the following data, compute median:

Marks	0−10	10−20	20−40	40−60	60−80	80−100
No. of Students	8	10	22	25	10	5

Answer 1

Class Interval	Frequency (f)	Cumulative Frequency (c.f.)
0 − 10 10 − 20	8 10	8 18 (c.f.)
20 − 40	22 (f)	40
40 − 60 60 − 80 80 − 100	25 10 5	65 75 80
	N = ∑f =80

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{\mathrm{th}}$ item, i.e.${\left(\frac{80}{2}\right)}^{\mathrm{th}}$ item, which is 40^th item.
This corresponds to the class interval of (20 − 40), so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=20+\frac{{\displaystyle \frac{80}{2}}-18}{22}\times 20 \\ \mathrm{or},\mathrm{Median}=20+\frac{22}{22}\times 20 \\ \mathrm{or},\mathrm{Median}=20+20=40 \\ \mathrm{Thus},\mathrm{Median}=40 \end{gathered}$$