Question

Find out median marks of the following marks distribution for 100 students.

Marks	0−10	10−20	20−30	30−40	40−50
Number of Students	8	30	40	12	10

Answer 1

Marks	No. of students	Cumulative frequency
0 − 10 10 − 20	8 30	8 8 + 30 = 38 (c.f.)
20 − 30	40 (f)	38 + 40 = 78
30 − 40 40 − 50	12 10	78 + 12 = 90 90 + 10 = 100
	N = 100

Median or M = Size of ${\left(\frac{N}{2}\right)}^{\mathrm{th}}$ item
or, M = Size of ${\left(\frac{100}{2}\right)}^{\mathrm{th}}$ item
or, M = Size of 50^th item

Hence, median lies in the class 20-30
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f}{f}\times i \\ \mathrm{or},\mathrm{M}=20+\frac{50-38}{40}\times 10 \\ \mathrm{or},\mathrm{M}=20+\frac{120}{40} \\ \mathrm{or},\mathrm{M}=20+3 \\ \Rightarrow \mathrm{M}=23marks \end{gathered}$$

Hence, the median marks is 23.