Question

Find the median from the following data:

Marks	No. of students
Below 10	12
Below 20	32
Below 30	57
Below 40	80
Below 50	92
Below 60	116
Below 70	164
Below 80	200

Answer 1

Class	Cumulative frequency	Frequency (f)
0-10	12	12
10-20	32	20
20-30	57	25
30-40	80	23
40-50	92	12
50-60	116	24
60-70	164	48
70-80	200	36
		N=∑f=200

$\begin{array}{l}N=200\\ \Rightarrow \frac{N}{2}=100\\ \text{The cumulative frequency just greater than 100 is 116 and}\mathrm{the\; corresponding\; class\; is\; 50-60}.\\ \\ \text{Thus, the median class is 50-60.}\\ \therefore l=50,h=10,f=24,cf=\text{c}\text{.f}\text{. of preceding class = 92 and}\frac{N}{2}=100\\ \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\}\\ \text{= 50 +}\left\{10\times \frac{(100-92)}{24}\right\}\\ \text{= 50 + 3.33}\\ \text{= 53.33}\\ \text{Hence, median = 53.33}\end{array}$