Question

Compute the median from the following data:

Marks	0-7	7-14	14-21	21-28	28-35	35-42	42-49
Number of students	3	4	7	11	0	16	9

Answer 1

Class	Frequency (f)	Cumulative frequency
0-7	3	3
7-14	4	7
14-21	7	14
21-28	11	25
28-35	0	25
35-42	16	41
42-49	9	50
	N=∑f=50

$$\begin{gathered} \begin{array}{l}N=50\\ \Rightarrow \frac{N}{2}=25\\ \text{The cumulative frequency just greater than 25 is 41 and the corresponding class is 35-42.}\\ \\ \text{Thus, the median class is 35-42.}\\ \therefore l=35,h=7,f=16,cf=\text{c}\text{.f}\text{. of preceding class = 25 and}\frac{N}{2}=25\end{array} \\ \therefore \mathrm{Median}=l+\frac{{\displaystyle \frac{N}{2}}-c.f}{f}\times h \\ \begin{array}{l}\text{=35+}\left\{7\times \frac{(25-25)}{16}\right\}\\ \text{=35+0}\\ \text{=35}\\ \end{array} \end{gathered}$$