Question

The following table gives the marks obtained by 50 students in a class test:

Marks	11-15	16-20	21-25	26-30	31-35	36-40	41-45	46-50
No. of students	2	3	6	7	14	12	4	2

Find the median.

Answer 1

First of all, we will convert the given data into exclusive form.

Class	Frequency(f)	Cumulative frequency
10.5-15.5	2	2
15.5-20.5	3	5
20.5-25.5	6	11
25.5-30.5	7	18
30.5-35.5	14	32
35.5-40.5	12	44
40.5-45.5	4	48
45.5-50.5	2	50
	N=∑f=50

$$\begin{gathered} N=50 \\ \Rightarrow \frac{N}{2}=25 \\ \text{The cumulative frequency just greater than 25 is 32 and the corresponding class is 30}\text{.5-35}\text{.5.} \\ \text{Thus, the median class is 30}\text{.5-35}\text{.5.} \\ \therefore l=30.5,h=5,f=14,cf=\text{c}\text{.f}\text{. of preceding class = 18 and}\frac{N}{2}=25 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ \text{=30}\text{.5+}\left\{5\times \frac{(25-18)}{14}\right\} \\ \text{=30}\text{.5+2}\text{.5} \\ \text{=33} \\ \text{Hence, median=33} \end{gathered}$$