Question

Calculate the median from the following frequency distribution:

Class	5-10	10-15	15-20	20-25	20-30	30-35	35-40	40-45
Frequency	5	6	15	10	5	4	2	2

Answer 1

Class	Frequency(f)	Cumulative frequency
5-10	5	5
10-15	6	11
15-20	15	26
20-25	10	36
25-30	5	41
30-35	4	45
35-40	2	47
40-45	2	49
	N=∑f=49

$$\begin{gathered} N=49 \\ \Rightarrow \frac{N}{2}=24.5 \\ \text{The cumulative frequency just greater than 24}\text{.5 is 26 and the corresponding class is 15-20.} \\ \text{Thus, the median class is 15-20.} \\ \mathrm{Now},l=15,h=5,f=15,cf=\text{c}\text{.f}\text{. of preceding class = 11 and}\frac{N}{2}=24.5 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ \text{=15+}\left\{5\times \frac{(24.5-11)}{15}\right\} \\ \text{=15+4}\text{.5} \\ \text{=19}\text{.5} \\ \text{Hence, median=19}\text{.5} \end{gathered}$$