Question

Calculate the median for the following frequency distribution:

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	3	6	8	15	10	8

Answer 1

Class	Frequency (f)	Cumulative frequency
0-10	3	3
10-20	6	9
20-30	8	17
30-40	15	32
40-50	10	42
50-60	8	50
	N = ∑f = 50

$$\begin{gathered} N=50 \\ =>\frac{N}{2}=25 \\ \text{The cumulative frequency just greater than 25 is 32 and the corresponding class is 30-40.} \\ \text{Thus, the median class is 30-40.} \\ \therefore l=30,h=10,f=15,cf=\text{c}\text{.f}\text{. of preceding class = 17 and}\frac{N}{2}=25 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ =30+\left\{10\times \frac{(25-17)}{15}\right\} \\ =30+\frac{16}{3} \\ =35\text{.33} \\ \text{Hence, median=35}\text{.33} \end{gathered}$$