Question

Find the median from the following data:

Class	1-5	6-10	11-15	16-20	21-25	26-30	31-35	35-40	41-45
Frequency	7	10	16	32	24	16	11	5	2

Answer 1

Converting into exclusive form, we get:

Class	Frequency(f)	Cumulative frequency
0.5-5.5	7	7
5.5-10.5	10	17
10.5-15.5	16	33
15.5-20.5	32	65
20.5-25.5	24	89
25.5-30.5	16	105
30.5-35.5	11	116
35.5-40.5	5	121
40.5-45.5	2	123
	N=∑f=123

$$\begin{gathered} N=123 \\ \Rightarrow \frac{N}{2}=61.5 \\ \text{The cumulative frequency just greater than 61}\text{.5 is 65 and the corresponding class is 15}\text{.5-20}\text{.5.} \\ \text{Thus, the median class is 15}\text{.5-20}\text{.5.} \\ \therefore l=15.5,h=5,f=32,cf=\text{c}\text{.f}\text{. of preceding class = 33 and}\frac{N}{2}=61.5 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ \text{=15}\text{.5+}\left\{5\times \frac{(61.5-33)}{32}\right\} \\ \text{=15}\text{.5+4}\text{.45} \\ \text{=19}\text{.95} \\ \text{Hence, median=19}\text{.95} \end{gathered}$$