Question

Calculate the median for the following data:

Age (in years)	19-25	26-32	33-39	40-46	47-53	54-60
Frequency	35	96	68	102	35	4

Answer 1

First, we will convert the data into exclusive form.

Class	Frequency(f)	Cumulative frequency
18.5-25.5	35	35
25.5-32.5	96	131
32.5-39.5	68	199
39.5-46.5	102	301
46.5-53.5	35	336
53.5-60.5	4	340
	N=∑f=340

$$\begin{gathered} N=340 \\ =>\frac{N}{2}=170 \\ \text{The cumulative frequency just greater than 170 is 199 and the corresponding class is 32}\text{.5-39}\text{.5.} \\ \text{Thus, the median class is 32}\text{.5-39}\text{.5.} \\ \therefore l=32.5,h=7,f=68,cf=\text{c}\text{.f}\text{. of preceding class = 131 and}\frac{N}{2}=170 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ \text{= 32}\text{.5+}\left\{7\times \frac{(170-131)}{68}\right\} \\ \text{= 32}\text{.5+4}\text{.01} \\ \text{= 36}\text{.51} \\ \text{Hence, median = 36}\text{.51} \end{gathered}$$