Question

The following table shows the daily wages of workers in a factory:

Daily wages (in Rs)	0-100	100-200	200-300	300-400	400-500
Number of workers	40	32	48	22	8

Find the median daily wage income of the workers.

Answer 1

Class	Frequency(f)	Cumulative frequency
0-100	40	40
100-200	32	72
200-300	48	120
300-400	22	142
400-500	8	150
	N=∑f=150

$$\begin{gathered} N=150 \\ \Rightarrow \frac{N}{2}=75 \\ \text{The cumulative frequency just greater than 75 is 120 and the corresponding class is 200-300.} \\ \text{Thus, the median class is 200-300.} \\ \therefore l=200,h=100,f=48,cf=\text{c}\text{.f}\text{. of preceding class=72 and}\frac{N}{2}=75 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ =200+\left\{100\times \frac{(75-72)}{48}\right\} \\ =200+6\text{.25} \\ =206\text{.25} \\ \text{Hence, the median daily wage income of the workers is Rs 206}\text{.25.} \end{gathered}$$