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 (cf)
0 – 100	40	40
100 – 200	32	72
200 – 300	48	120
300 – 400	22	142
400 – 500	8	150
	N = Σ𝑓 = 150

Now, N = 150
`⇒ N/2` = 75.
The cumulative frequency just greater than 75 is 120 and the corresponding class is 200 – 300.
Thus, the median class is 200 – 300.
∴ l = 200, h = 100, f = 48, cf = c.f. of preceding class = 72 and `N/2` = 75.
Now,
Median, M = `l + {h×((N/2−cf)/f)}`
            `= 200 + {100 × ((75 − 72)/48)}`
             = 200 + 6.25
             = 206.25
Hence, the median daily wage income of the workers is Rs 206.25.