Question

Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages (in Rs)	500­ − 520	520­ − 540	540 − 560	560 − 580	580 − 600
Number of workers	12	14	8	6	10

Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer 1

To find the class mark for each interval, the following relation is used.

Class size (h) of this data = 20

Taking 550 as assured mean (a), d_i, u_i, and f_iu_i can be calculated as follows.

Daily wages (in Rs)	Number of workers (fi)	xi	di = xi − 550		fiui
500­ − 520	12	510	− 40	− 2	− 24
520­ − 540	14	530	− 20	− 1	− 14
540 − 560	8	550	0	0	0
560 − 580	6	570	20	1	6
580 − 600	10	590	40	2	20
Total	50				− 12

From the table, it can be observed that

$$\begin{gathered} =550+\left(\frac{-12}{50}\right)20 \\ =550-\frac{24}{5} \\ =550-4.8 \\ =545.2 \end{gathered}$$

Therefore, the mean daily wage of the workers of the factory is Rs 545.20.