Question

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

Daily wages (in ₹)	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.

x_i = `("Upper class limits + Lower class limits")/2`

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	ui = `d_i/20`	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	∑fi = 50	-	-		-12

From the table, it can be observed that

∑f_i = 50

∑f_iu_i = −12

Mean, `barx = a+((∑f_i"u"_i)/(∑f_i))h`

`= 550+((-12)/50)20`

`= 550 - 24/5`

= 550 - 4.8

 = 545.20 

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