Question

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

Daily wages (in Rs)	100­ − 120	120­ − 140	140 −1 60	160 − 180	180 − 200
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 150 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 − 15	ui = di/20	fiui
100­ −120	12	110	− 40	− 2	− 24
120­ − 140	14	130	− 20	− 1	− 14
140 − 160	8	150	0	0	0
160 −180	6	170	20	1	6
180 − 200	10	190	40	2	20
Total	50				-12

From the table, it can be observed that

`sum f_i = 50`

`sumf_iu_i = -12`

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

= 150+(-12/50)20

= 150 - 24/5

= 150 - 4.8

 = 145.2

Therefore, the mean daily wage of the workers of the factory is Rs 145.20