Question

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

Daily wages (in Rs:)	100 - 120	120 - 140	140 - 160	160 - 180	180 - 200
Numbers 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

Let the assumed mean (A) = 150

Class interval	Mid value (xi)	di = xi -150	ui= \(\frac{xi-150}{20}\)	Frequency (fi)	fiui
100 - 120	110	-40	-2	12	-24
120 - 140	130	-20	-1	14	-14
140 - 160	150	0	0	8	0
160 - 180	170	20	1	6	6
180 - 200	190	40	2	10	20
				N = 50	\(\sum\)fiui = - 12

We have, 

A = 150

h = 20

Mean = A + h \(\times\frac{\sum f_iu_i}{N}\)

\(=150+20\times\frac{-12}{50}\)

\(=150\,-\frac{24}{5}=150-4.8\)

\(=145.2\)