Consider the following distribution of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.

Question :

Daily Wages in Rupees	0 – 120	120 – 140	14 – 160	160 – 180	180 – 200
Number of Workers	12	14	8	6	10

Solution :

Let the assumed mean A = 150 and class size h = 50

So, \(u_i\) = \(x_i – A\over h\) = \(x_i – 150\over 20\)

Class Interval	Mid-value (\(x_i\))	Frequency (\(f_i\))	\(u_i\) = \(x_i – 150\over 20\)	\(f_iu_i\)
100 – 120	110	12	-2	-24
120 – 140	130	14	-1	-14
140 – 160	150	8	0	0
160 – 180	170	8	1	6
180 – 200	190	10	2	20
Total		50		-12

So, \(\bar{x}\) = A + h\(\sum f_iu_i\over f_i\) = 150 + 20 \(\times\) \(-12\over 50\)

= 150 – 4.8 = 145.2

Hence, mean = 145.20