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

Daily wages (in Rs.) 100-120 120-140 140-160 160-180 180-200
Number of workers 12 14 8 6 10

Solution

To determinet the Class Mark (xi) we will use the formula mentioned below

Class Mark = (Upper class Limit + Lower Class Limit)/2

In this case, the value of mid-point (xi) is very large, so let us assume the mean value,

A = 150

the class interval is h = 20.

ui = (xi – A)/h 

=> u= (xi – 150)/20

Daily wages (Class interval) Number of workers frequency (fi) Mid-point (xi) u= (xi – 150)/20 fiui
100-120 12 110 -2 -24
120-140 14 130 -1 -14
140-160 8 150 0 0
160-180 6 170 1 6
180-200 10 190 2 20
Total Sum f= 50 Sum fiui = -12

Formula

The formula to find out the mean is:

Mean = x̄ = A + h∑fiui /∑f

= 150 + (20 × -12/50) 

= 150 – 4.8

= 145.20

Thus, mean daily wage of the workers = Rs. 145.20.

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