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 Rupees0 – 120 120 – 14014 – 160160 – 180180 – 200
Number of Workers12148610

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 IntervalMid-value (\(x_i\))Frequency (\(f_i\))\(u_i\) = \(x_i – 150\over 20\)\(f_iu_i\)
100 – 12011012-2-24
120 – 14013014-1-14
140 – 160150800
160 – 180170816
180 – 20019010220
Total50-12

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

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