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Question

Average of daily wage of 50 workers of a factory was Rs.200 with a standard deviation of Rs.40. Each worker is given a raise of Rs.20. What are the new average daily wage and standard deviation? Have the wages becomes more or less uniform?


Solution

N=50¯X=200σ=40Average wage=Total wagesNumber of workers200=Total wages50 

So, total wages = 200 × 50 = Rs  10,000

Now, increase in wage rate = Rs.20

Total raise = 50 × 20  = Rs 1,000

Total wage after raise = 10,000+1,000 = Rs 11,000

New Average wage=New Total wagesNumber of workers=11,00050=Rs220

Thus, mean increases by the amount of increase in wage of each worker as the absolute increase was equal for all.

Standard deviation will remain the same that is Rs. 40 as it is independent of origin and hence an addition of equal amount in all the value will not cause any chande in the standard deviation.

Uniformity of wages can be seen by coefficient of variation.

Previously, the coefficient of variation was:
CV=σx×100=40200×100=20

The new coefficient of variation after wage increases is given by :
CV=σx×100=40200×100=18.18

This shows that wages become more uniform now as the new CV is lower.

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