After settlement, the average weekly wage in a factory had increased from Rs. 8 to 12 and standard deviation had increased from Rs. 1 to 1.5. The wages have become higher and more uniform, after settlement.
Answers
According to the statement it is understood that the average weekly wages have increased from Rs.8 to Rs.12 i.e.,the total wages received per week by all the workers have increased. Therefore, after the settlement the weekly wage increased. In order to measure uniformity of the wages, the coefficient of the variation of the wages of the workers before and after the settlement has to be calculated , which is :
Coefficient of dispersion Before settlement = 1/8×100=12.5%
Coefficient of dispersion After settlement = 1.5/12×100 =12.5%
Since, there is no change in the variability of the wages. Thus, the statement is not correct.
Given : After settlement, the average weekly wage in a factory had increased from Rs. 8 to 12 and standard deviation had increased from Rs. 1 to 1.5.
To find : Authenticity of statement : wages have become higher and more uniform, after settlement.
Solution:
Coefficient of Variation = (Standard deviation /Mean) * 100 %
Earlier Average weekly wages = 8
Mean = 8
Standard Deviation = 1
Coefficient of Variation = (1/8)*100 = 12.5 %
After settlement, Average weekly wages = 12
Mean = 12
Standard Deviation = 1.5
Coefficient of Variation = (1.5/12)*100 = 12.5 %
12 > 8
Hence wages have become higher is Correct
Coefficient of Variation is same
hence no impact on uniformity
wages have become more uniform is not correct
wages have become higher is Correct but more uniform is not correct
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