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Question -

If in the previous question, each worker is given a hike of 10% in wages, how are the Mean and Standard Deviation values affected?



Answer -

Average wage = ₹ 200
Hike in wages = 10%
Since arithmetic mean is not independent of scale, the mean will also increase by 10%.
Hence, the new Mean will be
200 + 20 = ₹ 220
Standard Deviation is also not independent of scale, hence, the Standard Deviation will also increase by 10% Initial Standard Deviation = ₹ 40
So, New Standard Deviation = ₹40 +10% of 40
= ₹ (40 + 4)
= ₹ 44

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