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Question

# The standard deviation of a given set of data is 20. If each of the value in the data is increased by 3, then the new standard deviation is .

A
17
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B
23
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C
20
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D
20+3
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Solution

## The correct option is C 20When each of the value is increased by 3and if the old values are x1,x2,....,xn,then new data becomes x1+3,,...,xn+3New mean =(x1+3)+.....+(xn+3)n=x1+...+xnn+3×nn=old mean + 3But (Mean−xi) remains the same .Thus variance=∑(Mean−x1)2n remains the same.Hence SD=√variance remains the same.

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