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Question

The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be


A

40

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B

45

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C

40+2125

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D

none of these

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Solution

The correct option is A

40


Let the numbers be xi. Then,
¯x=xi25
Let yi=xi+5. Then,
¯y=(xi+5)25=¯x+5(yi¯y)=(xi+5)(¯x+5)=xi¯xσ(y)=(yi¯y)2n=(xi¯x)2n=σ(x)


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