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If you added 10 to every number in a data set of positive numbers, this would...

If you added 10 to every number in a data set of positive numbers, this would not change the standard deviation.

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Answer #1

Solution:

A number 10 is added  to every number in a data set of positive numbers, this would not change the standard deviation.

This is true.

Since change of origin does not affect on standard deviation.

Let variable is X and we add number 10 in X. then new variable would be : Y = X + 10

thus

SD(Y) = SD(X + 10)

SD(Y) =SD(X) + SD(10)

Since 10 is a constant number and standard deviation of constant is always 0. that is: SD(10) = 0

thus

SD(Y) =SD(X) + 0

SD(Y) =SD(X)

Thus standard deviation does not change by adding or subtracting a constant number from variable.

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