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