Useful Properties of Mean Variance Standard Deviation a Supp

Useful Properties of Mean, Variance, Standard Deviation (a) Suppose that a constant b is added to every value of a data set {x1,x2,x3,...,}, to produce a new data set {x1 + b, x2 +b, x3 + b,...xn +b}. Exactly how are the mean, variance, and standard deviation affected, and why?

Solution

4.

a)

The new mean will also increase by b.

However, the variance and standard deviation will stay the same.

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b)

The new mean will be the original multiplied by a.

The new standard deviation will be the original multiplied by |a|, as it is always positive.

The new variance will be the original multiplied by a^2.