Variances and Standard Deviations
Name: Jack B.
Why are variances additive but not standard deviations?
From the definition, the variance is the square of differences of
measurements from the mean divided by the number of samples. These are
positive algebraic quantities and by the rules of algebra can be added. The
standard deviation is the square root of the variance and the laws of
algebra do not allow adding two square roots. That disobeys the order of
arithmetic operations rules.
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Update: June 2012