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Question:
Why are variances additive but not standard deviations?



Replies:
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.

Vince Calder



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