It seems to me that a lot the concepts in statistics are rather arbitrary and don't seem be mathematically derived. For example, how is the equation for standard deviation derived? The textbook says that the standard deviation is the mean of all of the deviations of the values in the sample and since all the deviations add up to zero, the values are sqaured to get rid of the negative. I understand that, but why doesn't it just take the absolute value? Why is the square-root taken only after everything has been summed? Furthermore, why is it divided by (n-1) and not n? Also, can anyone explain the proof for Chebychev's rule? Thanks very much.