Why use the Standard Deviation instead of the Mean Absolute Deviation?
The square of the standard deviation is the Variance. The sample variance is a reasonable estimate of the population variance, regardless of the parent distribution. The same cannot be said for the Mean Absolute Deviation; that is, with the Mean Absolute Deviation, the divisor to be used (n or n-1 or whatever) depends upon the parent distribution whose Mean Absolute Deviation is being estimated.
