# Why sum of squares to calculate dispersion [duplicate]

The variance gives an idea of the dispersion of a distribution. To calculate the variance the sum of the difference of each value with the mean, each of these differences squared, is required. The differences are squared to avoid the use of negative numbers. But....why? Absolute values of the differences would just do the job. By using the sum of squares larger numbers are given a disproportionate weight in the computation. As an example, if a difference between a value and the mean is 2, the square of the difference is 4, but if this difference is 3, is square is 9, so a difference of 1 is amplified to a difference in 5. Why is this done? Why not using absolute values?

• A more general measure of variability is commonly referred to as the "spread" of a distribution. A "dispersion" is actually an even more precise value in the context of regression modeling. Commented Aug 1 at 4:54
• Who said you can't use absolute values? Go for it. There's already quite a rich literature on such robust measures of spread. Commented Aug 1 at 4:57
• We have many variations on this question here at CV. IMO, the main difference is that minimizing the squared error will elicit the expectation, whereas minimizing the absolute error will elicit the median. This makes a difference for asymmetric distributions. Commented Aug 1 at 5:23
• Another almost identical existing question here. Commented Aug 1 at 6:10