Timeline for Why square the difference instead of taking the absolute value in standard deviation?
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| Oct 21, 2014 at 23:46 | comment | added | Nick Cox | I like these ideas too, but there's a less well known parallel definition of the variance (and thus the SD) that makes no reference to means as location parameters. The variance is half the mean square over all the pairwise differences between values, just as the Gini mean difference is based on the absolute values of all the pairwise difference. | |
| May 14, 2014 at 17:06 | comment | added | Thomas Speidel | Just to add to @Frank's suggestion on Gini, there's a nice paper here: projecteuclid.org/download/pdf_1/euclid.ss/1028905831 It goes over various measures of dispersion and also give an informative historical perspective. | |
| May 14, 2014 at 12:55 | history | answered | Frank Harrell | CC BY-SA 3.0 |