Lots of good reasons posted to use the s.d. instead of the s.d.,
but here's an effect of squaring the errors that students seem to
appreciate intuitively: it's a way of inflating the big errors while
leaving the little ones relatively unchanged -- 1^2=1, 2^2=4, etc.
(If want to tell your students that taking the square root "undoes"
the effect, I suppose you have a problem, but this is at least true
for the variance.)
Another way to go is to show that the mean minimizes the total
squared error, not the total absolute error. (This isn't so intutive,
and comes as quite a surprise to many students.)
-David
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David G. Likely, Department of Psychology,
University of New Brunswick
Fredericton, N. B., E3B 5A3 Canada
History of Psychology:
http://www.unb.ca/web/psychology/likely/psyc4053.htm
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