Linda -
It looks as though a couple of people responded, but missed the point that
you already knew that the deviations themselves add to zero (I assume that's
why you indicated that it's the absolute value of the deviations your
student proposed using instead). Here's my understanding - mostly
assumptions on my part...
The average absolute deviation is a perfectly good descriptive statistic.
Were that all we needed, that's likely what we'd use. However, as I'm sure
you know, the standard deviation (and not the average deviation) appears in
most of the inferential methods involving means. We use the SD as our
descriptive statistic simply because there's no point in learning two
separate equally useful descriptive statistics, and the SD is the one we're
going to wind up using for other purposes anyway.
Paul Smith
Alverno College
Milwaukee
