The idea of why standard deviation is superior to
"average deviation" makes more sense if one looks at
plotting the "best fit" line to data points. If you
look at the 4 points below, most people will draw a
diagonal line right smack in between the points.
Asked why they think that is the best fit, they will
likely say it is the line that comes closest to all
the points. Put another way, they try to minimize
the y-distance from the points to the line, by getting
the lowest "average deviation" from the line.
(Points below look best in Courier:)
o
o o
o
But is that line the best? No, there are actually
an infinite # of lines that fit between those points--all with the SAME
average deviation from the
line! (Try it yourself with a ruler, changing the
slope of the line between the points.)
So, using average deviation, there is no "best
fit". However, if we use standard deviation from the line to the points
(Y-distances), there is only ONE
line that is the "best fit" (the least squares regression line): only
one with the lowest std. dev. from points to line.
So standard deviation gives you ONE best answer,
average deviation gives you no best answer.
Allen Shoemaker, Ph.D.
Calvin College
