In the chapter on variability, on page 105, in "calculating average distances", we see that the average distance comes to 0. Right below that, in "there are no dumb questions" section we have the question, "Can't we just take the positive distances and average those?" The answer seems to be:

"We could, but that's not what statisticians do, there's another way."

I appreciate that squaring the difference eliminates the negative values, but so does taking the absolute value. There must be a better mathematical or logical reason why the RMS is better (other then the handy elimination of negative signs or "that's just the way it's done" by statisticians")

Is there an inherit reason? Or is the standard deviation just an arbitrary but "well known" description of variance, perhaps the way the Dow Jones is an arbitrary but well known economic status indicator?