Why is standard deviation better than deviation about arithmetic mean?

Answer by Nishad Shah:

Consider a simple example. In the following figure, look at images B and C.

Who do you think is a better shooter of the two ?

Intuitively, most people will say B. Why ? Consistency.

When arithmetic mean is just a measure of the average score, standard deviation pretty much gives an idea about the consistency of data. So, while arithmetic mean of C is close to the bull's eye, he isn't a consistent shooter or more random. Where as B is too far away from 0, but still is consistent with his shots.

Which means B is a better shooter than C.

Why is standard deviation better than deviation about arithmetic mean?

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