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Economics · Ch 5 — Measures of Central Tendency

Two Interesting Properties of A.M.

5.2.4

Two Interesting Properties of A.M.

The arithmetic mean has two properties worth remembering.

(i) The sum of deviations about the mean is always zero. If you subtract the mean from every observation and add up the results, they cancel exactly:

∑(X−Xˉ)=0\sum (X - \bar{X}) = 0

The positive deviations of values above the mean are exactly balanced by the negative deviations of values below it — which is why the mean sits at the "centre of gravity" of the data. …