Arithmetic and Geometric Mean - Texas State University

We claim that then the optimal value of Q is the arithmetic mean. To prove this, write Q — = (M — Xi) + (Q — M) where Q is any value we accept for our measurement, and M is the arithmetic mean of the observed values. Then (Q - = (M - + (Q - + - - M) . Summing these equations, we note that the last terms sum to O, because ................
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