Statistics/Summary/Averages/Relationships among Arithmetic, Geometric and Harmonic Mean

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The Means mentioned above are realizations of the generalized mean

\bar{x}(m) = \left ( \frac{1}{n}\cdot\sum_{i=1}^n{|x_i|^m} \right ) ^{1/m}

and ordered this way: Minimum=\bar{x}(-\infty) < harmonic Mean=\bar{x}(-1) < geometric Mean=\bar{x}(0) < arithmetic Mean=\bar{x}(1) < Maximum=\bar{x}(\infty)

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