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=== Relationships among Arithmetic, Geometric and Harmonic Mean ===
The Means mentioned above are realizations of the generalized mean 
:<math> \bar{x}(m) = \left ( \frac{1}{n}\cdot\sum_{i=1}^n{|x_i|^m} \right ) ^{1/m} </math>
and ordered this way: 

:<math>
\begin{alignat}{2}
&\mathit{minimum}&\;=\;&\bar{x}(-\infty) \\
\mathrel<\;&\mathit{harmonic\ mean}&\;=\;&\bar{x}(-1) \\
\mathrel<\;&\mathit{geometric\ mean}&\;=\;&\lim_{m\rightarrow0}\bar{x}(m) \\
\mathrel<\;&\mathit{arithmetic\ mean}&\;=\;&\bar{x}(1) \\
\mathrel<\;&\mathit{maximum}&\;=\;&\bar{x}(\infty)
\end{alignat}
</math>

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