Editing Mean (section)

====Power mean====
The [[generalized mean]], also known as the power mean or Hölder mean, is an abstraction of the [[quadratic mean|quadratic]], arithmetic, geometric, and harmonic means. It is defined for a set of ''n'' positive numbers ''x''<sub>i</sub> by

<p style="margin-left:1.6em;">
<math>\bar{x}(m) = \left( \frac{1}{n} \sum_{i=1}^n x_i^m \right)^\frac{1}{m}</math> {{r|:2|style="position:absolute; right:0;"}}
</p>

By choosing different values for the parameter ''m'', the following types of means are obtained:

{{glossary|style=display:grid;grid-template-columns: max-content auto;margin-left:1.6em;}}
{{term|style=grid-column-start: 1;margin-top:auto;margin-bottom:auto;text-align:right;|term=<math>\lim_{m \to \infty}</math>}}
{{defn|style=grid-column-start: 2;margin-top:auto;margin-bottom:auto;text-align:left;|defn=[[maximum]] of <math>x_i</math>}}
{{term|style=grid-column-start: 1;margin-top:auto;margin-bottom:auto;text-align:right;|term=<math>\lim_{m \to 2}</math>}}
{{defn|style=grid-column-start: 2;margin-top:auto;margin-bottom:auto;text-align:left;|defn=[[quadratic mean]]}}
{{term|style=grid-column-start: 1;margin-top:auto;margin-bottom:auto;text-align:right;|term=<math>\lim_{m \to 1}</math>}}
{{defn|style=grid-column-start: 2;margin-top:auto;margin-bottom:auto;text-align:left;|defn=[[arithmetic mean]]}}
{{term|style=grid-column-start: 1;margin-top:auto;margin-bottom:auto;text-align:right;|term=<math>\lim_{m \to 0}</math>}}
{{defn|style=grid-column-start: 2;margin-top:auto;margin-bottom:auto;text-align:left;|defn=[[geometric mean]]}}
{{term|style=grid-column-start: 1;margin-top:auto;margin-bottom:auto;text-align:right;|term=<math>\lim_{m \to -1}</math>}}
{{defn|style=grid-column-start: 2;margin-top:auto;margin-bottom:auto;text-align:left;|defn=[[harmonic mean]]}}
{{term|style=grid-column-start: 1;margin-top:auto;margin-bottom:auto;text-align:right;|term=<math>\lim_{m \to -\infty}</math>}}
{{defn|style=grid-column-start: 2;margin-top:auto;margin-bottom:auto;text-align:left;|defn=[[minimum]] of <math>x_i</math>}}
{{glossary end}}