Difference between revisions of "Harmonic mean"

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The harmonic mean (frequently referred to as HM) is a special kind of mean (like [[Arithmetic mean]], [[Geometric mean]]). The harmonic mean of n numbers <math> x_1, x_2... x_n </math> is defined to be: <math> \frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}</math>.  
 
The harmonic mean (frequently referred to as HM) is a special kind of mean (like [[Arithmetic mean]], [[Geometric mean]]). The harmonic mean of n numbers <math> x_1, x_2... x_n </math> is defined to be: <math> \frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}</math>.  
  
The harmonic mean is a part of a frequently used inequality, the [[Arithmetic mean-Harmonic mean-Geometric mean inequality]]. The Inequality states that for a set of numbers <math>x_1, x_2,\ldots,x_n</math>: <math>\frac{x_1+x_2+\ldots+x_n}{n}\ge \frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}} \ge \sqrt[n]{x_1\cdot x_2 \ldots x_n}</math>
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The harmonic mean is a part of a frequently used inequality, the [[Arithmetic mean-Harmonic mean-Geometric mean inequality]]. The Inequality states that for a set of numbers <math>x_1, x_2,\ldots,x_n</math>: <math>\frac{x_1+x_2+\ldots+x_n}{n}\ge \sqrt[n]{x_1\cdot x_2 \ldots x_n}\ge \frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}} </math>

Revision as of 18:05, 18 June 2006

The harmonic mean (frequently referred to as HM) is a special kind of mean (like Arithmetic mean, Geometric mean). The harmonic mean of n numbers $x_1, x_2... x_n$ is defined to be: $\frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}$.

The harmonic mean is a part of a frequently used inequality, the Arithmetic mean-Harmonic mean-Geometric mean inequality. The Inequality states that for a set of numbers $x_1, x_2,\ldots,x_n$: $\frac{x_1+x_2+\ldots+x_n}{n}\ge \sqrt[n]{x_1\cdot x_2 \ldots x_n}\ge \frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}$