Difference between revisions of "Harmonic mean"
IntrepidMath (talk | contribs) m (added internal link to AM-HM-GM) |
IntrepidMath (talk | contribs) (Restated inequality, explicitly labeled) |
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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>. |
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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 \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> | ||
Revision as of 16:52, 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 
is defined to be: 
.
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 
: ![$\frac{x_1+x_2+\ldots+x_n}{n}\ge \frac{n} {\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}} \ge \sqrt[n]{x_1\cdot x_2 \ldots x_n}$](http://latex.artofproblemsolving.com/6/d/3/6d352553691f37e7d6c1564620abf38551708228.png)
