132.204.53.174: /* References */

2014-12-04T22:27:24Z

References

en>Anrnusna: /* References */journal name, replaced: Proc. Lond. Math. Soc. → Proceedings of the London Mathematical Society using AWB

2013-10-17T11:57:53Z

References: journal name, replaced: Proc. Lond. Math. Soc. → Proceedings of the London Mathematical Society using AWB

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In [[statistics]], given a set of data,

:<math>X=\{x_1,x_2\dots,x_n\}</math>

and corresponding [[weight function|weights]],

:<math>W=\{w_1, w_2,\dots,w_n \}</math>

the '''weighted geometric mean''' is calculated as

:<math> \bar{x} = \left(\prod_{i=1}^n x_i^{w_i}\right)^{1 / \sum_{i=1}^n w_i} = \quad \exp \left( \frac{\sum_{i=1}^n w_i \ln x_i}{\sum_{i=1}^n w_i \quad} \right) </math>

Note that if all the weights are equal, the weighted geometric mean is the same as the [[geometric mean]].

Weighted versions of other means can also be calculated. Probably the best known weighted mean is the weighted arithmetic mean, usually simply called the [[weighted mean]]. Another example of a weighted mean is the [[weighted harmonic mean]].

The second form above illustrates that the [[logarithm]] of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values.

==See also==
*[[average]]
*[[central tendency]]
*[[summary statistics]]
*[[Weighted mean]]

[[Category:Means]]
[[Category:Mathematical analysis]]

{{statistics-stub}}

Ramanujan tau function - Revision history

132.204.53.174: /* References */

en>Anrnusna: /* References */journal name, replaced: Proc. Lond. Math. Soc. → Proceedings of the London Mathematical Society using AWB