Weighted geometric mean: Difference between revisions
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In [[statistics]], given a set of data, | In [[statistics]], given a set of data, | ||
:''X'' = { ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub>} | :''X'' = { ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''n''</sub>} | ||
and corresponding | and corresponding 'weights', | ||
:''W'' = { ''w''<sub>1</sub>, ''w''<sub>2</sub>, ..., ''w''<sub>''n''</sub>} | :''W'' = { ''w''<sub>1</sub>, ''w''<sub>2</sub>, ..., ''w''<sub>''n''</sub>} | ||
the '''weighted geometric mean''' is | the '''weighted geometric mean''' is | ||
:<math> \bar{x} = \left(\prod_{i=1}^n x_i^{w_i}\right)^{1 / \sum_{i=1}^n w_i} = \quad \exp \left( \frac{1}{\sum_{i=1}^n w_i} \; \sum_{i=1}^n w_i \ln x_i \right) </math> | :<math> \bar{x} = \left(\prod_{i=1}^n x_i^{w_i}\right)^{1 / \sum_{i=1}^n w_i} = \quad \exp \left( \frac{1}{\sum_{i=1}^n w_i} \; \sum_{i=1}^n w_i \ln x_i \right) </math> | ||
If all the weights are equal, the weighted geometric mean is equal to 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]]. | ||
[[ | |||
Latest revision as of 23:40, 15 November 2007
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In statistics, given a set of data,
- X = { x1, x2, ..., xn}
and corresponding 'weights',
- W = { w1, w2, ..., wn}
the weighted geometric mean is
If all the weights are equal, the weighted geometric mean is equal to 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.