Weighted geometric mean: Difference between revisions
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imported>Gareth Leng No edit summary |
imported>Gareth Leng No edit summary |
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:''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>} | ||
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:<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]]. | 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]]. | 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]]. | ||
Revision as of 13:03, 23 January 2007
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.