# Difference between revisions of "Geometric mean"

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− | + | Given a set of ''n'' numbers, the '''Geometric Mean''' is the ''nth'' root of the product of the numbers. It is analogous to the [[Arithmetic Mean]], except with products. | |

+ | == Examples == | ||

+ | Find the geometric mean of the numbers <math>x_1, x_2, x_3, x_4 ... x_n</math> | ||

+ | We want the nth root of the product of the n numbers. There are n numbers so our geometric mean would be <math>\sqrt[n]{x_1 x_2 x_3 x_4 ... x_n}</math> | ||

+ | |||

+ | |||

+ | |||

+ | Find the geometric mean of the numbers 6, 4, 1 and 2. | ||

+ | There are 4 numbers, so we want the 4th root. The numbers' product is 48, so our answer is <math>\sqrt[4]{48}=2\sqrt[4]{3}</math> | ||

The Geometric Mean is a component of the well-known [[Arithmetic Mean-Geometric Mean]] [[Inequality]]. | The Geometric Mean is a component of the well-known [[Arithmetic Mean-Geometric Mean]] [[Inequality]]. | ||

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+ | == Practice Problems == | ||

+ | |||

+ | == See Also == | ||

+ | *[[Arithmetic Mean]] | ||

+ | *[[AM-GM]] |

## Revision as of 11:25, 22 June 2006

Given a set of *n* numbers, the **Geometric Mean** is the *nth* root of the product of the numbers. It is analogous to the Arithmetic Mean, except with products.

## Examples

Find the geometric mean of the numbers We want the nth root of the product of the n numbers. There are n numbers so our geometric mean would be

Find the geometric mean of the numbers 6, 4, 1 and 2. There are 4 numbers, so we want the 4th root. The numbers' product is 48, so our answer is

The Geometric Mean is a component of the well-known Arithmetic Mean-Geometric Mean Inequality.