# Difference between revisions of "Geometric mean"

Ragnarok23 (talk | contribs) (Made it nice and LaTeXy, detailed a little more) |
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== Practice Problems == | == Practice Problems == | ||

+ | ===Introductory Problems=== | ||

+ | * [[1966 AHSME Problems/Problem 3]] | ||

== See Also == | == See Also == | ||

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

*[[AM-GM]] | *[[AM-GM]] |

## Revision as of 10:59, 2 April 2008

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.