Difference between revisions of "Geometric mean"
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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 ![$\sqrt[n]{x_1 x_2 x_3 x_4 ... x_n}$](http://latex.artofproblemsolving.com/a/3/1/a3130ae3a2589afda5349016de5aac527ad9bfe8.png)
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 ![$\sqrt[4]{48}=2\sqrt[4]{3}$](http://latex.artofproblemsolving.com/e/3/1/e31700b222f05495f624090fedb69b2dbed2a7e3.png)
The Geometric Mean is a component of the well-known Arithmetic Mean-Geometric Mean Inequality.
