# Difference between revisions of "Geometric mean"

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 $x_1, x_2, x_3, x_4 ... x_n$ We want the nth root of the product of the n numbers. There are n numbers so our geometric mean would be $\sqrt[n]{x_1 x_2 x_3 x_4 ... x_n}$

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 $\sqrt[4]{48}=2\sqrt[4]{3}$

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