Definition:Geometric Mean

Definition
Let $x_1, x_2, \ldots, x_n \in \R_{>0}$ be (strictly) positive real numbers.

The geometric mean of $x_1, x_2, \ldots, x_n$ is defined as:


 * $\displaystyle G_n := \paren {\prod_{k \mathop = 1}^n x_k}^{1/n}$

That is, to find out the geometric mean of a set of $n$ numbers, multiply them together and take the $n$th root.

Also see

 * Definition:Mean


 * Definition:Arithmetic Mean
 * Definition:Harmonic Mean
 * Definition:Hölder Mean


 * Cauchy's Mean Theorem