# The Geometric Mean The geometric mean of two numbers $a$ and $b$ (where $a \le b$) is a number $m$ such that $ \frac m a = \frac b m $ In other words, the geometric mean of two numbers is a number that is located exactly in-between the two numbers in a [[Geometric Sequence]]. The geometric mean can be used as a measure of central tendency of a population, in which case it is calculated by taking the n-th root of the product of all elements. $ m = \left( \prod_{i=1}^n x_i \right)^\frac {1}{n} $ The geometric mean is similar to [[The Arithmetic Mean]].