# Geometric mean

From Encyclopedia of Mathematics

*of positive numbers $a_1,\dotsc,a_n$*

The number equal to the real positive $n$-th root of their product, i.e. to

$$(a_1\dotsm a_n)^{1/n}.$$

The geometric mean is always smaller than the arithmetic mean, except when all the numbers are equal (then these two means are equal). The geometric mean of two numbers is also known as the proportional mean.

**How to Cite This Entry:**

Geometric mean.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Geometric_mean&oldid=44630