Is the nth root of a product of n terms used in place of the average anywhere?

Question

In applied usage we typically take the average of values or terms which is done by summing them and dividing by the number of terms (for simple average): $$\sum_{i=1}^n \frac{a_i}{n}$$

It dawned on me that the use of this form of mixing terms over some other form might be arbitrary. Why not?: $$\sqrt[n]{\prod_{i=1}^n a_i} $$ Is this equivalent to something that is already used extensively? Does it have a name?

Answer 1

This is called the geometric mean of the $a_i$. Here is its Wikipedia page.