Geometric mean

N-th root of the product of n numbers

In mathematics, the geometric mean (also known as the mean proportional) is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of ⁠ n {\displaystyle n} ⁠ numbers is the nth root of their product, i.e., for a collection of numbers a1, a2, ..., an, the geometric mean is defined as a 1 a 2 ⋯ a n t n . {\displaystyle {\sqrt[{n}]{a_{1}a_{2}\cdots a_{n}{\vphantom {t}}}}.} Hence, the geometric mean of two numbers is the square root of their product, for example with numbers ⁠ 2 {\displaystyle 2} ⁠ and ⁠ 8 {\displaystyle 8} ⁠ the geometric mean is 2 ⋅ 8 = {\displaystyle \textstyle {\sqrt {2\cdot 8}}={}} 16 = 4 {\displaystyle \textstyle {\sqrt {16}}=4} .

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