Geometric mean

In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers x₁, x₂, ..., x_n, the geometric mean is defined as

For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, ${\displaystyle {\sqrt {2\cdot 8}}=4}$. As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, ${\displaystyle {\sqrt[{3}]{4\cdot 1\cdot 1/32}}=1/2}$.

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