: Mathematics: geometric mean

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geometric mean

In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real 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 $n$ th root of the product of $n$ numbers, i.e., for a set of numbers $a 1, a 2, ..., a n$ , the geometric mean is defined as
${\\displaystyle \\left(\\prod _{i=1}^{n}a_{i}\ ight)^{\ rac {1}{n}}={\\sqrt[{n}]{a_{1}a_{2}\\cdots a_{n}}}}$
or, equivalently, as the arithmetic mean in logscale:
${\\displaystyle \\exp {\\left({{\ rac {1}{n}}\\sum \\limits _{i=1}^{n}\\ln a_{i}}\ ight)}}$

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