Concept# Geometric mean

Summary

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 nth root of the product of n numbers, i.e., for a set of numbers a1, a2, ..., an, the geometric mean is defined as
:\left(\prod_{i=1}^n a_i\right)^\frac{1}{n} = \sqrt[n]{a_1 a_2 \cdots a_n}
or, equivalently, as the arithmetic mean in logscale:
:\exp{\left( {\frac{1}{n}\sum\limits_{i=1}^{n}\ln a_i} \right)}
Most commonly the numbers are restricted to being non-negative, to avoid complications related to negative numbers not having real roots, and frequently they are restricted to being positive, to enable the use of logarithms.
For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, \sqrt{2 \cdot 8} = 4. As another examp

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