geometric mean

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geometric mean

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Noun

geometric mean (plural geometric means)

1. (mathematics) A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values.

   The geometric mean of 2, 4 and 1 is ${\displaystyle {\sqrt{2\times 4\times 1}}}$ = 2

   The geometric mean of the arithmetic mean and the harmonic mean is the geometric mean. In symbols: if ${\displaystyle A(x,y)={x+y \over 2}}$, ${\displaystyle H(x,y)={2xy \over x+y}}$, and ${\displaystyle G(x,y)={\sqrt {xy}}}$, then ${\displaystyle G(A(x,y),H(x,y))={\sqrt {{x+y \over 2}\cdot {2xy \over x+y}}}={\sqrt {xy}}=G(x,y)}$.

Hypernyms

• measure of central tendency
• Pythagorean mean

Coordinate terms

• arithmetic mean
• harmonic mean
• quadratic mean

Translations