Geometric Mean

The geometric mean of a sequence ${a_i}_(i=1)^n$ is defined by

(1)

Thus,

			(2)
			(3)

and so on.

The geometric mean of a list of numbers may be computed using GeometricMean[list] in the Wolfram Language package DescriptiveStatistics` .

For , the geometric mean is related to the arithmetic mean and harmonic mean by

(4)

(Havil 2003, p. 120).

The geometric mean is the special case of the power mean and is one of the Pythagorean means.

Hoehn and Niven (1985) show that

(5)

for any positive constant .

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