# GeometricMean

GeometricMean[list]

gives the geometric mean of the values in list.

# Details • For the list {x1,x2,,xn}, the geometric mean is given by .
• GeometricMean handles both numerical and symbolic data.
• GeometricMean[{{x1,y1,},{x2,y2,},}] gives {GeometricMean[{x1,x2,}],GeometricMean[{y1,y2,}]}.

# Examples

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## Basic Examples(2)

Geometric mean of a list:

Geometric mean of columns of a matrix:

## Scope(9)

Exact input yields exact output:

Approximate input yields approximate output:

GeometricMean for a matrix gives columnwise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the geometric mean of WeightedData:

Find the geometric mean of EventData:

Find the geometric mean of a TimeSeries:

Find the geometric mean of data involving quantities:

## Generalizations & Extensions(1)

Compute results for a SparseArray:

## Applications(1)

Find the geometric mean for the heights of children in a class:

## Properties & Relations(3)

GeometricMean is logarithmically related to Mean for positive values:

GeometricMean is logarithmically related to HarmonicMean for positive values:

For positive data, HarmonicMean[d]GeometricMean[d]Mean[d]:

Prove the inequality symbolically:

Introduced in 2007
(6.0)