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)