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:

Wolfram Research (2007), GeometricMean, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMean.html.

Text

Wolfram Research (2007), GeometricMean, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMean.html.

CMS

Wolfram Language. 2007. "GeometricMean." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeometricMean.html.

APA

Wolfram Language. (2007). GeometricMean. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeometricMean.html

BibTeX

@misc{reference.wolfram_2022_geometricmean, author="Wolfram Research", title="{GeometricMean}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricMean.html}", note=[Accessed: 08-August-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_geometricmean, organization={Wolfram Research}, title={GeometricMean}, year={2007}, url={https://reference.wolfram.com/language/ref/GeometricMean.html}, note=[Accessed: 08-August-2022 ]}