GeometricMean

GeometricMean[data]

gives the geometric mean of the values in data.

Details

Examples

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Basic Examples  (2)

Geometric mean of a list:

Geometric mean of columns of a matrix:

Scope  (13)

Basic Uses  (6)

Exact input yields exact output:

Approximate input yields approximate output:

Find the geometric mean of WeightedData:

Find the geometric mean of EventData:

Find the geometric mean of a TimeSeries:

The geometric mean depends only on the values:

Compute a weighted geometric mean:

Find the geometric mean of data involving quantities:

Array Data  (5)

GeometricMean for a matrix gives columnwise means:

Mean for a tensor works across the first index: »

Works with large arrays:

When the input is an Association, GeometricMean works on its values:

SparseArray data can be used just like dense arrays:

Find the geometric mean of a QuantityArray:

Image and Audio Data  (2)

Channelwise geometric mean value of an RGB image:

Geometric mean intensity value of a grayscale image:

On audio objects, GeometricMean works channelwise:

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:

Possible Issues  (1)

GeometricMean may return complex values when data contains negative values:

For different sample realizations, the geometric mean is real:

Wolfram Research (2007), GeometricMean, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMean.html (updated 2023).

Text

Wolfram Research (2007), GeometricMean, Wolfram Language function, https://reference.wolfram.com/language/ref/GeometricMean.html (updated 2023).

CMS

Wolfram Language. 2007. "GeometricMean." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. 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_2023_geometricmean, author="Wolfram Research", title="{GeometricMean}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/GeometricMean.html}", note=[Accessed: 04-March-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_geometricmean, organization={Wolfram Research}, title={GeometricMean}, year={2023}, url={https://reference.wolfram.com/language/ref/GeometricMean.html}, note=[Accessed: 04-March-2024 ]}