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

open allclose all

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: 26-March-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_geometricmean, organization={Wolfram Research}, title={GeometricMean}, year={2007}, url={https://reference.wolfram.com/language/ref/GeometricMean.html}, note=[Accessed: 26-March-2023 ]}