# HarmonicMean

HarmonicMean[list]

gives the harmonic mean of the values in list.

# Details

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

# Examples

open allclose all

## Basic Examples(2)

Harmonic mean of symbolic values:

Harmonic mean of columns of a matrix:

## Scope(9)

Exact input yields exact output:

Approximate input yields approximate output:

HarmonicMean for a matrix gives columnwise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the harmonic mean of WeightedData:

Find the harmonic mean of EventData:

Find the harmonic mean of a TimeSeries:

Find the harmonic mean of data involving quantities:

## Generalizations & Extensions(1)

Compute results for a SparseArray:

## Applications(1)

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

## Properties & Relations(4)

HarmonicMean is the inverse of Mean of the inverse of the data:

HarmonicMean is logarithmically related to GeometricMean for positive values:

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

Prove the inequality symbolically:

HarmonicMean[Range[n]] is inversely related to :

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_harmonicmean, author="Wolfram Research", title="{HarmonicMean}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/HarmonicMean.html}", note=[Accessed: 09-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_harmonicmean, organization={Wolfram Research}, title={HarmonicMean}, year={2007}, url={https://reference.wolfram.com/language/ref/HarmonicMean.html}, note=[Accessed: 09-June-2023 ]}