HarmonicMean

HarmonicMean[data]

gives the harmonic mean of the values in data.

Details

Examples

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Basic Examples  (2)

Harmonic mean of symbolic values:

Harmonic mean of columns of a matrix:

Scope  (12)

Basic Uses  (6)

Exact input yields exact output:

Approximate input yields approximate output:

Find the harmonic mean of WeightedData:

Find the harmonic mean of EventData:

Find the harmonic mean of a TimeSeries:

The harmonic mean depends only on the values:

Compute a weighted harmonic mean:

Find the harmonic mean of data involving quantities:

Array Data  (4)

HarmonicMean for a 2D matrix gives columnwise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the harmonic mean of a QuantityArray:

Image and Audio Data  (2)

Channelwise harmonic mean value of an RGB image:

Harmonic mean intensity value of a grayscale image:

On audio objects, HarmonicMean works channelwise:

Applications  (1)

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

Properties & Relations  (6)

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

HarmonicMean is very sensible to values close to zero:

This agrees with the definition:

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 HarmonicNumber[n]:

The harmonic mean of the shifted data is larger than the shifted harmonic mean of the original data (assuming the shift is a positive number):

Possible Issues  (1)

HarmonicMean will return 0 when the audio channels have a 0 in them; this is common for real-world audio samples:

Mean will clip channel values to values that can be represented with machine numbers:

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

Text

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

CMS

Wolfram Language. 2007. "HarmonicMean." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. 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_2025_harmonicmean, author="Wolfram Research", title="{HarmonicMean}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/HarmonicMean.html}", note=[Accessed: 30-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_harmonicmean, organization={Wolfram Research}, title={HarmonicMean}, year={2023}, url={https://reference.wolfram.com/language/ref/HarmonicMean.html}, note=[Accessed: 30-May-2025 ]}