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ContraharmonicMean—Wolfram Language Documentation

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BUILT-IN SYMBOL

Details

For the list {x₁,x₂,…,x_n}, the contraharmonic mean is given by .
The order p Lehmer mean is given by .
ContraharmonicMean handles both numerical and symbolic data.
ContraharmonicMean[{{x₁,y₁,…},{x₂,y₂,…},…}] gives {ContraharmonicMean[{x₁,x₂,…}],ContraharmonicMean[{y₁,y₂,…}]}.

Examplesopen allclose all Basic Examples (2)

Symbolic values:

Means of each column:

Scope (9)

Exact input yields exact output:

Approximate input yields approximate output:

ContraharmonicMean for a matrix gives columnwise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the contraharmonic mean of WeightedData:

Find the contraharmonic mean of EventData:

Find the contraharmonic mean of a TimeSeries:

Find the contraharmonic mean for data involving quantities:

Properties & Relations (2)

The contraharmonic mean is a quotient of two means:

The geometric mean of the arithmetic and contraharmonic means is the root mean square:

Wolfram Research (2008), ContraharmonicMean, Wolfram Language function, https://reference.wolfram.com/language/ref/ContraharmonicMean.html. Text Wolfram Research (2008), ContraharmonicMean, Wolfram Language function, https://reference.wolfram.com/language/ref/ContraharmonicMean.html.CMS Wolfram Language. 2008. "ContraharmonicMean." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ContraharmonicMean.html.APA Wolfram Language. (2008). ContraharmonicMean. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ContraharmonicMean.htmlBibTeX @misc{reference.wolfram_2025_contraharmonicmean, author="Wolfram Research", title="{ContraharmonicMean}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ContraharmonicMean.html}", note=[Accessed: 11-July-2025 ]}BibLaTeX @online{reference.wolfram_2025_contraharmonicmean, organization={Wolfram Research}, title={ContraharmonicMean}, year={2008}, url={https://reference.wolfram.com/language/ref/ContraharmonicMean.html}, note=[Accessed: 11-July-2025 ]}

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