# ContraharmonicMean

ContraharmonicMean[list]

gives the contraharmonic mean of the values in list.

ContraharmonicMean[list,p]

gives the order p Lehmer contraharmonic mean.

# Details

• For the list {x1,x2,,xn}, 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,}]}.

# Examples

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## 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.html

#### BibTeX

@misc{reference.wolfram_2024_contraharmonicmean, author="Wolfram Research", title="{ContraharmonicMean}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ContraharmonicMean.html}", note=[Accessed: 20-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_contraharmonicmean, organization={Wolfram Research}, title={ContraharmonicMean}, year={2008}, url={https://reference.wolfram.com/language/ref/ContraharmonicMean.html}, note=[Accessed: 20-July-2024 ]}