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: 22-November-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: 22-November-2024 ]}