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ContraharmonicMean[list]

gives the contraharmonic mean of the values in list.

ContraharmonicMean[list,p]

gives the order p Lehmer contraharmonic mean.

Details
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Basic Examples  
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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:

Wolfram Language code: ContraharmonicMean[{a, b, c, d}]

Means of each column:

Wolfram Language code: ContraharmonicMean[{{1, 2}, {5, 4}, {6, 7}}]

Scope  (9)

Exact input yields exact output:

Wolfram Language code: ContraharmonicMean[{1, 2, 3, 4}]
Wolfram Language code: ContraharmonicMean[{π, E, 2}, 1 / 2]

Approximate input yields approximate output:

Wolfram Language code: ContraharmonicMean[{1., 2., 3., 4.}]
Wolfram Language code: ContraharmonicMean[N[{1, 2, 3, 4}, 30], 7]

ContraharmonicMean for a matrix gives columnwise means:

Wolfram Language code: ContraharmonicMean[Array[Subscript[a, ##]&, {2, 2}]]

Works with large arrays:

Wolfram Language code: ContraharmonicMean[RandomReal[1, 10 ^ 7]]
Wolfram Language code: ContraharmonicMean[RandomReal[1, {10 ^ 6, 3}]]

SparseArray data can be used just like dense arrays:

Wolfram Language code: ContraharmonicMean[SparseArray[{{1} -> 1, {2} -> 7}]]
Wolfram Language code: ContraharmonicMean[SparseArray[{{1, 1} -> 1, {2, 1} -> 2, {2, 2} -> 3}]]

Find the contraharmonic mean of WeightedData:

Wolfram Language code: ContraharmonicMean[WeightedData[{1, 2, 3}, {Subscript[w, 1], Subscript[w, 2], Subscript[w, 3]}]]
Wolfram Language code: data = {8, 3, 5, 4, 9, 1, 4, 2, 2, 3}; weights = {0.15, 0.09, 0.12, 0.10, 0.16, 0.3, 0.11, 0.08, 0.08, 0.09};
Wolfram Language code: ContraharmonicMean[WeightedData[data, weights]]

Find the contraharmonic mean of EventData:

Wolfram Language code: e = {1.0, 2.1, 3.2, 4.5, 5.7}; ci = {0, 0, 0, 1, 0};
Wolfram Language code: ContraharmonicMean[EventData[e, ci]]

Find the contraharmonic mean of a TimeSeries:

Wolfram Language code: ContraharmonicMean[TemporalData[TimeSeries, {{{0.15864140638143098, 0.3435049074668335, -1.9621462271938013, -1.6890669314901334, 0.6954484987268401, -1.9567202370040935, -1.3930016185102279, -2.0833128365294504, 1.7359349394508587, -1.7039727275329852, -1. ... 29228893625929153, -0.5363532084601115, -2.796595136284031, 1.2765327710447636, -2.9905979211205196}}, {{0, 107, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1]]

Find the contraharmonic mean for data involving quantities:

Wolfram Language code: data = Quantity[RandomReal[1, 6], "Meters"]
Wolfram Language code: ContraharmonicMean[data]

Properties & Relations  (2)

The contraharmonic mean is a quotient of two means:

Wolfram Language code: v = {a, b, c};
Wolfram Language code: ContraharmonicMean[v] == Mean[v ^ 2] / Mean[v]

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

Wolfram Language code: v = {a, b, c};
Wolfram Language code: GeometricMean[{Mean[v], ContraharmonicMean[v]}] == RootMeanSquare[v]
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_2026_contraharmonicmean, author="Wolfram Research", title="{ContraharmonicMean}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ContraharmonicMean.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_contraharmonicmean, organization={Wolfram Research}, title={ContraharmonicMean}, year={2008}, url={https://reference.wolfram.com/language/ref/ContraharmonicMean.html}, note=[Accessed: 12-June-2026]}