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Contraharmonic Mean

The contraharmonic mean of nonnegative numbers x_1, ..., x_n, not all zero, is

C=(sum_(i=1)^(n)x_i^2)/(sum_(i=1)^(n)x_i).

It is the Lehmer mean of order 1. The contraharmonic mean is at least the arithmetic mean, with equality if and only if all the x_i are equal.

See also

Arithmetic Mean, Harmonic Mean, Lehmer Mean, Mean, Root-Mean-Square

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References

Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 121, 2003.

Cite this as:

Weisstein, Eric W. "Contraharmonic Mean." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ContraharmonicMean.html

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