Chisini Mean

A general class of means introduced by Italian mathematician Oscar Chisini (pronounced keeseenee) in 1929.

Given a function of n variables f(x_1,...,x_n), the Chisini mean of n values x_1,...,x_n associated with f is defined as the number M such that


Of course, the function f must be chosen in such a way that there always is exactly one number M with this property.

The most common means are Chisini means associated with the functions listed in the following table. Every weighted mean corresponds to the weight vector (p_1,...,p_n).

meanfunction f(x_1,...,x_n)
arithmetic meanx_1+...+x_n
weighted arithmetic meanp_1x_1+...+p_nx_n
geometric meanx_1...x_n
weighted geometric meanx_1^(p_1)...x_n^(p_n)
harmonic meanx_1^(-1)+...+x_n^(-1)
weighted harmonic mean(p_1)/(x_1)+...+(p_n)/(x_n)
quadratic meanx_1^2+...+x_n^2
weighted quadratic meanp_1x_1^2+...+p_nx_n^2

See also

Arithmetic Mean, Geometric Mean, Harmonic Mean, Mean

This entry contributed by Margherita Barile

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Chisini, O. "Sul concetto di media." Periodico di Matematiche 4, 106-116, 1929.

Referenced on Wolfram|Alpha

Chisini Mean

Cite this as:

Barile, Margherita. "Chisini Mean." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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