Chisini Mean

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

Given a function of  variables , the Chisini mean of  values  associated with  is defined as the number  such that

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

mean	function
arithmetic mean
weighted arithmetic mean
geometric mean
weighted geometric mean
harmonic mean
weighted harmonic mean
quadratic mean
weighted quadratic mean

REFERENCES:

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