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Encyclopedia > Chisini mean

A function f of n variables xn is a Chisini mean, if and only if, for every vector <x1 ... xn>, there exists a unique M such that f(M,M, ... , M) = f(x1,x2, ... , xn).


The arithmetic, harmonic, geometric and quadratic means are all Chisini means, as are the weighted variants thereof.


They were introduced by Oscar Chisini, in the paper Chisini, O. "Sul concetto di media." Periodico di Matematiche 4, 106-116, 1929.




  Results from FactBites:
 
Mean - Encyclopedia, History, Geography and Biography (1508 words)
The mean is the unique value about which the sum of squared deviations is a minimum.If you calculate the sum of squared deviations from any other measure of central tendency, it will be larger than for the mean.This explains why the standard deviation and the mean are usually cited together in statistical reports.
The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or most likely (mode).
The geometric mean is an average that is useful for sets of numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean).
  More results at FactBites »


 
 

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