Was ist ein numerischer Mittelwert?

Zur axiomatischen Präzisierung einer fundamentalen Idee

Abstract

The notion of means (averaging) has been a "basic idea" in mathematics from its very beginnings. How do we precisely define this term  that has been previously described only vaguely through concrete examples? Pythagoreans were the first to develop a theory of numerical means. From this starting point, historically inspired, we have used the so-called Chuquet mean to obtain an axiomatic formulation of a numerical mean.