  The arithmetic average of a collection of observed values of a homogeneous
collection of quantities is often taken to be the most representative
observation. There are several arguments supporting this choice the moment of
inertia being the most familiar. But what does this mean?
  In this note, we bring forth the Kolmogorov-Nagumo point of view that the
arithmetic average is a special case of a sequence of functions of a special
kind, the quadratic and the geometric means being some of the other cases. The
median fails to belong to this class of functions. The Kolmogorov-Nagumo
interpretation is the most defensible and the most definitive one for the
arithmetic average, but its essence boils down to the fact that this average is
merely an abstraction which has meaning only within its mathematical set-up.
