[AntonioLao]

Statistical averages either scare or fascinate. Average income usually cannot satisfy the average wage earners. Average height encourages high heels shoes. Average look helps create lucrative cosmetic industries. Many have difficulty maintaining average weights, average IQ, average waits, average talks, average sleeps, average walks, average driving speed, and average living conditions. In a word, average means boredom. In another perspective, statistical averages promote insurance businesses, distinguish sporting standards, and exercise sensible decision-making processes. A government insisting on a rule of averages can lead either to communism (equal public properties ownership) or fascism (total subservient). Both forms prevent or discourage the free enterprises of a democracy.

On the other hand, statistical averages allow physicists to differentiate bosons from fermions, to formulate the kinetic theory of heat; and in mathematics, the theory of probability for random events thus raising the absolute importance of Gaussian or normal continuous distribution into a probability law for large numbers for a central limit theorem. Nature uses averages to identity all elementary particles among themselves: the mass of every electron is the same, the mass of every proton is the same, the mass of every neutron is the same, and the rest mass of every photon is zero. However, all these can occupy different quantum states of energy. A state of spacetime wherein mass is quantized and energy is continuous becomes a state of a two dimensional anyon http://en.wikipedia.org/wiki/Anyon. It is a privileged state exclusively reserved for the whole universe.