A Non-Zero Dispersion Leads to a Non-Zero Bias of the Mean

Abstract

An existence theorem for a bias of the mean in the presence of data dispersion is proved. The aims are to use this theorem in experiments interpretation, probability theory, statistics, economics and management. The ultimate aims are to explain the well-known problems of utility and decision theories, such as risk aversion, the underweighting of high and the overweighting of low probabilities, the Allais paradox, etc. The results may be used to estimate preferences, choices, decisions, (ir)rational behavior at data uncertainty, noises, experimental errors in management, investment, insurance, etc.