Uncertainty is ever-present and is an integral part of life. Recognising the existence of uncertainty and its possible effects on decision-making may be important for the profitability, financial success, or even survival of an organisation. A relatively new discipline, - known as probability management, - has recently emerged as part of operations research/management science. This paper will attempt to provide a brief introduction to the concepts of probability management and the motivation behind its development. One of the major driving forces resulting in this development is the phenomenon known as the ‘flaw-of-averages’. The flaw-of-averages has important consequences in industrial engineering, financial, business, and economic models. The classic newsvendor problem will be used as an illustrative example. However, the main purpose of this paper is to discuss the most important characteristics of the flaw-of-averages. It will investigate and attempt to quantify some of the generic factors that may have an influence on the existence and severity of the flaw-of-averages and its expected consequences. Various models will be developed, and experiments will be conducted using Microsoft Excel as a modelling tool and an experimental approach based on Monte Carlo simulation modelling.