The normal distribution

The so-called normal distribution is a continuous, unimodal and symmetrical probability distribution of which the distributive curve (section 3.5) is bell-shaped (figure 5.1.1). This distribution was discovered independently by the Frenchman Pierre Simon de Laplace (1749–1827) and the German Karl Friedrich Gauss (1777-1855), who both studied mathematics, physics and astronomy. The normal distribution is expected according to probability theory when the variation of a continuous random variable (variate) is due to causes which are very numerous and independent from each other, which act additively, and which all have small and approximately equal effects. The normal distribution is theoretical and is almost never perfectly observed in reality. For instance, even though the normal distribution extends in principle from -∞ to + ∞, most biological variates, such as the concentration of a chemical substance in an organism, the length or the weight of an individual organism, or the number of individuals in a biological population, cannot take negative numerical values (section 4.3). In practice, the normal distribution is nevertheless obtained approximately in many fields, such as physics, biology, psychology, etc., when the variation is due largely to objective (real) factors as well as when it is due mostly to inaccuracies or accidental measuring errors. Moreover, even when the normal distribution by itself is not suitable, it can often be satisfactorily replaced by a related distribution, the lognormal distribution (chapter 14).