Why isn't everything distributed normally?

Definition of normal distribution

The normal distribution assumes a symmetrical form of distribution of numerical data and is also called the Gaussian bell curve - after the German mathematician Carl Friedrich Gauß. The normal distribution is a distribution model of statistics. Their curve is symmetrical, the median and mean are identical. The normal distribution is often used in large populations - for example, body size in Germany is “normally distributed”. For the normal distribution, around two-thirds of all measured values ​​are within one standard deviation from the mean. With the removal of two standard deviations, it is already over 95 percent. In numerous occurrences in the natural and social sciences, the normal distribution is the basis for the approximate description, explanation and prognosis of facts. The central limit theorem, which originates from the normal distribution, is considered the most important statement of statistics.

The first statistical findings on the phenomenon of normal distribution go back to the Belgian mathematician Adolphe Quetelet and the British researcher Francis Galton. Both of them examined the body measurements of Belgian soldiers around 1870 and found that numerous properties such as body weight, height, chest size, etc. were normally distributed around an average value.

Please note that the individual definitions in our statistics lexicon are simplified explanations. The aim here is to bring the individual terms closer to the broadest possible user group. In this respect, it is possible that individual definitions do not fully correspond to scientific standards.