Definition Normal distribution

The normal distribution assumes a symmetric distribution of numerical data. It is also called the Gaussian distribution – after the German mathematician Carl Friedrich Gauss.

In statistics, the normal distribution is a model of distribution. Its bell-shaped curve is symmetrical, median and arithmetic mean are identical. 

The normal distribution often applies to large populations, for example 'body height' is normally distributed in the US. In a normal distribution, about two thirds of all measured values are within the range of a standard deviation in relation to the mean. With the removal of two standard deviations we are already at 95%.

The normal distribution is used as a basis for approximation, description and forecasting in many cases concerning the natural as well as social sciences. The central limit theorem, the most important statement in statistics, is derived from normal distribution.

The Belgian mathematician Adolphe Quetelet and the British scientist Francis Galton are credited with the first statistical insights into the topic of normal distribution. Around 1870 they studied body measurements of Belgian soldiers and discovered that many characteristics such as body weight, height and chest measurements were distributed normally around a central value. 

Please note that the definitions in our statistics encyclopedia are simplified explanations of terms. Our goal is to make the definitions accessible for a broad audience; thus it is possible that some definitions do not adhere entirely to scientific standards.

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