Definition Normal distribution

In statistics, a normal distribution is a model of distribution. It is also called the Gaussian distribution – after the German mathematician Carl Friedrich Gauss. A normal distribution assumes a symmetric distribution of numerical data. Its bell-shaped curve is symmetrical, and its median and arithmetic mean are identical. 

A normal distribution is used when referring to large populations, e.g., "body height" in the U.S. In a normal distribution, about two-thirds of all measured values are within the range of a standard deviation in relation to the mean.

The normal distribution is often used as a basis for estimating, describing, and forecasting in 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 have been credited with the first statistical insights into the topic of normal distribution. In 1870, they studied the 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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