normal distribution

The normal distribution is a type of ideal probability distribution which tends to occur for a value that is the sum of many small random values. Many phenomena that we measure are the result of numerous factors, each of which can be slightly different in different instances, which makes measurement of many instances of the measured phenomena close to a normal distribution. For example, a person's height results from a lot of factors affecting details in the way the person grew, some of them, for example being factors affecting to what length their thigh bones grew. As a result, the measurement of many people can result in something close to a normal distribution. The function describing the normal distribution is the Gaussian function and another name for the distribution is Gaussian distribution. Its shape when graphed is the familiar bell curve. The central limit theorem states that the combination of such factors tends toward a normal distribution.

The normal distribution has particular mathematical properties, a history of techniques for analyzing it, and for combining such probability distributions. When summing individual distributions that are "somewhat near normal", the composite distribution tends to be even closer to normal. For this reason, the normal distribution is often used as an approximation for distributions that are not completely characterized: the results can be and often are valid. It is part of a competent statistician's abilities to spot cases where this type of result is likely to be invalid.