normal distribution

In common usage, normality is treated as synonymous with natural, conventional, acceptable, or ordinary. In statistics, normality is defined as the most commonly occurring, the numerically most frequent type, which is then used as the base-line for identifying the unusual and the statistically rare.

A hypothetical mathematical distribution, the normal distribution provides an idealized model for comparison with observed variable distributions, and is the most commonly used mathematical model in statistical inference . In form it is a symmetrical, bell-shaped curve. The normal distribution for any particular variable is defined by its mean and standard deviation.

The mathematical properties of the normal distribution can be used to estimate the proportion in a sample falling above or below any particular reading or measurement for any variable to which the model is being applied. It is said to be relatively ‘robust’ to non-normality in observed variable distributions: in other words, in many circumstances it will serve as a reasonable model, even in cases where observed variable distributions appear to be rather inadequate approximations to normality. Even when a population does not itself have a normal distribution, the distribution of sample means will tend to approximate to a normal distribution. See also variation (statistical) ; central tendency (measures of).