Broadly, normalization (also spelled normalisation) is any process that makes something more normal, which typically means conforming to some regularity or rule, or returning from some state of abnormality. It has specific meanings in various fields:

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The normal distribution also arises in many areas of statistics: for example, the sampling distribution of the mean is approximately normal, even if the distribution of the population the sample is taken from is not normal.

In that case, the assumption of normality is not justified, and it is the logarithm of the variable of interest that is normally distributed.

Normality is the central assumption of the mathematical theory of errors.

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