Central Limit Theorem

As the sample size of independent, identically distributed, random observations increases, the distribution of a variable representing a sum of these observations (i.e., the sampling distribution) approaches the normal distribution (regardless of the distribution of these observations in the population). This principle explains the importance and ubiquity of the normal distribution in statistical inference. See also, Elementary Concepts.

The term Central Limit Theorem was first used by Polya, 1920; German, "Zentraler Grenzwertsatz."