Central limit theorem

The central limit theorem is a fundamental theorem in statistics. It states that:

the distribution of an average of samples, taken from any type of underlying probability function having a finite variance, will approach a Normal distribution as the sample size increases.

If the sample size is only one, then the distribution of the average of samples will not approach a Normal distribution, but will approach the distribution of the underlying probability function. But as the sample size increases, the distribution of their averages increasingly approaches a Normal distribution.