Central limit theorem
The central limit theorem states formally that the average of a large number of independent identically distributed random variables will have a normal distribution.
The central limit theorem is important in sampling theory.
It explains that sample means follow a normal distribution - regardless of the actual distribution of the parent population - and that the sample mean is an unbiased estimate of the parent population mean.
The central limit theorem also explains why larger samples will - on average - produce better estimates of the parent population mean.
The central limit theorem is sometimes known as the law of large numbers.