central limit theorem

(NL: centrale limietstelling)

The central limit theorem says that the probability distribution of the sample mean will resemble the normal distribution as the sample size increases.

Or, more specifically, if you take a sufficiently large (\(n >30\)) random sample from a population with expected value \(\mu\) and standard deviation \(\sigma\), then the sample mean \(\bar{x}\) will have a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{n}}\). This holds regardless of the distribution of the population!

The central limit theorem is foundational for many statistical methods, such as confidence intervals and hypothesis tests. It dictates the conditions under which we can (to a certain extent) generalize a result from a sample to the population.