What Is the Central Limit Theorem? Definition, Types, Examples & Uses

What Is the Central Limit Theorem?

Subject: Mathematics

Book: Maths Mastery

The Central Limit Theorem (CLT) states that, for large sample sizes, the sampling distribution of the sample mean approximates a normal distribution, regardless of the population’s original distribution. This principle underpins many statistical tests (z-tests, t-tests) and justifies the normal approximation for binomial distributions under certain conditions. For example, if you repeatedly draw random samples of size n from any population and plot the means, that distribution becomes more “bell-shaped” as n grows. Understanding the CLT is critical to modern statistics, enabling inferences about population parameters from sample data.