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.
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