Learn the Central Limit Theorem in statistics with definition, formula, proof, and examples. Understand its importance, solved problems, and applications for JEE and advanced level exams. The Central Limit Theorem (CLT ) relies on multiple independent samples that are randomly selected to predict the activity of a population. The Central Limit Theorem in Statistics states that as the sample size increases and its variance is finite , then the distribution of the sample mean approaches the normal distribution, irrespective of the shape of the population distribution. Learn how the sampling distribution of the mean approaches a normal distribution as the sample size increases, with examples of uniform and binomial distributions. See plots, formulas, and explanations of the central limit theorem .
