Central Limit Theorem for Distributions

The Central Limit Theorem states that when you take a large number of independent samples from any population distribution—regardless of its shape—and calculate their averages, those averages tend to form a normal (bell-shaped) distribution. This means that even if the original data isn’t normally distributed, the distribution of sample means will approximate a normal curve as the sample size grows. This principle is fundamental because it allows us to make inferences about populations using sample data, simplifying analysis and hypothesis testing in many fields.