The Central Limit Theorem by W. H. Smith

The Central Limit Theorem, as explained by W. H. Smith, states that when you take many random samples from a population and calculate their averages, those averages tend to form a bell-shaped (normal) distribution, regardless of the original population's distribution. This means that with enough samples, the average becomes predictable and follows a normal pattern, making it easier to estimate and make decisions about the population. Essentially, this theorem explains why many natural and social phenomena tend to cluster around a mean, enabling statisticians to make reliable inferences from sample data.