The Central Limit Theorem

The Central Limit Theorem (CLT) states that when you take many random samples from a population and average them, the distribution of those averages will form a normal distribution (bell-shaped curve), regardless of the population's original shape. This means that with a large enough sample size, the average of the samples will be close to the population average. The CLT is fundamental in statistics because it allows for reliable conclusions about a population based on sample data, facilitating hypothesis testing and confidence intervals.