The Central Limit Theorem: The Most Powerful Idea in Statistics
Ever wondered why so many things in statistics end up looking like a bell curve? Well, the answer is in the Central Limit Theorem (CLT), which is referred to as the most important theorem in statistics, and it’s really amazing how it works. What Does the CLT Say? In simple terms: Whenever we have many random samples from a certain population and find out the average of each of the samples, the distribution of the averages obtained will become normally distributed in spite of the form of the original distribution, as long as the size of the samples is large enough. This means that regardless of how weird the original distribution looks like, the average of many samples will form a bell shape.. The Formal Version Let's say that we have a population whose average and spread are known. In this case, when taking samples of a certain size at random from such a population, we can assume that the sampling distribution of the average will be normal and has the following prop...