Central Limit Theorem

The central limit theorem (CLT) is a statistical theory that states that

• Given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

• So, for a population with finite mean p and a finite non-zero variance 01%2, the sampling distribution of the mean approaches a normal distribution with a mean of p and a variance of 0A2/n as the sample size (n) increases.

• The amazing and counter-intuitive thing about the central limit theorem is that no matter what the shape of the original (parent) distribution, the sampling distribution of the mean approaches a normal distribution