Central Limit Theorem

The central limit theorem (CLT) states that, for a large enough sample (), the distribution of the sample mean will approach normal distribution. This holds for a sample of independent random variables from any distribution with a finite standard deviation.

Let be a random data set of size , that is, a sequence of independent and identically distributed random variables drawn from distributions of expected values given by and finite variances given by . The sample average is:

For large , the distribution of sample sums is close to normal distribution where: