Central Limit Theorem (CLT)

The central limit theorem (CLT) states that the distribution of sample means approximates a Normal Distribution as the sample size gets larger, regardless of the population's distribution. I.e. When a sample of data is taken from a very large data source, it is assumed to be Normally Distributed.


The distribution of the sum (or average) of a large number of independent, identically distributed random variables approaches a normal distribution, regardless of the original distribution of the variables.


  • Classical CLT: Deals with the sum of random variables.
  • Lindeberg–Lévy CLT: Deals with the average of random variables.