Central Limit Theorem

Everybody should know Central Limit Theorem. You know right?

Basically, Central Limit Therom states that:

• The sampling distribution of the sample mean from a random sample representing the underlying population regardless of the population distribution is approximately normal.


• The mean for such sampling distribution is the population mean.


• The variance for such sampling distribution is the population variance divided by the sample size n.

A good mnemonic device to help remember the Central Limit Theorem is X ~ N(miu, sigma-squared/n). Literally it means X, the sample mean is a random variable that has an approximate normal distribution N that can be fully described by two characteristics, miu (the population mean) and sigma-squared/n (the squared of the population standard deviation divided by the sample size).

One of the utility of Central Limit Theorem is to help you establish a framework when estimating population parameters using sample statistics.