Press "Enter" to skip to content

The Central Limit Theorem

Mala Mahadevan explains the Central Limit Theorem with an example:

The central limit theorem states that the sampling distribution of the mean of any independent,random variable will be normal or nearly normal, if the sample size is large enough. How large is “large enough”? The answer depends on two factors.

  • Requirements for accuracy. The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required.
  • The shape of the underlying population. The more closely the original population resembles a normal distribution, the fewer sample points will be required. (from

The main use of the sampling distribution is to verify the accuracy of many statistics and population they were based upon.

Read on for an example and to see how to calculate this in T-SQL.