# Central Limit Theorem

### Why use it?

The Central Limit Theorem (CLT) is a foundation for parametric hypothesis testing. Understanding this theorem furthers knowledge of how to apply inferential statistics to data.

### What does it do?

The Central Limit Theorem states that the means of random samples drawn from *any* distribution with mean µ and variance σ^{2} will have an approximately normal distribution with a mean equal to µ and a variance equal to σ^{2}/n. The CLT allows the use of confidence intervals, hypothesis testing, DOE, regression analysis, and other analytical techniques on data.

### How do I do it?

Most software packages, such as Minitab^{®} can display data samples from normal distributions in an informative graphic.

**Example:**

The CLT can be better understood by reviewing an example of its application. This example takes samples from a uniform distribution which is a non-normal distribution. Notice that as the sample size n increases, the variation decreases and the sampling distribution tends to look more like the normal distribution.

Non-Normal Distribution

Non-normal Distribution

Non-normal Distribution