Central Limit Theorem

This states that whenever a random sample of size n is taken from any distribution with mean "" and variance "" then the sample mean "" will be approximately normally distributed with mean "" and variance "".
This states that the mean of any set of random values from a distribution (with a finite mean and variance) tends to the normal distribution.
The larger the sample size (n) the better the approximation to the normal
Very useful when it comes to inference
This allows us to use hypothesis tests (which assume normality) even when our data does not appear normal.

Lets consider a population that is not normally distributed
Randomly select a sample of 30 from the population and take all the measurements of one particular characteristic and calculate the average value.
If you keep repeating this with different samples of 30 and keep plotting the averages then these will be normally distributed.