Central Limit Theorem
” The distribution of an average tends to be Normal, even when the distribution from which the average is computed is decidedly non-Normal “.
“Thus, the Central Limit theorem is the foundation for many statistical procedures, including Quality Control Charts, because the distribution of the phenomenon under study does not have to be Normal because it’s average will be.”
From Charles Annis’ page on the central limit theorem
A nice simple illustration of the distribution of the means of samples of 2, 3, 4 and so on for a variable drawn from a uniform distribution with an animated gif at the bottom of the page to make the point.