Central Limit Theorem
The central limit theorem establishes that when independent events are added the sum tends toward a normal distribution (a bell curve) even if the original variables themselves are not normally distributed.
This provides a way to understand characteristics of a population of data points using only samples taken from that population.
An Example
To see this visually, look at the example below. Random 0s and 1s were generated, and then their means calculated for sample sizes ranging from 1 to 512. Note that as the sample size increases the tails become thinner and the distribution becomes more concentrated around the mean.
BY DANIEL RESENDE - [GITHUB](HTTPS://GITHUB.COM/RESENDEDANIEL/MATH/TREE/MASTER/17-CENTRAL-LIMIT-THEOREM), CC BY-SA 4.0, HTTPS://COMMONS.WIKIMEDIA.ORG/W/INDEX.PHP?CURID=40231947