The Central Limit Theorem

The Central Limit Theorem is perhaps the most remarkable result in all of statistics: take any population with a finite mean and variance, repeatedly draw large samples and calculate their average, and the distribution of those averages will be approximately normal — regardless of the original distribution. Whether your data is uniform, exponential, or wildly skewed, the averages will cluster into a perfect bell curve. This is why the normal distribution appears so often in nature: it emerges from the accumulation of many small independent effects.