Mathematics
The Central Limit Theorem and Why Averages Behave Predictably
Quick fact
The Central Limit Theorem guarantees that, for any population with a finite variance, the distribution of sample means approaches a normal distribution as sample size (n) grows, regardless of the population's shape—even if the population is heavily skewed or bimodal.
Why this is interesting
You've probably noticed that averages are everywhere—test scores, polls, heights. But have you ever wondered why those averages always seem to follow a familiar bell-shaped curve, even when the underlying data are wildly skewed?