Mathematics
The central limit theorem and why averages become normal
Quick fact
The Central Limit Theorem states that the distribution of sample averages from any population with finite variance approaches a normal distribution as the sample size increases, even if the original population is highly skewed, like an exponential distribution, which is why pollsters can estimate election outcomes with just a few thousand respondents.
Why this is interesting
Ever wondered why so many natural and social phenomena—from heights to test scores—show up in the familiar bell curve? The answer lies in a powerful statistical guarantee that turns any messy distribution into a normal one, but only when you take averages.