Throughout the previous articles, we’ve had the chance to examine the normal distribution and its properties. And then we moved forward: we built confidence intervals, conducted hypothesis tests, calculated margins of error. In all these steps, the normal distribution was there, always present, like a quiet thread running through everything.
But there’s a question we may have asked ourselves without yet finding a satisfying answer: why does the normal distribution work so well, even when our data aren’t normal at all? Who said that organic traffic, conversion rates, or session durations follow a bell curve? In most cases, they don’t follow one at all.
The answer lies in one of the most elegant and powerful results in all of mathematics: the Central Limit Theorem (often abbreviated as CLT). It’s the theorem that, in a sense, justifies all of inferential statistics.
Continue reading “The Central Limit Theorem: Why Statistics Works (Even When Data Isn’t Normal)”