4 The grand exhibit of normality
This chapter covers
- The normal distribution, its properties, and its central role in statistics
- The Empirical Rule, Chebyshev’s theorem, and other tools to understand data spread
- The Central Limit Theorem (CLT) and how it generalizes samples to a normal distribution
The normal distribution is the most famous of probability distributions, and for good reason. When we observe a bell-shaped curve in the frequency of values in our data, we believe the data is normally distributed. The normal distribution generalizes many use cases in statistics and provides powerful tools to infer attributes about a population from a sample. It is foundational to many other techniques in the rest of this book, from confidence intervals to hypothesis testing. We will not only observe the normal distribution in data that naturally follows a bell curve, but we will also discover its relevance to non-normal data through the central limit theorem. This chapter is definitely the turning point, where statistics go from mildly interesting to complete mind pops!