Statistics and probability fundamentals

Statistics is the backbone of data science. It is what separates a data scientist from someone who just runs code: the ability to reason about uncertainty, to know when a pattern is real, and to quantify how confident you should be. This chapter builds the intuition you will rely on for the rest of your career.

3.1 Describing data#

3.2 Distributions and the normal curve#

A distribution describes how values are spread. The normal (bell-shaped) distribution appears everywhere, partly because of the Central Limit Theorem: the average of many independent samples tends toward a normal distribution, even when the underlying data is not normal. This is why so much of statistics assumes normality and why sample averages are so well behaved.

3.3 Probability and Bayes#

Probability quantifies uncertainty. The one result every data scientist must internalize is Bayes' theorem, which tells you how to update a belief when new evidence arrives. Its most famous lesson is that base rates matter enormously.

3.4 Inference: from sample to truth#

You almost never see all the data; you see a sample and infer something about the whole. Two ideas carry most of the weight. A confidence interval gives a plausible range for the true value rather than a single point, which is far more honest. And hypothesis testing gives a disciplined way to ask whether an observed difference is likely real or just noise. We cover testing in depth, including p-values, at the intermediate tier; for now, understand that both are about quantifying uncertainty rather than pretending it away.

3.5 Practice#