AP Statistics Study Guide

The course begins with describing data: exploring one variable through shape, center, and spread, and two variables through scatterplots, correlation, and the least-squares regression line $\hat{y}=a+bx$. It then turns to collecting data — the difference between a sample survey, an observational study, and an experiment, and why random sampling and random assignment are what license conclusions in the first place.

The middle of the course builds the probability engine: probability, random variables, and distributions (including the binomial and normal models), then sampling distributions, the crucial idea that a statistic like $\bar{x}$ has its own predictable distribution. The final stretch is inference — confidence intervals and significance tests for proportions, for means, for relationships in categorical data via chi-square, and for the slope of a regression line. Every inference procedure follows the same skeleton: state, check conditions, calculate, conclude in context. Internalize that skeleton and the last units become variations on one theme.

AP Statistics spans nine units, and the College Board specifies the exam weighting as ranges rather than a single fixed split, so treat the following as relative emphasis.

• Exploring One-Variable Data and Exploring Two-Variable Data — together a large share of the exam and the descriptive foundation everything else builds on.
• Collecting Data — central because the validity of every later conclusion depends on study design.
• Probability, Random Variables, and Distributions and Sampling Distributions — the theoretical core that makes inference possible.
• The four inference units — for proportions, means, chi-square categorical data, and regression slopes — collectively the largest emphasis on the exam, especially in free-response.

The takeaway: descriptive statistics and study design are heavily tested early-course skills, but inference is where the most points concentrate, and all four inference units share one reusable structure.

Statistics rewards interpretation and disciplined writing. A routine that works:

1. Master one inference template and reuse it. Identify the procedure, check the conditions, compute the interval or test statistic and $p$-value, then write a conclusion in context. The same four steps cover nearly every inference question.
2. Practice writing conclusions in full sentences. The free-response section grades communication: a correct number with a vague or out-of-context conclusion loses credit.
3. Connect every formula to its picture. Know what a sampling distribution looks like, what a $p$-value represents as an area, and why a wider interval means more confidence. Understanding beats memorizing.
4. Work in mixed sets and review with full solutions. Studying one unit at a time hides the real challenge — deciding which procedure a scenario calls for. Reading a worked explanation for a problem you missed, including why each wrong choice was tempting, is worth more than three problems you already get right.

• Confusing causation with association — only a randomized experiment supports a cause-and-effect claim.
• Misinterpreting confidence and $p$-values: a 95% interval is about the long-run method, not a 95% probability for one interval, and a small $p$-value is evidence against $H_0$, not the probability it is true.
• Skipping the condition checks (random, independence, large enough sample/Normality) that every inference procedure requires.
• Choosing the wrong procedure, such as running a means test on categorical data or mixing up one-sample and two-sample setups.
• Writing conclusions without context — "reject $H_0$" earns little; tying the decision back to the actual population and variable earns the point.

Every unit below has a focused practice set with full written explanations and a rationale for every wrong choice, plus a worked-solutions page you can read straight through. Start with a unit you're shaky on, then take a mixed set across the whole subject to pressure-test whether you can pick the right procedure under time. It's free and needs no account.