Study guide

AP Statistics

Turn data into conclusions you can actually defend — one concept at a time.

AP Statistics is the practice of drawing honest conclusions from data you can never see all of. Across the course you learn to describe data, design studies that produce trustworthy evidence, model randomness with probability, and — the part exams reward most — use a single sample to say something confident about a whole population through confidence intervals and significance tests. Each explainer below gives you the definition, the one formula or procedure that matters, a worked example, and the mistake that quietly costs points. Everything here is free to read, no account needed.

Topic explainers

Each one gives you the definition, the formula that matters, a worked example, and the classic mistake.

• Confidence Intervals for a ProportionA confidence interval for a proportion turns a single sample percentage into a plausible range for the true population proportion, plus a statement of how confident you are that the range captured it.
• Sampling DistributionsA sampling distribution is the distribution of a statistic — like a sample mean or sample proportion — across every possible sample of a given size, and it's what lets you judge how far one sample might land from the truth.
• Chi-Square TestsChi-square tests compare the counts you actually observed in categories against the counts you'd expect under a hypothesis, measuring whether the mismatch is bigger than chance alone would produce.
• Least-Squares RegressionA least-squares regression line is the single straight line that makes the total squared vertical distance from the data points as small as possible — the best linear summary of how one quantity moves with another.
• Conditional ProbabilityConditional probability is the chance of one event given that another has already happened — it's how you update a probability once you learn something new.
• Significance Tests for a ProportionA significance test for a proportion weighs sample evidence against a claim about a population proportion, asking whether the result you saw would be surprising if the claim were true.
• Interpreting P-ValuesA p-value is the probability of getting evidence at least as extreme as your sample if the null hypothesis were true — a small p-value means your data would be surprising under the null.

Free-response walkthroughs

Original exam-style prompts with a model response and the scoring logic — what earns each point and why.

• Significance Test for a Proportion — FRQ Walkthrough
• Confidence Interval for a Proportion — FRQ Walkthrough
• Chi-Square Test of Independence — FRQ Walkthrough
• Interpreting Regression Output — FRQ Walkthrough