AP Statistics: Complete Study Guide
Every topic in the AP Statistics course, organised the way the course teaches it — describing data, probability, sampling, inference, and regression. Free, with worked examples throughout.
Unit 1 — Describing Data
Summarising a dataset before you try to draw conclusions from it. Centre, spread and shape.
Organising data
- Frequency Distribution — turning raw data into a table you can actually read.
- Types of Frequency Distribution — cumulative, relative and bivariate tables.
- Sampling Methods — random, stratified, systematic and cluster sampling, and the bias each one controls for.
Measures of centre
- Mean, Median and Mode — which one to use, and when each misleads.
- Mean and its Types — arithmetic, geometric and harmonic mean.
- Quartiles, Deciles and Percentiles
Measures of spread and shape
- What is Standard Deviation? — the formula, and the n versus n−1 decision that catches everyone.
- What is Variance?
- Quartile Deviation and the Interquartile Range
- Skewness and Kurtosis — why two datasets with identical means and standard deviations can look nothing alike.
- Outlier Detection: IQR and Z-Scores
- Descriptive Statistics: How Data Misleads
Unit 2 — Probability and Distributions
The mathematics of uncertainty, and the named distributions that model it.
Probability foundations
- Sample Space — the vocabulary every later topic depends on.
- Probability with Examples — coins, dice and cards, done properly.
- Dependent, Independent and Conditional Probability
- Bayes’ Theorem and the Base Rate Fallacy — why a 99% accurate test usually gives a false positive.
Random variables and distributions
- Expected Value and Variance of Random Variables
- Binomial Distribution — counting successes in a fixed number of trials.
- Poisson Distribution — counting events when there is no fixed number of trials.
- Normal Distribution and Z-Scores
Practise it properly
Reading statistics and doing statistics are different skills. The Statistics Made Simple Complete Bundle pairs the 246-page textbook with 1,569 practice questions and fully worked answers, 18 companion datasets, and R and Stata workshops.
Unit 3 — Sampling and Estimation
How a sample tells you about a population, and how much to trust it.
- The Central Limit Theorem — the single result that makes inference possible.
- Standard Error vs Standard Deviation — one describes your data, the other describes your estimate.
- Confidence Intervals: What They Are and How to Read Them — the formula, and the “95% confident” trap that catches almost everyone.
Unit 4 — Hypothesis Testing
The largest source of marks in the course, and the largest source of misunderstanding.
- Hypothesis Testing: Step-by-Step Guide — the five steps, applied to worked examples.
- The P-Value Explained — what it means, and the three things it does not.
- Type I and Type II Errors — alpha, beta, power, and the trade-off between them.
- Chi-Square Test — goodness of fit and independence, for categorical data.
- One-Way ANOVA — comparing three or more group means at once.
- t-Tests and Significance in Practice — with the Card–Krueger minimum wage study.
Unit 5 — Relationships Between Variables
Correlation, regression, and the traps that turn a good analysis into a wrong conclusion.
- Basics of Correlation
- Regression in Statistics — least squares, by hand.
- Correlation vs Causation
- Simpson’s Paradox — when the aggregate contradicts every subgroup.
- Index Numbers — Laspeyres, Paasche and base-year effects.
Going Further — Econometrics
Beyond AP Statistics: what regression looks like at undergraduate level.
This hub covers the AP Statistics syllabus and maps closely onto Cambridge A-Level statistics units and IB Mathematics: Applications and Interpretation. For economics topics, see the Complete Content Library. Every guide here is free and updated as the syllabus changes.