AP Statistics (College Board): complete guide to the units, the skills, and the exam

College Board AP Statistics is designed to be the equivalent of a one-semester, introductory, non-calculus-based college statistics course. The course is built on four big ideas (variation and distribution, patterns and uncertainty, data-based predictions, decisions and conclusions, and probability and simulation) and a set of statistical skill categories, and the content is organized into nine units. There is no coursework; describing data, reasoning under uncertainty, and justifying conclusions are examined directly in both sections of the exam. This page is the index: below is a map of the units, the exam structure, and how to study each one. This library covers all nine units in full.

The nine AP Statistics units

The College Board organizes the content into nine units. Each carries an exam weighting (the share of multiple-choice questions it tends to contribute).

Unit 1 Exploring One-Variable Data (15 to 23%)

Variables and their types, displaying categorical data with tables and bar graphs, displaying quantitative data with dotplots, stemplots, and histograms, describing a distribution by shape, center, spread, and unusual features, summary statistics and resistance, boxplots and the outlier rule, comparing distributions, and the normal model with z-scores and the empirical rule.

Unit 2 Exploring Two-Variable Data (5 to 7%)

Association between two variables, two-way tables with joint, marginal, and conditional distributions, scatterplots, correlation, least-squares regression, residuals and residual plots, the coefficient of determination, and transformations for non-linear data.

Unit 3 Collecting Data (12 to 15%)

Sampling methods, observational studies versus experiments, randomisation, bias, and the scope of conclusions.

Unit 4 Probability, Random Variables, and Probability Distributions (10 to 20%)

Basic probability, conditional probability and independence, random variables, and the binomial and geometric distributions.

Unit 5 Sampling Distributions (7 to 12%)

The behavior of sample statistics, the central limit theorem, and sampling distributions of proportions and means.

Unit 6 Inference for Categorical Data: Proportions (12 to 15%)

Confidence intervals and significance tests for one and two proportions.

Unit 7 Inference for Quantitative Data: Means (10 to 18%)

Confidence intervals and significance tests for one and two means using the t distribution.

Unit 8 Inference for Categorical Data: Chi-Square (2 to 5%)

Chi-square tests for goodness of fit, homogeneity, and independence.

Unit 9 Inference for Quantitative Data: Slopes (2 to 5%)

Confidence intervals and significance tests for the slope of a regression line.

Exam structure

The AP Statistics exam is 3 hours and has two equally weighted sections. A graphing calculator is permitted throughout.

• Section I, multiple choice - 40 questions, 1 hour 30 minutes, 50%.
• Section II, free response - 6 questions, 1 hour 30 minutes, 50%. Five shorter questions plus one longer investigative task.

The free-response questions are written from the statistical skill categories, so they ask you to select methods, build and read displays, compute probabilities and statistics, and justify conclusions in context, with the investigative task extending familiar ideas to a new setting.

How to study AP Statistics

AP Statistics rewards clear description, careful reasoning under uncertainty, and justification in context.

1. Work from the Course and Exam Description. Each topic (for example 2.5 Correlation) maps to specific learning objectives and essential knowledge statements that exam questions are written from.
2. Learn the skills, not just the answers. Practice selecting methods, building and reading representations, computing, and justifying conclusions, because the free-response questions are scored on these skills.
3. Describe and compare in context. Describing a distribution (shape, center, spread, unusual features) and comparing distributions with explicitly comparative language are the most heavily rewarded verbal skills in Units 1 and 2.
4. Mind the cautions. Correlation is not causation, the normal model needs approximately normal data, and predictions outside the data range (extrapolation) are unreliable; the exam tests these limits constantly.
5. Use the calculator well, but show the reasoning. The calculator computes statistics, probabilities, and regressions; you must still present setups, check conditions, and interpret results in context.

The units, topic by topic

Each topic has a Course-and-Exam-Description-level answer page with worked exam questions and cross-links, plus an overview guide and quiz. Browse the set at /ap/statistics/syllabus. This library covers all nine units in full:

• Unit 1: introducing statistics: what can we learn from data, the language of variation: variables, representing a categorical variable with tables, representing a categorical variable with graphs, representing a quantitative variable with graphs, describing the distribution of a quantitative variable, summary statistics for a quantitative variable, graphical representations of summary statistics, comparing distributions of a quantitative variable, the normal distribution.
• Unit 2: introducing statistics: are variables related, representing two categorical variables, statistics for two categorical variables, representing the relationship between two quantitative variables, correlation, linear regression models, residuals, least squares regression, analyzing departures from linearity.
• Unit 3: introducing statistics: do the data we collected tell the truth, introduction to planning a study, random sampling and data collection, potential problems with sampling, introduction to experimental design, selecting an experimental design, inference and experiments.
• Unit 4: introducing statistics: random and non-random patterns, estimating probabilities using simulation, introduction to probability, mutually exclusive events, conditional probability, independent events and unions of events, introduction to random variables and probability distributions, mean and standard deviation of random variables, combining random variables, introduction to the binomial distribution, parameters for a binomial distribution, the geometric distribution.
• Unit 5: introducing statistics: why is my sample not like yours, the normal distribution, revisited, the central limit theorem, biased and unbiased point estimates, sampling distributions for sample proportions, sampling distributions for differences in sample proportions, sampling distributions for sample means, sampling distributions for differences in sample means.
• Unit 6: introducing statistics: why be normal?, constructing a confidence interval for a population proportion, justifying a claim based on a confidence interval for a population proportion, setting up a test for a population proportion, interpreting P-values, concluding a test for a population proportion, potential errors when performing tests, confidence intervals for the difference of two proportions, justifying a claim based on a confidence interval for a difference of population proportions, setting up a test for the difference of two population proportions, carrying out a test for the difference of two population proportions.
• Unit 7: introducing statistics: should I worry about error?, constructing a confidence interval for a population mean, justifying a claim about a population mean based on a confidence interval, setting up a test for a population mean, carrying out a test for a population mean, confidence intervals for the difference of two means, justifying a claim about the difference of two means based on a confidence interval, setting up a test for the difference of two population means, carrying out a test for the difference of two population means, selecting, implementing, and communicating inference procedures.
• Unit 8: introducing statistics: are my results unexpected?, setting up a chi-square goodness of fit test, carrying out a chi-square test for goodness of fit, expected counts in two-way tables, setting up a chi-square test for homogeneity or independence, carrying out a chi-square test for homogeneity or independence, selecting an appropriate inference procedure for categorical data.
• Unit 9: introducing statistics: do those points align?, confidence intervals for the slope of a regression model, justifying a claim about the slope of a regression model based on a confidence interval, setting up a test for the slope of a regression model, carrying out a test for the slope of a regression model, selecting an appropriate inference procedure.

For the official Course and Exam Description

The College Board publishes the full Course and Exam Description, released free-response questions, scoring guidelines and sample questions at apcentral.collegeboard.org. Always study from the current Course and Exam Description and the College Board's own released exams, because question style and the statistical skill categories are board-specific.