AP (Advanced Placement) Statistics is a lot of surface area for one exam: five units in the revised 2026–27 CED, four statistical practices, and a dozen or so inference procedures. A good set of revision notes doesn't try to reproduce a textbook; it distills each unit to what actually gets tested and what students most commonly get wrong.
This guide is that distillation. Every unit gets its big idea, its core concepts, the formulas worth flagging on the reference sheet, and the topics that appear most on recent released exams. If you'd rather work from full worked solutions on real released papers, Cognito's AP Statistics past papers group them by year.
Unit 1: Exploring one-variable data and collecting data (20 to 30 percent)
Big idea: variation and distribution. Real data varies; the first job is to describe how it varies.
Core concepts: mean, median, standard deviation, IQR, range. Shape (skewed, symmetric, bimodal), outliers (1.5 x IQR rule), center, spread. Displays: dotplot, stemplot, histogram, boxplot. Comparing distributions with side-by-side boxplots.
Most tested: SOCS (shape, outliers, center, spread) with context. Never just 'the distribution is skewed left'; always 'the distribution of test scores is skewed left, meaning most students scored high with a few scoring much lower'. Scoring guidelines consistently require context.
Watch for: standardized score (z-score = (value minus mean) / standard deviation) and its interpretation. The Empirical Rule (68-95-99.7) for approximately Normal data.
Unit 5: Regression analysis (10 to 20 percent)
Big idea: quantifying the relationship between two variables.
Core concepts: scatterplot, correlation coefficient r (from -1 to 1), linear regression line y-hat = b0 + b1 x, r-squared, residuals, residual plots, influential points.
Most tested: interpretation of slope in context ('a one-hour increase in study time is associated with a predicted 6.5-point increase in test score'). Interpretation of r-squared in context ('98.3 percent of the variability in test scores is explained by the linear relationship with study hours'). Identifying an outlier or influential point from a scatterplot or residual plot.
Watch for: extrapolation warnings. If a prompt asks you to predict y for an x outside the observed range, note that this is extrapolation and may be unreliable.
Collecting data (now inside Unit 1)
Big idea: how data are collected determines what conclusions you can draw. Random sampling supports generalization; random assignment supports causation.
Core concepts: SRS, stratified, cluster, systematic, convenience. Sampling bias: undercoverage, nonresponse, response bias, wording bias. Experiments vs observational studies. Random assignment, blinding, blocking, placebo, confounding, lurking variables.
Most tested: identifying the sampling method and its likely bias; describing an experimental design with random assignment and blocking; distinguishing when you can and can't make causal claims.
Watch for: the 'to whom can these results be generalized' question. If the sample isn't random, generalization is limited to the sampled population; if there's no random assignment, no causal claim can be made even if the study is well-run.
Unit 2: Probability, random variables and distributions (15 to 25 percent)
Big idea: patterns and uncertainty. Individual outcomes are random; long-run patterns are predictable.
Core concepts: probability of an event, mutually exclusive vs independent, addition rule, multiplication rule, conditional probability P(A given B) = P(A and B) / P(B). Random variables: discrete (expected value, variance, standard deviation), binomial (P(X = k) = (n choose k) p^k (1-p)^(n-k)). Continuous: uniform, Normal.
Most tested: conditional probability from a two-way table, expected value of a described discrete random variable, binomial probability calculations (both for exactly k and for at least k).
Watch for: the difference between mutually exclusive (can't both happen) and independent (one doesn't affect the other). Students confuse them regularly.
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Sampling distributions (introduced alongside inference procedures)
Big idea: what happens to a sample statistic across repeated samples.
Core concepts: sampling distribution of x-bar has mean mu and standard deviation sigma / sqrt(n). Sampling distribution of p-hat has mean p and standard deviation sqrt(p(1-p)/n). Central Limit Theorem: for large enough n, both are approximately Normal.
Most tested: computing the mean and standard deviation of a sampling distribution given population parameters; using the Central Limit Theorem to justify Normal-based reasoning; identifying whether sampling distribution conditions are met.
Watch for: the difference between sigma (population sd, in the sampling distribution formula) and s (sample sd, used when sigma is unknown for inference). Also the shift from z-procedures (when sigma is known) to t-procedures (when sigma is unknown, almost always in practice).
Units 3 and 4: Inference for proportions and means (15 to 25 percent and 10 to 20 percent)
Big idea: data-based predictions. Confidence intervals and significance tests use sample data to make claims about populations.
Core procedures (Unit 3, proportions): one-proportion z-interval and z-test, two-proportion z-interval and z-test, plus chi-square tests for independence and homogeneity. Conditions: random sample, 10 percent, np and n(1-p) at least 10.
Core procedures (Unit 4, means): one-sample t-interval and t-test, two-sample t-interval and t-test, matched pairs (one-sample t on the differences). Conditions: random sample, 10 percent, Normal population or large sample.
Most tested: identifying the correct procedure from wording; running the four-step inference (state, plan, do, conclude) with all conditions and context; interpreting confidence intervals ('we are 95 percent confident that the TRUE mean lies between L and U'); interpreting p-values in context.
Watch for: matched pairs. Students often try to run a two-sample t on paired data, which is wrong. If subjects are the same before and after, or matched between groups, use one-sample t on the differences.
Chi-square (now inside Unit 3)
Big idea: extending inference to categorical data with more than two categories.
Core concepts: chi-square statistic = sum of ((observed minus expected)^2 / expected). Two tests: independence (one sample, two variables, testing association), homogeneity (multiple samples, one response, testing sameness of distribution).
Most tested: identifying which of the two tests applies; computing expected counts; interpreting the p-value in context; noting when expected counts less than 5 make the chi-square approximation questionable.
Watch for: the difference between independence (one sample cross-classified) and homogeneity (multiple samples of a response). The test statistic and formula are identical; the null hypothesis wording differs and rubrics check for both.
Regression analysis (Unit 5 in the revised course)
Big idea: describing and interpreting the linear relationship between two quantitative variables.
Core concepts: scatterplots, the correlation coefficient r, the least-squares regression line, residual plots, r-squared, and interpreting slope and intercept in context. Inference for slope is no longer part of the course.
Most tested: interpreting slope and intercept in context; reading a residual plot to check whether a linear model is appropriate; interpreting r-squared in context.
A high-yield revision habit for AP Stats: for each unit, work through 4 to 6 released FRQs and mark them against the official scoring guidelines. Content-first revision has diminishing returns after the first pass; writing to the rubric is where many of the remaining points come from.
Practice AP Statistics with our past papers
Every recent released AP Statistics paper grouped by year, with worked solutions organized by CED unit so revision can target the topics your practice papers show you missing.
