https://www.statslearn.org Free interactive AP Statistics guides, calculators that show every step, and practice problems with full worked solutions. en-us Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/guides/ap-statistics-cram-sheet https://www.statslearn.org/guides/ap-statistics-cram-sheet A condensed AP Statistics review by unit: the formulas, interpretation templates, condition checklists, exam format, and the classic point-losers. Guide Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/guides/ap-statistics-frq-guide https://www.statslearn.org/guides/ap-statistics-frq-guide Use State, Plan, Do, Conclude to write full-credit AP Statistics inference FRQs: name the parameter, check conditions, show work, and answer in context. Guide Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data Unit 1 covers one-variable data (graphs, center, spread, outliers) plus sampling and study design, at 20-30% of the AP Statistics multiple-choice section. Course unit Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables AP Statistics Unit 2 covers probability rules, random variables, and the binomial and normal distributions, 15-25% of the multiple-choice section. Course unit Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions https://www.statslearn.org/ap-statistics/unit-3-inference-proportions Unit 3 is 15-25% of the AP Statistics multiple-choice section: confidence intervals and significance tests for one and two proportions, plus chi-square tests. Course unit Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-4-inference-means https://www.statslearn.org/ap-statistics/unit-4-inference-means AP Statistics Unit 4 covers inference for means: sampling distributions, the t-distribution, and one-sample, paired, and two-sample t intervals and tests. Course unit Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-5-regression-analysis https://www.statslearn.org/ap-statistics/unit-5-regression-analysis AP Statistics Unit 5 covers scatterplots, correlation, linear regression, and residuals, worth 10-20% of the multiple-choice section. Course unit Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-1-introducing-statistics https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-1-introducing-statistics AP Statistics topic 1.1: how a statistical study uses sample data to answer an investigative question about a population, plus the terms N and n. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-10-investigative-questions-data-collection https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-10-investigative-questions-data-collection AP Statistics topic 1.10: the investigative question, census, experiment, observational study, survey, confounding, and generalizing a sample. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-11-random-sampling https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-11-random-sampling AP Statistics topic 1.11: simple random, stratified, cluster, and systematic sampling, plus sampling with and without replacement, and when each fits. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-12-sampling-problems https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-12-sampling-problems AP Statistics topic 1.12: bias in sampling, including voluntary response, undercoverage, nonresponse, and response bias, and why random selection helps. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-13-experimental-design https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-13-experimental-design AP Statistics topic 1.13: elements of a well-designed experiment, control and blinding, and completely randomized, randomized block, and matched pairs. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-2-variables https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-2-variables AP Statistics topic 1.2: observational units and variables, categorical vs quantitative, discrete vs continuous, and parameter vs statistic explained. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-3-categorical-tables-summary-statistics https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-3-categorical-tables-summary-statistics AP Statistics topic 1.3: frequency and relative frequency tables for one categorical variable, with proportions, percentages, and ratios worked out. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-4-categorical-graphs https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-4-categorical-graphs AP Statistics topic 1.4: bar charts and pie charts for one categorical variable, reading them to justify claims and to compare two or more data sets. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-5-quantitative-graphs https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-5-quantitative-graphs AP Statistics topic 1.5: histograms, stem-and-leaf plots, and dotplots for one quantitative variable, plus how histogram bin width changes the shape. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-6-describing-distributions https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-6-describing-distributions AP Statistics topic 1.6: describing a quantitative distribution by shape, center, spread, and unusual features such as outliers, gaps, and clusters. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-7-summary-statistics https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-7-summary-statistics AP Statistics topic 1.7: mean, median, quartiles, range, IQR, and standard deviation, which measures resist outliers, and the 1.5 IQR outlier rule. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-8-boxplots-and-summary-graphs https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-8-boxplots-and-summary-graphs AP Statistics topic 1.8: the five-number summary and boxplots, modified boxplots for outliers, and reading skew from the mean and the median. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-9-comparing-distributions https://www.statslearn.org/ap-statistics/unit-1-exploring-one-variable-data/1-9-comparing-distributions AP Statistics topic 1.9: comparing distributions of one quantitative variable with graphs and summaries, and z-scores for relative position. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-1-two-way-tables https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-1-two-way-tables AP Statistics topic 2.1 for Fall 2026: two-way tables, side-by-side and segmented bar charts, mosaic plots, and reading them for association. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-10-binomial-distribution https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-10-binomial-distribution AP Statistics topic 2.10 for Fall 2026: what makes a variable binomial, the probability formula, and the mean np and standard deviation root np(1-p). AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-11-normal-distribution https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-11-normal-distribution AP Statistics topic 2.11 for Fall 2026: the normal curve and its two parameters, the standard normal, the empirical rule, and areas as probabilities. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-12-sampling-distributions-clt https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-12-sampling-distributions-clt AP Statistics topic 2.12 for Fall 2026: sampling distributions, simulating them, randomization distributions, and the central limit theorem for a mean. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-2-two-categorical-summary-statistics https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-2-two-categorical-summary-statistics AP Statistics topic 2.2 for Fall 2026: joint, marginal, and conditional relative frequencies from a two-way table, and comparing them for association. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-3-simulation https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-3-simulation AP Statistics topic 2.3 for Fall 2026: estimating probabilities with simulation, long-run relative frequency, and the law of large numbers. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-4-introduction-to-probability https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-4-introduction-to-probability AP Statistics topic 2.4 for Fall 2026: sample space, equally likely outcomes, the 0 to 1 probability scale, and the complement rule for not E. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-5-mutually-exclusive-events https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-5-mutually-exclusive-events AP Statistics topic 2.5 for Fall 2026: joint probability, the intersection of two events, and why mutually exclusive (disjoint) events have P(A and B) = 0. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-6-conditional-probability https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-6-conditional-probability AP Statistics topic 2.6 for Fall 2026: conditional probability P(A given B), the formula with the intersection, and the general multiplication rule. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-7-independent-events-unions https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-7-independent-events-unions AP Statistics topic 2.7 for Fall 2026: independent events, the multiplication rule for independence, and the general addition rule for the union of events. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-8-random-variables https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-8-random-variables AP Statistics topic 2.8 for Fall 2026: discrete random variables, probability distributions whose probabilities sum to 1, and cumulative distributions. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-9-parameters-of-random-variables https://www.statslearn.org/ap-statistics/unit-2-probability-random-variables/2-9-parameters-of-random-variables AP Statistics topic 2.9 for Fall 2026: the mean (expected value) and standard deviation of a discrete random variable, plus interpreting them in context. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-1-estimators https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-1-estimators AP Statistics topic 3.1: learn what makes an estimator unbiased and how a sample proportion works as a point estimate for a population proportion. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-10-confidence-interval-two-proportions https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-10-confidence-interval-two-proportions AP Statistics topic 3.10: build a two-sample z-interval for the difference between two proportions and find its standard error and margin of error. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-11-justifying-claims-two-proportions https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-11-justifying-claims-two-proportions AP Statistics topic 3.11: interpret a confidence interval for the difference between two proportions and use whether it contains 0 to justify a claim. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-12-setting-up-two-proportion-test https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-12-setting-up-two-proportion-test AP Statistics topic 3.12: choose the two-sample z-test for a difference in proportions, write the hypotheses, and check conditions with the pooled p-hat. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-13-carrying-out-two-proportion-test https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-13-carrying-out-two-proportion-test AP Statistics topic 3.13: compute the two-sample z-statistic for two proportions with the pooled standard error, find the p-value, and conclude. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-14-setting-up-chi-square https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-14-setting-up-chi-square AP Statistics topic 3.14: chi-square distributions, choosing between homogeneity and independence, writing hypotheses in words, and checking conditions. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-15-carrying-out-chi-square https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-15-carrying-out-chi-square AP Statistics topic 3.15: calculate expected counts, the chi-square statistic, degrees of freedom, and the p-value for a homogeneity or independence test. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-2-sampling-distribution-sample-proportion https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-2-sampling-distribution-sample-proportion AP Statistics topic 3.2: the mean, standard deviation, and normality conditions for the sampling distribution of a sample proportion p-hat. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-3-confidence-interval-proportion https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-3-confidence-interval-proportion AP Statistics topic 3.3: build a one-sample z-interval for a population proportion, check conditions, and find the standard error and margin of error. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-4-justifying-claims-ci-proportion https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-4-justifying-claims-ci-proportion AP Statistics topic 3.4: interpret a confidence interval for a proportion, justify claims from it, and link sample size, confidence level, and width. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-5-setting-up-test-proportion https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-5-setting-up-test-proportion AP Statistics topic 3.5: choose the one-sample z-test for a proportion, write the null and alternative hypotheses, and verify the three conditions. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-6-p-values https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-6-p-values AP Statistics topic 3.6: what a p-value means, how to find it for one-sided and two-sided tests, and how small p-values give evidence for the alternative. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-7-carrying-out-test-proportion https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-7-carrying-out-test-proportion AP Statistics topic 3.7: compute the one-sample z-statistic for a proportion, find the p-value, compare it to alpha, and state a conclusion in context. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-8-errors-in-testing https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-8-errors-in-testing AP Statistics topic 3.8: Type I and Type II errors, the power of a test, what raises power, and how error consequences shape alpha and sample size. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-9-sampling-distribution-difference-proportions https://www.statslearn.org/ap-statistics/unit-3-inference-proportions/3-9-sampling-distribution-difference-proportions AP Statistics topic 3.9: the mean, standard deviation, and conditions for the sampling distribution of the difference between two sample proportions. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-4-inference-means/4-1-sampling-distribution-sample-mean https://www.statslearn.org/ap-statistics/unit-4-inference-means/4-1-sampling-distribution-sample-mean AP Statistics topic 4.1: find the mean and standard deviation of the sampling distribution of a sample mean, and check when it is approximately normal. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-4-inference-means/4-10-carrying-out-two-sample-test https://www.statslearn.org/ap-statistics/unit-4-inference-means/4-10-carrying-out-two-sample-test AP Statistics topic 4.10: compute the two-sample t-statistic and p-value for a difference of means, compare to alpha, and conclude about the populations. AP topic Tue, 28 Jul 2026 00:00:00 GMT https://www.statslearn.org/ap-statistics/unit-4-inference-means/4-2-confidence-interval-mean https://www.statslearn.org/ap-statistics/unit-4-inference-means/4-2-confidence-interval-mean AP Statistics topic 4.2: describe t-distributions and build a one-sample t-interval for a population mean or mean difference, with conditions and formulas. AP topic Tue, 28 Jul 2026 00:00:00 GMT