AP Statistics Notes — All 9 Units

AP Statistics is built around four major themes: exploring data, sampling and experimentation, anticipating patterns (probability), and statistical inference. The FRQ section rewards complete, correctly-reasoned justifications — not just correct numbers.

Unit 1: Exploring One-Variable Data

Categorical vs. quantitative variables. Distributions: shape (symmetric, skewed left/right, bimodal), center (mean vs. median), spread (range, IQR, standard deviation). Outliers: 1.5×IQR rule. Normal distribution: z-scores, empirical rule (68-95-99.7%). Dotplots, histograms, stemplots, boxplots.

Unit 2: Exploring Two-Variable Data

Scatterplots: direction, form, strength. Correlation r (no causation!). Least-squares regression line ŷ = a + bx (slope b = r·(sy/sx)), residuals, residual plots for checking linearity, coefficient of determination r².

Units 3–4: Data Collection

Sampling methods: SRS, stratified, cluster, systematic — and why each matters for bias. Observational study vs. experiment. Experimental design: random assignment, control group, blinding, blocking. Why only experiments can establish causation.

Unit 5: Probability

Basic probability rules, complement, addition rule, multiplication rule (independent vs. dependent events), conditional probability P(A|B). Discrete random variables: expected value E(X) = Σx·P(x), variance. Binomial distribution: B(n, p), mean = np, SD = √(np(1−p)). Geometric distribution.

Unit 6: Sampling Distributions

Central Limit Theorem: x̄ is approximately normal for large n regardless of population shape. Standard error of x̄ = σ/√n. Sampling distribution of p̂: mean = p, SE = √(p(1−p)/n).

Units 7–9: Inference

Confidence intervals: estimate ± margin of error = estimate ± z*(SE) or t*(SE). Hypothesis testing: H₀ vs. Hₐ, test statistic, p-value, conclusion in context (reject or fail to reject H₀). Type I error (false positive, α) vs. Type II error (false negative, β). Tests: one-proportion z, two-proportion z, one-sample t, two-sample t, paired t, chi-square (GOF, independence, homogeneity), linear regression t-test.

The AP Stats FRQ golden rule: always state your conclusion in context of the problem — "There is convincing evidence that the mean..." not just "reject H₀."

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