AP Statistics Study Guide — Complete Review by Unit

AP Statistics covers data analysis and statistical inference across 9 units. About 16% of students score a 5. The exam is 40 MCQs plus 5 short FRQs and 1 investigative task (40% of your score). The investigative task requires you to connect multiple statistical concepts — it's where most 5s are won or lost.

Unit 1: Exploring One-Variable Data (15–23% of exam)

Distributions of quantitative data: shape (symmetric, skewed, bimodal), center (mean vs. median — median resists outliers), and spread (IQR vs. standard deviation). Know how to read and interpret dotplots, histograms, stemplots, and boxplots. Categorical data: bar charts and relative frequency tables. The most tested concept: what happens to mean, median, and standard deviation when an outlier is added or removed.

Unit 2: Exploring Two-Variable Data (5–7% of exam)

Scatterplots, correlation (r), and least-squares regression lines (LSRL). Know how to interpret the slope and y-intercept in context. Residuals = observed − predicted. A residual plot with no pattern confirms the linear model is appropriate. Influential points vs. outliers: an influential point changes the slope when removed; an outlier has a large residual.

Unit 3: Collecting Data (12–15% of exam)

Sampling methods (SRS, stratified, cluster, systematic) and their biases. Experimental design: treatment, control, randomization, blinding. Confounding variables vs. lurking variables. Know why random assignment allows causal conclusions but random sampling only allows generalization. This unit appears frequently in FRQ part (b)s.

Unit 4 & 5: Probability (30–40% of exam combined)

Unit 4: Basic probability rules (complement, addition, multiplication), conditional probability, independence. Unit 5: Random variables (discrete vs. continuous), binomial distribution (n, p, expected value = np, SD = √(np(1−p))), geometric distribution. Normal distribution and z-scores. Central Limit Theorem: the sampling distribution of x̄ is approximately Normal with mean μ and SD σ/√n for large n regardless of population shape.

Units 6–9: Inference (35–45% of exam)

The heart of AP Stats. Confidence intervals and hypothesis tests for means (z and t), proportions (z), difference of means, difference of proportions, chi-square tests (goodness of fit, independence, homogeneity), and slope of LSRL. For every inference procedure, you must: identify conditions (Random, Normal/Large Sample, Independent), show the calculation, and write a conclusion in context.

FRQ Writing Strategy

• Always write conclusions in context. "We reject H₀" is incomplete. "We have sufficient evidence that the mean response time for the new drug is different from the standard drug's mean response time of 30 minutes" earns full credit.
• State and check conditions. Most FRQs require you to verify Random, Normal, and Independent before proceeding. Skipping conditions costs 1–2 points.
• Define parameters before testing. Let μ = the true mean... or p = the true proportion...
• Investigative task: Read carefully — it has 4–5 parts that build on each other. Budget 25 minutes for it.

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