AP Statistics Review Guide: Every Unit with FRQ Strategies

AP Statistics is the AP exam where the math is the easy part and the vocabulary is where students lose points. Readers are looking for specific language in specific places. If you know the four-part template for every inference question and the three conditions to check, the exam turns into a fill-in-the-blanks exercise.

What the exam looks like

3 hours. Section I is 40 multiple choice in 90 minutes. Section II is 6 free response in 90 minutes, one of which is the investigative task (worth about twice as much as a regular FRQ). Calculator allowed throughout, formula sheet provided.

Unit 1: Exploring One-Variable Data

Roughly 15 to 23 percent of the exam, combined with Unit 2. Topics: distributions, center and spread, outliers, boxplots, histograms, z-scores, normal distribution.

Skills. Describe a distribution using SOCS (shape, outliers, center, spread) in context. Compute z-scores and use the empirical rule (68, 95, 99.7). Identify outliers using the 1.5 IQR rule.

Unit 2: Exploring Two-Variable Data

Topics: scatterplots, correlation, linear regression, residuals, influential points, coefficient of determination.

Skills. Compute and interpret r and r-squared. Identify linearity from residual plots (no pattern means linear). Interpret slope and intercept in context. Distinguish correlation from causation in your written answer.

Unit 3: Collecting Data

Roughly 12 to 15 percent. Topics: sampling methods (SRS, stratified, cluster, systematic), experimental design (control, randomization, replication, blinding), observational studies, bias.

Skills. Distinguish an experiment from an observational study (you need random assignment for causation). Identify sources of bias (nonresponse, undercoverage, response bias). Explain why randomization matters.

Unit 4: Probability, Random Variables, and Probability Distributions

Roughly 10 to 20 percent. Topics: probability rules, conditional probability, independence, expected value, variance, binomial and geometric distributions.

Skills. Apply the addition and multiplication rules. Compute expected value as a weighted sum. Recognize a binomial situation (fixed n, two outcomes, independent, constant p). Geometric: trials until the first success.

Unit 5: Sampling Distributions

Topics: sampling distribution of the mean, sampling distribution of the proportion, central limit theorem.

Skills. Standard error of a sample mean equals sigma over sqrt of n. Standard error of a sample proportion equals sqrt of (p(1 minus p) over n). Central limit theorem: if n is large enough, the sampling distribution of the mean is approximately normal regardless of the population shape.

Unit 6: Inference for Categorical Data, Proportions

Roughly 12 to 15 percent. Topics: one-sample z-interval for a proportion, two-sample z-interval and z-test, one-sample z-test for a proportion.

Unit 7: Inference for Quantitative Data, Means

Roughly 10 to 18 percent. Topics: one-sample t-interval and t-test, two-sample t-interval and t-test, matched pairs.

Same four-part template: name the procedure, check conditions, compute, interpret in context. For means, the normal condition is either 'population is normal' or 'n greater than 30' (CLT).

Unit 8: Inference for Categorical Data, Chi-Square

Three types: goodness of fit (one sample compared to expected), independence (one sample, two variables), homogeneity (multiple samples compared).

Skills. Compute expected counts. Chi-square statistic is the sum of (observed minus expected) squared over expected. Degrees of freedom depend on the test type.

Unit 9: Inference for Quantitative Data, Slopes

Topics: inference for the slope of a regression line, confidence interval for slope, t-test for slope.

Skills. The slope has a standard error provided on the computer output. The test statistic is t equals (b minus 0) over SE of b. Degrees of freedom is n minus 2.

The four-part FRQ template

1. Name the procedure in full: one-sample t-interval for the true mean, two-proportion z-test for the difference in proportions, etc.
2. State and check the conditions. Quote the problem for random. Check 10 percent. Check normal.
3. Compute. Show the formula with numbers substituted, then the interval or test statistic and p-value.
4. Interpret in context. Use the words 'we are 95 percent confident' or 'there is convincing evidence at the alpha equals 0.05 level that.'

Common mistakes

• Skipping the condition check. That is always worth a point, sometimes two.
• Using a z-test when you should use a t-test (t when sigma is unknown, which is almost always).
• Writing 'the data' when the question is about the population.
• Confusing Type I and Type II errors. Type I: reject H0 when it is true. Type II: fail to reject H0 when it is false.

Stats is about communication. If you can name the procedure, check the conditions, do the arithmetic, and write an interpretation in context, you are a 5.