AP Statistics Practice Questions by Unit — 2026 Review Guide

Describing distributions using shape, center, spread, and outliers (SOCS). Calculating and interpreting mean, median, standard deviation, IQR, and percentiles. Identifying and calculating outliers using the 1.5 × IQR rule. Understanding the effect of transformations (adding a constant, multiplying by a constant) on summary statistics.

Describing distributions without context — saying "the distribution is skewed right" earns less credit than "the distribution of exam scores is skewed right, meaning most students scored relatively low with a few very high scores." Forgetting that adding a constant shifts center and position measures but does not change spread measures like standard deviation and IQR.

Practice writing full distribution descriptions using SOCS every time you look at a graph. For transformations, build a reference table: what changes and what stays the same when you add a constant vs. multiply by a constant.

Interpreting the slope and y-intercept of a regression line in context. Calculating and interpreting residuals (residual = observed − predicted). Using r and r² — correlation coefficient and coefficient of determination — and interpreting what each means about the relationship. Identifying influential points and outliers in regression.

Interpreting the y-intercept without acknowledging whether x = 0 is meaningful in context. Confusing r and r² — r describes the direction and strength of the linear relationship; r² describes the proportion of variation in y explained by the linear relationship with x. Saying correlation implies causation.

Practice writing slope and intercept interpretations in full sentences with context every time. Memorize the residual formula and what a positive vs. negative residual means. Know the properties of r: it has no units, it is between −1 and 1, and it is sensitive to outliers.

Sampling methods — simple random sample, stratified random sample, cluster sample, systematic sample — and the advantages of each. Sources of bias — voluntary response bias, undercoverage, nonresponse bias. Experimental design components — control group, treatment group, random assignment, blinding, blocking. The distinction between observational studies and experiments and what conclusions each allows.

Confusing random sampling (who is selected) with random assignment (how subjects are assigned to treatments) — only random assignment allows causal conclusions. Identifying a sampling method without explaining why it was used or what bias it addresses. Not distinguishing between what an observational study can conclude (association) vs. what an experiment can conclude (causation).

Know all four sampling methods well enough to describe and critique them. For experiments, memorize the four principles: control, randomization, replication, and blocking. Practice writing conclusions that match the study design — observational studies show association, experiments can show causation.

Basic probability rules — addition rule, multiplication rule for independent and dependent events, complement rule. Conditional probability using P(A|B) = P(A and B) / P(B). Expected value and standard deviation of a random variable. Binomial distribution — conditions (BINS: Binary, Independent, fixed Number of trials, Same probability), calculating probabilities, mean, and standard deviation. Geometric distribution — expected number of trials until first success.

Checking binomial conditions without explaining them in context — you must verify each of the four BINS conditions specifically for the problem at hand. Confusing independence and mutual exclusivity — two events cannot be both mutually exclusive and independent (unless one has probability zero). Calculator syntax errors on binompdf vs. binomcdf.

Practice identifying which distribution applies to a given scenario before calculating anything. For binomial problems, write out all four BINS conditions explicitly every time — this is a common FRQ scoring point. Know when to use binompdf (exactly k successes) vs. binomcdf (at most k successes).

The Central Limit Theorem — for large enough samples, the sampling distribution of the sample mean is approximately normal regardless of the population distribution. The mean and standard deviation of sampling distributions for both means and proportions. Using sampling distributions to calculate probabilities about sample statistics.

Confusing the standard deviation of the population with the standard error of the sampling distribution — the standard error is σ/√n for means and √(p(1−p)/n) for proportions. Not checking conditions for normality before applying normal calculations. Confusing what the sampling distribution describes — it describes the behavior of a statistic across many samples, not the distribution of individual data values.

Understand the Central Limit Theorem conceptually before doing calculations — be able to explain in plain language what a sampling distribution is and why it matters. Practice calculating standard error for both means and proportions and interpreting what it represents.

Constructing and interpreting one-sample z-intervals for proportions. Conducting and interpreting one-sample z-tests for proportions. Two-sample inference — confidence intervals and hypothesis tests comparing two proportions. Checking conditions for inference: random, normal (np ≥ 10 and n(1−p) ≥ 10), and independent (10% condition).

Writing incorrect confidence interval interpretations — the correct form is "We are 95% confident that the true proportion of [context] is between [lower] and [upper]." Not checking all three conditions before performing inference. Confusing the null and alternative hypotheses — the null hypothesis always contains equality.

Memorize the correct interpretation templates for confidence intervals and hypothesis tests and practice writing them in context until they are automatic. Checking conditions is worth explicit scoring points on the FRQ — never skip them. Practice the full four-step inference procedure: State, Plan, Do, Conclude.

One-sample t-intervals and t-tests — when to use t instead of z (unknown population standard deviation), degrees of freedom (n − 1), and checking conditions. Two-sample t-procedures — comparing means from two independent groups. Paired t-procedures — when observations are naturally paired, using the differences as the data.

Using z-procedures when t-procedures are required — whenever the population standard deviation is unknown (which is almost always in practice), use t. Confusing two-sample t-procedures with paired t-procedures — if the data is paired (before/after, matched subjects), you must use the paired procedure. Degrees of freedom errors when doing two-sample t by hand.

Build a decision tree for choosing the right procedure: one sample or two? Paired or independent? Mean or proportion? This decision-making process is tested both directly and as part of FRQ setup. Practice the full four-step procedure for both intervals and tests.

Chi-square goodness of fit test — does observed data match an expected distribution? Chi-square test for homogeneity — do two or more populations have the same distribution of a categorical variable? Chi-square test for independence — are two categorical variables independent within a single population? Calculating expected counts and the chi-square statistic. Checking the expected counts condition (all expected counts ≥ 5).

Choosing the wrong chi-square test — homogeneity involves multiple populations with one categorical variable; independence involves one population with two categorical variables. The calculation is identical but the conclusion and context differ. Not checking the expected counts condition before proceeding.

Know the distinction between all three chi-square tests and practice identifying which one applies to a given scenario. For the FRQ, always state hypotheses in terms of the specific context — not just "the variables are independent" but "there is no association between [variable 1] and [variable 2] in the population of [context]."

Constructing a confidence interval for the true slope β. Conducting a t-test for the slope — the null hypothesis is typically H₀: β = 0 (no linear relationship). Reading computer output for regression inference — identifying the slope, standard error of the slope, t-statistic, and p-value from a regression table. Checking conditions for regression inference: Linear, Independent, Normal, Equal variance, Random (LINER).

Not knowing how to read a computer regression output table — the exam frequently provides output and asks you to use it rather than calculate from raw data. Forgetting that the null hypothesis for slope inference is β = 0, not β = 1. Not checking LINER conditions.

Practice reading and interpreting computer regression output — identify the slope estimate, its standard error, the t-statistic, and the p-value and know what each means. Know the LINER conditions and how to check each one from a residual plot.