FRQs 1-5 – Free Response

Overview

The AP Stats FRQ section is the second half of the AP Statistics exam, and Questions 1-5 (Part A) give you 65 minutes to answer five free-response questions worth 4 points each. These five questions count for 37.5% of your total exam score, while the sixth question (the Investigative Task) adds the rest of Section II. Unlike multiple-choice, here you have to show full statistical reasoning, not just pick an answer.

Each of the five Part A questions has a predictable focus: Question 1 is data collection, Question 2 is data exploration, Question 3 is probability and sampling distributions, Question 4 is inference, and Question 5 combines two or more skill categories. Most questions have multiple parts (a, b, c, sometimes d) that build on each other. The thing graders reward most is communication. A calculation with no explanation rarely earns full credit.

This guide covers Part A. For the sixth question, see the FRQ 6 Investigative Task guide, and for the first section see the Multiple-Choice Questions guide.

How AP Stats FRQs Are Scored

Each of the five Part A questions is scored from 0 to 4 holistically, and within a question every part gets one of three component ratings: E (essentially correct), P (partially correct), or I (incorrect). This system rewards sound reasoning even when you make a small arithmetic slip, as long as your work shows what you intended.

Your part ratings combine into the 0-4 score for the whole question. A rough guide:

The takeaway: partial credit is everywhere. Showing you know the right procedure and why conditions matter can earn points even on a part you can't finish.

Heads up: starting with the May 2027 exam, AP Statistics moves to a fully digital format with only 4 free-response questions (each worth more), and several topics get removed. None of that applies to the 2025-26 exam, which still has all six FRQs as described here.

How to Answer AP Stats FRQs, Step by Step

Treat each response like a short statistical report. Your reader (the grader) needs to follow your logic from the problem to the answer, so state what you're doing, why, and what your result means in context.

Define and set up before you calculate

For any question involving a random variable, define it in words first. Instead of jumping to P(X > 50), write "Let X = the weight of a randomly selected apple in grams. We need P(X > 50)." That one sentence prevents errors and shows the grader you know what you're computing.

For inference, name your parameter and state hypotheses in both symbols and words. This is where structure earns or loses points.

Check conditions, with work shown

Proper condition checking is one of the biggest score differentiators. Don't just list conditions, show they're met.

For means (confidence intervals and tests), verify random sampling (or random assignment for experiments), the 10% condition if sampling without replacement, and normality (via sample size or the shape of the data). Tie each one to the problem: "The problem states students were randomly selected" proves you found the randomness in context.

For proportions, check random sampling, the 10% condition, and the success/failure condition. Actually compute the numbers: 50(0.3) = 15 and 50(0.7) = 35, both at least 10, so the condition is satisfied.

Use your calculator, but show what you're doing

Let the calculator handle the arithmetic, but write what you're running and the values you put in. Something like "Using 2-PropZTest with x₁ = 45, n₁ = 200, x₂ = 38, n₂ = 180 gives z = 2.34 and p-value = 0.0192." That tells the grader you chose the right procedure and ran it correctly. The calculator does computation; you still do the thinking.

Always conclude in context

This is where points leak away. For a hypothesis test, compare your p-value to α, make a decision about the null, then say what that means for the original question. A p-value of 0.007 with α = 0.05 isn't the answer by itself. Because 0.007 < 0.05, you reject the null and conclude there is convincing evidence of a difference. For a confidence interval, explain what the interval says about the population parameter, not about individual observations.

Attempt every part

Later parts often depend on earlier ones, but you can still earn points on a later part even if your earlier answer was wrong. The build also gives hints. If part (a) wants a scatterplot and part (b) asks about correlation, the question is steering you toward a relationship between the variables. If you're truly stuck, describe what you would do: "I would check normality with a normal probability plot." That shows understanding and can earn partial credit.

What Each AP Stats FRQ Tests

The five Part A questions follow consistent themes, so you can prep for each one.

Question 1: Data Collection

This question focuses on how data is gathered and what conclusions are valid. You might design a study, find a flaw in a given design, or explain what can be concluded.

First, decide whether you're looking at an observational study or an experiment. For experiments, look for random assignment, control, and replication. For sampling, identify the population, the method, and possible bias. Precision in language matters here: random sampling lets you generalize to a population, while random assignment lets you make causal conclusions. They are not the same thing.

Question 2: Exploring Data

These questions ask you to describe distributions, compare groups, or analyze relationships. Decide whether you have one variable (histogram, boxplot, mean/median) or two (scatterplot, correlation, regression). For comparing groups, you'll often use parallel boxplots.

Always comment on shape, center, variability, and unusual features, and use comparative language when you have two groups. Thorough description earns points. Don't just say "skewed right," explain what that tells you about the data, and if there's an outlier, discuss whether it's plausible in context and how it affects your analysis.

Question 3: Probability and Sampling Distributions

You'll calculate probabilities, work with distributions, or describe sampling variability. Identify your random variable (discrete or continuous) and the distribution that applies. For sampling distributions, the statistic (mean, proportion, difference) sets your approach, and you'll often describe shape, center, and spread or use the Central Limit Theorem.

Question 4: Inference

The inference question is the most procedural and rewards a complete, structured response. First decide between a hypothesis test (deciding about a claim) and a confidence interval (estimating a parameter), then identify the parameter to pick the right procedure.

For a hypothesis test, include:

1. Parameter definition and hypotheses (symbols and words)
2. Conditions verified with work shown
3. Test statistic and p-value
4. A decision about the null using the α comparison
5. A conclusion in context

For a confidence interval, include:

1. Parameter definition
2. Conditions verified
3. Calculation showing the critical value and standard error
4. The interval
5. Interpretation in context

The conclusion is where people lose points, so make sure it answers the original question.

Question 5: Multi-Focus

Question 5 deliberately combines two or more skill categories, often telling a story through data. You might explore data, then run inference, or use probability to inform a design decision. Read the whole question first so you see how the parts connect, then show those connections. If part (a) reveals an outlier and part (c) asks for inference, mention how that outlier affects your choice of procedure.

AP Stats FRQ Examples

Here are two examples of the kinds of questions you'll see. On the real exam there are six free-response questions total.

Example (data exploration and inference): A geologist studying lead concentration in soil takes random samples from two regions, A and B, and the histograms show each distribution in parts per million (ppm).

• (A) Write a few sentences comparing the two distributions. A full-credit answer compares shape, center, and variability using comparative language, and notes any unusual features.
• (B) To test whether the mean lead concentration differs between regions, the geologist runs the appropriate test, all conditions are met, and the p-value is 0.007. Is there convincing evidence at α = 0.05 of a difference? Justify your answer. Because 0.007 < 0.05, reject the null hypothesis. There is convincing statistical evidence that the mean lead concentration differs between region A and region B.

Example (probability distribution): Past records show 80% of moviegoers buy something at the snack bar. A random sample of 3 is selected. Let S be the number who make a purchase.

• (A) Complete the probability distribution table for S (the given values are P(0) = 0.008 and P(3) = 0.512). This is a binomial setting, so P(1) = 0.096 and P(2) = 0.384.
• (B) Calculate and interpret the expected value of S. E(S) = 3(0.8) = 2.4, meaning that over many repeated samples of 3 moviegoers, the long-run average number who buy something is 2.4.

Time Management

With 65 minutes for five questions, you average about 13 minutes per question, but not every question needs equal time.

Minutes 0-5: Survey and plan

Skim all five questions. Spot the ones that feel easiest for you and note which require graphs (those eat time) versus which are mostly computational.

Minutes 5-50: Work through the questions

Start where you're most confident. A solid answer on an easy question is worth the same as a struggle through a hard one. Read carefully, plan before writing, and show your work clearly. Exploring-data questions often run 15-16 minutes because of graphing; an efficient inference question might take 10-12.

Minutes 50-65: Review and grab loose points

Return to anything you skipped and add context to any conclusions you rushed. Check that you answered what was actually asked. If you're stuck on a part, write what you would do, define parameters, or name the test you'd use. Those educated attempts add up. Try to cap any single question at about 15 minutes so you reach all five.

Common Mistakes

• Skipping the conclusion in context. A p-value or interval alone isn't a finished answer. State your decision about the null and connect it to the original question, or explain what the interval says about the population parameter.
• Listing conditions without showing work. Naming "success/failure condition" earns nothing on its own. Compute the values, like 50(0.3) = 15 ≥ 10, and tie randomness to the actual wording of the problem.
• Misreading skew from center. When the mean is greater than the median, that typically signals right skew (a few high values pull the mean up), and a mean below the median signals left skew. Mixing these up is a classic, commonly tested error.
• Confusing random sampling with random assignment. Random sampling lets you generalize to a population; random assignment lets you draw causal conclusions. An experiment on volunteers with random assignment can show causation but can't generalize beyond those volunteers.
• Misinterpreting a confidence interval. A 95% CI gives plausible values for the population parameter, not the range where 95% of individuals fall. The interval is about the mean, not single observations.
• Confusing independence with mutual exclusivity, or P(A|B) with P(B|A). These are different ideas, and conditional probability order matters. Define your events clearly so you don't flip them.

Practice and Next Steps

The best prep is timed practice with real scoring. Work through the FRQ practice with instant scoring to see how your responses stack up against the E/P/I rubric, and pull more questions by topic from the FRQ question bank. When you study released questions, don't just check the final number, study the scoring guidelines to see how full-credit responses are structured.

For broader review, the AP Statistics exam page lays out the full exam, and a full-length practice exam lets you rehearse pacing across both sections. Sharpen your written reasoning vocabulary with the key terms glossary, and once you have practice scores, run them through the AP score calculator to see where you stand.