AP Statistics Free-Response Section and Its Types
The FRQ section represents 50% of the composite score on the AP Statistics exam. It also represents 50% of the total time spent on the AP Statistics exam. The FRQ section is split into 2 parts. The question types, the skills they require you to apply, and the units from which these questions appear are listed below.
| Question type | Units Covered | Skills Assessed |
|---|---|---|
| 1 multi-part question primarily focuses on collecting data | Unit 3 | Selecting Methods |
| 1 multi-part question primarily focuses on exploring data | Units 1 and 2 | Data Analysis |
| 1 multi-part question, primarily on probability and sampling distributions | Units 4 and 5 | — |
| 1 question with a primary focus on inference | Units 6 - 9 | Statistical Argumentation |
| 1 question on 2 or more skill categories | — | Multiple Skills Assessed |
The second part of the FRQ, Part B, is the investigative task. The purpose of the investigative task is to assess multiple skill categories and content areas, focusing on the application of skills and content in new contexts or in non-routine ways. It is common for the investigative task to include hypothesis tests and other material that would not be included as part of the AP Statistics course but which can be understood by applying the concepts learned in the course.
At least 3 questions from Part A, as well as the investigative task in Part B, will assess statistical argumentation.
AP Statistics FRQ Examples
We will now go over some examples of AP Stats FRQ questions from the 2019 exam to give you an idea of what to expect. However, note that the College Board® provides all this information on its website; we have compiled it here for quick reference.
We have explained each example with two types of answers that can earn you full credit. An essentially correct answer includes all the components of the question, with each component correctly addressed. As a reference, we have also added the ideal solution provided by AP to help you understand the College Board's answer criteria. You can compare the 2 answer categories to identify the components for AP Stats FRQs.
Part A - Question 1 (a)
The sizes, in square feet, of the 20 rooms in a student residence hall at a certain university are summarized in the following histogram.
- Based on the histogram, write a few sentences describing the distribution of room size in the residence hall.
Explanation:
For the sake of ease, we are considering only the first sub-part of Question 1. While solving a question like this, below are a few pointers that will help you:
The intent of this Question
Test your ability to describe features of a distribution using a histogram.
Essentially Correct Answer Includes
An answer to this part of Question 1 is considered "Essentially Correct" if it includes each of these four components detailed by AP.
- The shape is bimodal, OR there are two peaks, OR there are two clusters.
- The center is between 200 and 300 square feet.
The spread is addressed by stating the range, which is a value between 150 and 250 square feet, OR the interquartile range is a value between 50 and 150 square feet, OR all room sizes are between 100 and 350 square feet.
The response includes context.
Ideal Solution provided by AP
The distribution of the sample of room sizes is bimodal and roughly symmetric, with most room sizes falling into two clusters: 100 to 200 square feet and 250 to 350 square feet. The center of the distribution is between 200 and 300 square feet. The range of the distribution is between 150 and 250 square feet. There are no apparent outliers.
*Source: Refer to question 1 of Part A of the 2019 released items from the CollegeBoard Released FRQs
Part B - Investigative Task: Question 6 (a - c)
Emma is moving to a large city and is investigating the typical monthly rental prices of available one-bedroom apartments. She obtained a random sample of rental prices for 50 one-bedroom apartments taken from a website where people voluntarily list available apartments.
Describe the population for which it is appropriate for Emma to generalize the results from her sample. The distribution of the 50 rental prices of the available apartments is shown in the following histogram.
- Emma wants to estimate the typical rental price of a one-bedroom apartment in the city. Based on the distribution shown, what is a disadvantage of using the mean rather than the median as an estimate of the typical rental price?
- Instead of using the sample median as the point estimate for the population median, Emma wants to use an interval estimate. However, computing an interval estimate requires knowing the sampling distribution of the sample median for samples of size 50. Emma has one point, her sample median, in that sampling distribution. Using information about rental prices that are available on the Web site, describe how someone could develop a theoretical sampling distribution of the sample median for samples of size 50.
Explanation:
The intent of this Question
- For (a): Recognize the population to which results from a random sample may be generalized.
- For (b): Describe a disadvantage of using a sample mean rather than a sample median to indicate typical values when the sample distribution is skewed.
- For (c): Describe how the theoretical sampling distribution of the sample median could be constructed.
Essentially Correct Answer Includes
For Parts (a) and (b), the answers are collectively considered “essentially correct” if they include each of these three components detailed by AP.
- In part (a), the correct population (listings of one-bedroom apartments on the website) is identified.
- In part (b), identifying that using the sample mean instead of the sample median overestimates the typical rental price. The disadvantage of using the sample mean that is reported in part (b) is correctly linked to some feature of the distribution (e.g. skewness) that is evident in the histogram.
For part (c), the answer is considered "essentially correct" if it includes both of these components detailed by AP.
- Indicates that Emma would need to obtain every possible sample of 50 one-bedroom apartments.
- Indicates that Emma would need to compute the median rental price for each sample.
Ideal Solution provided by AP
- Part (a): Because random sampling was used, the results of the sample may be generalized to the population of rental prices for one-bedroom apartments in the city that are listed on this particular website at the time the sample was taken.
- Part (b): Because the distribution of the 50 rental prices in the sample is skewed to the right, the sample median provides a better indicator of typical rental prices than the sample mean. Some very large rental prices result in a sample mean that is substantially larger than the more typical rental prices. As a result, the sample mean would overestimate the typical rental price, whereas the sample median would be a more accurate representation of typical rental prices.
- Part (c): To determine the sampling distribution of median rental prices for random samples of 50 one-bedroom apartments from this population, Emma would need to obtain every possible sample of 50 one-bedroom apartments from this website and compute the median of each sample. The collection of all possible sample medians is the theoretical sampling distribution for sample median.
*Source: Refer to question 6 of Part B of the 2019 released items from the CollegeBoard Released FRQs
How To Answer Every AP Statistics FRQ on the Exam Day
Unlike multiple-choice questions, AP Stats FRQ responses require you to show your work and sometimes create graphs. They are scored by AP readers based on the accuracy of the methods and the completeness of the explanations.
FRQs are scored in 2 steps:
- Each part is rated as correct, partially correct, or incorrect.
- Each part is scored from 0 to 4 points, with full credit requiring correctness in all sections.
Hence, the goal is to maximize points with the skills you already have, meaning making smart decisions, managing time, and attempting every part becomes quintessential. Here’s a look at solving each FRQ with precision:
- Identify what the question is asking before you start
Read each part carefully and determine whether you need to calculate, describe, interpret, or justify. This helps you avoid missing key components.
- Show your work clearly and logically
Write out each step of your solution so the grader can follow your process. Even if your final answer is incorrect, clear steps can still earn partial credit.
- Answer in complete, context-based sentences
Your responses should address the problem’s context, not just numbers. This is especially important for interpretations and conclusions.
- Include all required components in your explanation
Many FRQs require multiple elements. For example, when describing a distribution, you may need to mention center, spread, shape, and unusual features.
- Use correct statistical terminology and units
Terms like mean, standard deviation, confidence interval, and proper units help show that you understand the concept and are applying it correctly.
Finally, answer each part fully before moving on, since each part is scored separately. When you follow this structure, your responses become easier to evaluate and more likely to earn full credit. Remember, the goal is to make your reasoning clear, complete, and aligned with what AP readers expect.
Strategy to Mastering AP Statistics FRQs Before the Exam
Before the exam, your focus should be on building the skills needed to think statistically and communicate your reasoning clearly. FRQs are not just about getting the right answer, but about explaining how you arrived at it. Here are some effective strategies to prepare:
- Follow a structured study plan: Practice FRQs across different topics and master them through study guides so you revisit areas like sampling methods, probability, and inference throughout your preparation.
- Practice under timed conditions: Occasionally set a timer so you get used to completing multiple FRQs within the exam’s time limits.
- Strengthen your understanding of key topics: Review official scoring guides to understand what earns full credit and where answers typically fall short.
- Work through a variety of FRQs: Practice different types of questions so you can recognize patterns and know how to approach each one.
- Review scoring guidelines after practicing: Compare your answers with scoring guides or model responses to understand what graders look for in strong FRQ answers.
Consistent practice builds both speed and clarity, which are essential for scoring well on AP Statistics FRQs. The more you work through different question types and review your explanations, the easier it becomes to organize your reasoning and communicate it effectively during the exam. Several students opt for an AP Stats review course to streamline their practice and enhance exam performance.
Where Can You Practice AP Statistics FRQs?
Once you understand how FRQs work and how to approach them, the next step is practicing with high-quality questions that reflect the format and difficulty of the real exam. Practicing with realistic questions helps you strengthen your reasoning, improve your explanations, and get comfortable with multi-step statistical problems.
Here are some reliable places to find AP Statistics FRQ practice.
- Official College Board FRQs: The College Board releases past AP Statistics free response questions along with scoring guidelines and sample responses. These are the most accurate examples of the types of questions you will see on the exam.
- AP Statistics textbooks and classroom materials: Many AP Statistics textbooks include FRQ-style questions at the end of chapters. These help reinforce concepts while giving you practice writing full statistical explanations.
- Teacher-provided practice assignments: Your AP Statistics teacher may share additional FRQ worksheets or past exam questions throughout the year. These are often aligned closely with what you have learned in class.
- Online practice platforms with detailed explanations: Some online AP prep platforms provide large sets of FRQ-style questions along with step-by-step explanations, helping you understand both the correct answer and the reasoning behind it.
Practicing with a mix of official questions and structured practice tools can help you build confidence with FRQs. Platforms like UWorld offer exam-level AP Statistics practice questions, clear explanations, flashcards, and study tools that help you strengthen your statistical reasoning and prepare more effectively for the free response section.
Frequently Asked Questions (FAQ)
Where can I get the AP Statistics past exam FRQs?
How detailed do my explanations need to be on AP Stats FRQs?
References
- AP Statistics Course and Exam Description. (2020). Apcentral.collegeboard.org. Retrieved on December 19, 2024 from https://apcentral.collegeboard.org/media/pdf/ap-statistics-course-and-exam-description.pdf
- AP Statistics. (n.d.). Apcentral.collegeboard.org. Retrieved on December 19, 2024 from https://apstudents.collegeboard.org/courses/ap-statistics/assessment
- AP® Statistics Free-Response Questions. (2019). Apcentral.collegeboard.org. Retrieved on December 19, 2024 from https://apcentral.collegeboard.org/media/pdf/ap19-frq-statistics.pdf
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