# AP® Statistics Free Response Questions (FRQs)

AP® Statistics is one of the most versatile College Board® AP exams out there. To score high on this exam, you must make sure to do well in both sections of the exam - the free-response and multiple-choice sections. However, the free-response questions of the AP Stats exam can be a little tricky to ace. But worry not! This guide will discuss key strategies and how to use them to accurately answer the FRQ section. We will also discuss in detail the question types, units, and topics with some FRQ examples.

### Format of AP Statistics FRQ section

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 two parts. The first part, **Part A**, represents **37.5%** of the **composite exam score** and lasts **65 minutes** to answer **five** free-response **questions**. The question types, the skills they require you to apply, and the units from which these questions appear are listed in the table below.

Question type | Units Covered | Skills Assessed |
---|---|---|

One multi-part question primarily focuses on collecting data | Unit 3 | Selecting Methods |

One multi-part question primarily focuses on exploring data | Units 1 and 2 | Data Analysis |

One multipart question, primarily on probability and sampling distributions | Units 4 and 5 | — |

One question with a primary focus on inference | Units 6 - 9 | Statistical Argumentation |

One question on two or more skill categories | — | Multiple Skills Assessed |

The second part of the FRQ, **Part B**, is the investigative task. Part B represents **12.5%** of the **composite score** and lasts for **25 minutes**. 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 three questions from Part A, as well as the investigative task in Part B, will assess statistical argumentation.

## How to Answer AP Statistics FRQs?

Free-response questions, unlike multiple-choice questions, require you to write an answer rather than only select an option for an answer. This means you will need to show your work, including any method you used to arrive at your answer. Sometimes you will even need to create graphs. To really understand how to do well on the FRQs, it helps to know how the FRQs are scored.

Unlike the multiple-choice questions, which are scored by a machine, the free-response questions are scored by college faculty and AP teachers. These ‘AP Readers’ score the FRQs based on the precision of the methods as well as the accuracy and completeness of the results and explanations. This is done in two steps.

First, each part of the question is scored based on whether it meets the criteria for being essentially correct, partially correct, or incorrect. There are typically several components to a complete question that the AP Readers will check. If you check all of the boxes, you will earn an essentially correct answer for that part of the question. Next, each response is categorized based on the scores assigned to each part and awarded a score between 0 and 4 points. For example, it typically takes being essentially correct on all sections or parts of the question to earn 4 points for the overall question.

What does this mean for how you should write free-response questions? Several strategies are important.

### Strategy 1: Explain your answer in detail, but be concise with individual points

To earn full credit, your response to an FRQ must fulfill multiple criteria based on the intention of the question. Checking off those "boxes" should be your objective. This means making your answer detailed and broad, as well as being accurate. But you will not earn more points for devoting a lot of time to an individual component.

For example, an FRQ may require you to describe a distribution in a graph. The criteria for the answer will include such things as (1) center, (2) spread, (3) shape, and (4) unusual features. An answer with four sentences, each tackling one of those components correctly, will earn full credit. However, an answer with five sentences focusing only on 'center’ will have a much lower score.

### Strategy 2: Keep an eye on the clock

Time is an important factor for every AP exam. For Part A of the FRQ section of the AP Stats exam, you will technically have thirteen minutes per question. But you should aim to spend ten to twelve minutes on questions. You will want to check your answers and focus more on more difficult questions, so leaving time left over is best. You will have twenty-five minutes for Part B, which will include multiple parts. You will have 4-5 minutes for each part of that section. This may mean you have to consider a trade-off. If a particular part of a question will take too long to answer and you do not feel confident, it is OK to skip it to avoid running out of time. You do not need a perfect score to earn a 5 on the AP Stats exam, so missing some points is OK if it allows you to earn more points at another point.

### Strategy 3: Use key terms you learned in class and use proper units

The criteria that you need to fulfill in an FRQ answer are often directly related to the key terms you learned in class. Using those terms makes it easier for an AP reader to recognize that you are meeting those criteria.

An important example is the units you use to refer to any statistical data. A common criterion that AP readers look for in answers is that the answer properly refers to the context of the question, and the use of proper units in your answer is important.

### Strategy 4: Answer each part of multi-part questions in order

The parts of a multi-part question on the AP Stats exam often build on one another. Even when the exam does not explicitly state it, the answers to previous parts can often be used to solve later parts. For this reason, try to answer multi-part questions in the order they are presented. This may not always be possible or practical, but it should be your default strategy.

### Strategy 5: Decide beforehand when you want to do Part B (the investigative task)

The last FRQ of the exam is the investigative task in Part B. This question represents a greater percentage of the exam than any FRQ from Part A. You may want to strategize the way you tackle it. If you like getting more difficult and meaningful questions out of the way, you can start working on them before finishing Part A. Doing so may help with time management and getting the most points in the time you have to finish the FRQ section.

But at most, only go over the time meant for Part B (25 minutes) by a couple minutes. While Part B is worth more than the other FRQs, it is not an overwhelming amount. If you have tackled the majority of Part B and are stuck on one part, move back to Part A.

## AP Statistics FRQ Examples

We will now go over some examples of FRQ questions from the 2019 AP Exam to give you an idea of what to expect. However, note that all of this information is provided by the College Board on their website, and we have only compiled them 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 a complete answer with all the components of the question correctly addressed. As a reference, we have also added the **ideal solution provided by AP** to help you understand the answering criteria put forward by the College Board. You can compare the two answer categories to identify the components for AP Stats FRQs.

Present all of your work. You will be graded on the accuracy and completeness of your results and explanations, as well as the correctness of your techniques, so make sure to clearly indicate these.

### 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.

(a) 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:

**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 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.

(a) 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.

(b) 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?

(c) 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:

**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 question 6 of Part B of the 2019 released items from the CollegeBoard Released FRQs

### How can I practice AP Statistics free-response questions?

The most effective way to practice AP Statistics free-response questions is to use the FRQ sections of past exams for practice runs. Pay particular attention to what you need to do to stay within the time allotted for the exam. Once you have finished a practice run, grade your answers yourself using the scoring guidelines provided by the College Board.

## Frequently Asked Questions (FAQ)

### How many FRQs are there on the AP Statistics exam?

There are five free-response questions included with Part A and one free-response question included with Part B. However, several FRQs contain multiple parts.

### How are AP Statistics FRQs graded?

The FRQ section constitutes 50% of the AP Statistics exam. The FRQs are graded by AP readers based on the correctness of the methods as well as the accuracy and completeness of the results and explanations.

### How long is the FRQ section of the AP Statistics exam?

The total time allotted for the FRQ section of the AP Statistics is 90 minutes, split between Part A (65 minutes) and Part B (25 minutes).

### Where can I get the AP Statistics past exam FRQs?

The College Board releases past exam questions where you can download FRQs from. In addition, you can download scoring guidelines, sample responses from exam takers, and scoring distributions.