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4 Top Tips for AP Statistics Free-Response Questions

Posted by Christine Sarikas | Apr 9, 2018 12:00:00 PM

Advanced Placement (AP)

 

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The free-response section is usually the most intimidating part of the AP Statistics exam. You’ll need to answer questions with multiple parts, show off your stats skills, and be able to explain each of your answers. However, once you understand the types of questions you'll be asked, the free-response section is actually pretty straightforward.

In this in-depth guide to the AP Statistics free-response section, we go over the types of questions you can expect to see, give sample questions with complete answer explanations, explain how you’ll be graded, and provide tips to help you ace this section of the exam.

 

What’s the Format of AP Statistics Free-Response Section?

On the day of the AP Stats exam, your test will have two sections. First, you will have 90 minutes to answer 40 multiple-choice questions, then you’ll move onto the free-response section. You'll be able to use a graphing calculator for the entire test. For a more in-depth look at exam format and content it tests, check out our complete guide to the AP Stats Exam.

Here's the format of the free-response section:

  • 90 minutes long
  • 5 short-answer questions
  • 1 Investigative Task

The five short-answer questions are meant to each be solved in about 12 minutes, and the Investigative Task is meant to be solved in about 30 minutes. However, you’ll be free to spend as much time on each question as you want (although we recommend sticking close to those guidelines to make sure you don’t run out of time before you get to all the questions).

The free-response section is worth 50% of your total AP Statistics score. For each free-response question, you’ll receive a score from 0 to 4 depending on the accuracy and completeness of your answer. Your Investigative Task score will be scaled so that it’s worth about three times as much as a single short-answer question.

 

AP Stats Free-Response Sample Questions

Below is an example of each of the two types of free-response questions you’ll see on the AP Statistics exam. These questions both come from the 2016 AP Statistics exam. For each question, I’ll go through the answer step-by-step so you can see what a strong answer looks like. I’ll also include what information graders are looking for so you can see exactly where you earn points.

 

Short-Answer Question

There will be five short-answer questions on the AP Stats exam, and each will include several different parts you need to answer. You’re expected to spend about 12 minutes on each short-answer question.

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Part A

To answer this question, you’ll need to analyze the histogram and see what information you can get from it. This can include the distribution of the histogram, its range, and its center. 

From the histogram, you can see that the distribution of Robin’s tip amounts is skewed to the right. The range is from $0 to $22.50, with most tips (47 of them) between $0 and $5. 

You can also see that there’s a gap between the largest tip amount (which is between $20 and $22.50) and the second-largest tip amount (which is between $12.50 and $15). This makes the largest tip amount appear to be an outlier since no other tip amounts are near it.

You can also calculate the median and determine that it is a tip between $2.50 and $5. Additionally, the mean is between $2.62 and $5.13.

Include all these components in your answer.

What the Graders Are Looking For

  • Shape
  • Mention of the outlier
  • Correctly calculating the center (either median or mean)
  • Variability: Mention either the range of the histogram or that most tip amounts are between $0 and $5.
  • Context: Providing the correct numbers/data in the above answers

 

Part B

The mean: If the $8 tip was changed to $18, the effect that would have on the mean is equal to $10/60. (60 because that’s the number of tips included in the histogram, and $10 because that’s how much the tip increased by). $10/60= $⅙ or about 17 cents. So the mean will increase by about 17 cents.

The median: From part a, we already know that the median is between $2.50 and $5. Since both $8 and $18 are greater than the median (and the total number of tips is staying the same), the median would be unchanged.

What the Graders Are Looking For

  • Mentioning the mean will increase
  • Correctly justifying why the mean will increase
  • Mentioning the median will not change
  • Correctly justifying why the median won’t change

 

Investigative Task

The final question on your AP Statistics Exam is the Investigative Task. It’s the most in-depth question on the test, and you should spend about 30 minutes completing it. The Investigative Task will have several parts you need to answer and require multiple statistics skills. 

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There’s a lot going on here, but let’s break the question down and go through it part by part.

 

Part A

This question wants to know if the scatterplot supports the newspaper’s report about number of semesters and starting salary. Looking back at the question, we can see that the newspaper reported that the more semesters needed to complete an academic program at a university, the higher the starting salary for the first year at a job.

Does the scatterplot support this? If it did, we’d see a positive association between starting salary and number of semesters: if one increases, the other would as well.

Looking at the scatterplot, there is a clear positive association between starting salary and number of semesters, so the scatterplot does support the newspaper’s report.

What Graders Are Looking For

  • Mentioning positive correlation
  • Using positive correlation to  justify that the scatterplot supports the newspaper report

 

Part B

There’s a lot of information in the table, but we’re interested in the numbers under the Coef (or coefficient) column since they are what apply to the least-squares regression line.

For y=mx + b, we know that m is the slope and b is the y-intercept. As the constant, we know that 34.018 is b. Therefore, 1.1594 is the slope.

If you want to visualize it better, you can write out y= 1.1594x + 34.018

So the slope of the line is 1.1594. We know that slope is the change in y over the change in x, or, in this case, the change in starting salary over the change in number of semesters. So the slope is telling us how much starting salary changes for each additional semester.

Our slope is 1.1594, but since the units for the y-axis is thousands of euros, we have to multiply the slope by a thousand and add the euros unit. This gives us 1,159.40 euros.

This means that, for every additional semester a program requires, predicted starting salary increases by 1,159.40 euros.

What Graders Are Looking For

  • Correctly identifies the slope is 1.1594
  • Correctly interprets the slope as the change in starting salary for each additional semester
  • The interpretation of the slope includes non-deterministic language, such as “predicted starting salary” or “estimated starting salary” when interpreting the slope

 

Part C

For the next part of the question, we have the same scatterplot, but it has been revised to show three different groups of majors. For part C, we’re looking specifically at business majors, indicated by circles on the scatterplot.

From the scatterplot, we can see that the more semesters a student takes, the lower their starting salary typically is. For example, we can see that a business major who took ten semesters has a lower average starting salary than someone who only took five semesters.

Since as one variable increases the other decreases, that means there is a negative linear association between number of semesters and starting salary for business majors.

What Graders Are Looking For

  • States the association is negative
  • States the association is strong or linear or both
  • Refers to both variables (salary and semesters) in context

 

Part D

For this question you’re being asked to compare the median starting salaries for the three majors. The first step to doing this is finding the median starting salary for each major.

Since there are eight data points for each major, the median will be between the fourth and fifth largest starting salaries for each major. You don’t need to be exact here; you can just eyeball the answer, and sketch in a line to the y-axis if it helps.

For business majors, the fourth-highest salary looks to hit the y-axis around 39 and the fifth-highest salary to be around 37. So the median starting salary for business majors would be about 38,000 euros (remembering the y-axis unit is thousands of euros). Physics majors look to have a starting salary around 48,000 euros, and for chemistry majors the median is around 55,000 euros.

Since you need to compare them, you’d mention that chemistry majors have the highest starting salary, physics majors are in the middle, and business majors have the lowest median starting salary.

What Graders Are Looking For

  • Correctly compares the three majors and which has the highest and which has the lowest median salary
  • Gives reasonable values for the median salaries

 

Part E

How could the newspaper report be improved? Looking at the first scatterplot, it appears as though there is a positive correlation between number of semesters a student takes and their starting salary. We saw this in Part A.

However, in the second scatter plot, which breaks average starting salary down by major, it’s clear that, within a major, there is actually a negative correlation between the number of semesters a student completes and their average starting salary. We saw this in Part C.

We saw in Part D that majors that require more semesters to complete tend to have higher starting salaries (with chemistry having both the highest number of semesters and the highest starting salary). Within a major, students who take more semesters tend to have lower average starting salaries.

The newspaper report should be modified to account for major so that readers can see that majors that require more semesters have higher average starting salaries, but, within a major, students who take a greater number of semesters tend to have lower average starting salaries.

What Graders Are Looking For

  • Must note that there is a negative association for each of the majors
  • Also must note that there is an overall positive association

 

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4 Tips for Solving AP Statistics Free-Response Questions

Below are four of the most helpful tips you can follow to make it easier to score high on the free-response section of the AP Stats test.

 

#1: Always Explain Your Answer

As you could see from the scoring guidelines for the sample questions, your explanation for your answer is often worth at least as much as the correct answer itself. In statistics, using the proper equation isn’t worth much unless you can justify your answer.

This means that you should always include a detailed explanation when asked for it in AP Stats free response. If you’re asked to compare three medians, don’t just solve for the medians and list them; be sure to explain which is largest, which is smallest, and what that means in greater context.

If you skimp on your responses, even if your math is perfect, you’ll end up disappointed with your score.

 

#2: Answer Questions One Part at a Time

The AP Statistics free-response questions can sometimes appear overwhelming, especially the Investigative Task questions which always include many different parts.

Don’t be intimidated by long questions! Just focus on one part of the question at a time. You’ll often discover that the individual parts of a question aren’t that hard to solve on their own; it just looks like a lot at first glance.

Also, while for other AP exams we sometimes recommend skipping around to whichever parts of different questions you feel most comfortable answering, for AP Statistics, we recommend starting at the beginning of each free-response question and methodically working your way through it. The answers you get for earlier parts of the question are often needed to answer later parts, so jumping around could cause you to waste time and end up confused.

 

#3: Know Your Vocabulary

You might think that since AP Stats is a math course, vocabulary won’t be an important part of the test, but you need to know a good amount of vocab to do well on this exam. Confusing right- and left-skewed or random sampling and random allocation, for example, could cause to you to lose lots of points on the exam.

To avoid these types of mistakes, stay on top of any new statistics terms you learn in class throughout the school year. Making flashcards of key vocab and quizzing yourself regularly is a great way to stay up-to-date on new terms. Many AP Stats prep books also include a glossary of important terms you should know.

Before the AP Stats exam, you should know all important vocab words like the back of your hand. Having a general idea isn’t good enough. As we mentioned earlier, a big part of stats is being able to support your answers, and to do this you’ll often need to use stats vocab in your explanations. Just stating the term won’t earn you nearly as many points as being able to explain what the term is and how it supports your answer.

 

#4: Don't Leave the Investigative Task for the End

The Investigative Task is the final question in the AP Statistics free-response section, but we don't recommend saving it for last. Because this question is worth three times as much as any of the other free-response questions, you want to make sure you answer it well, or it could really impact your final score. Leaving this question until the end could mean you run out of time before you answer it.

We recommend answering the Investigative Task question second, after you've completed one of the shorter free-response questions. This ensures you have enough time to complete it. And remember, don't lose track of time on this section! You'll want to spend about 30 minutes on the Investigative Task and about 12 minutes on each of the other questions. When this section starts, write down the times you should wrap up each question if you think this will help you stay on track.

 

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How to Practice AP Statistics Free-Response Questions

The best way to study for the AP Stats Free-Response section is to answer lots of practice free-response questions. Fortunately, the College Board makes this easy to do! On their website, you can find official free-response questions from 1998-2017. This means you have access to dozens of high-quality free-response questions!

Because there are so many AP Stats free-response problems, you can begin completing practice problems a few months into your class (say around November) and continue up until the AP exam. At the beginning of the year, when you’re still learning a lot of the course material, you can read through the questions to find the ones that focus on topics you’ve already covered. In order to get the most of these practice problems, use a timer and give yourself the same timing limitations the real exam will have.

For additional practice question sources for both free-response and multiple-choice questions, check out our guide to every AP Statistics practice test available online.

 

What's Next?

Want more information about the AP Statistics Exam? Check out our in-depth guide to the AP Stats test and learn all about the exam format, what types of questions you'll see, and the topics you need to know to get a great score!

How many AP classes should you take? Get your answer based on your interests and your college goals.

Wondering which other math classes you should take? Math is often the trickiest subject to choose classes for, but our guide will help you figure out exactly which math classes to take for each year of high school.

 

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Christine Sarikas
About the Author

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.



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