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# Statistics Free Response Questions

john le

⏱️ June 11, 2020

📅⌨️

The one thing you need to know about these FRQs:

 Show all your work no matter what and leave your answer in context of the question!

## Overview of the AP Stats Free Response Questions

Section II of the AP Exam includes six free response questions. Set A of the FRQs (questions 1-5, 75% of Section II Score) assesses you on different skills for the AP Exam. Set B of the FRQs (Question 6, 25% of Section II Score) is the investigative task which focuses on multiple skills and content areas, requiring you to apply that knowledge to the multiple-part question in new contexts or non-routine ways.

 💡 For 2020 OnlyThere will only be two FRQs on this online exam, one question that weighs 55% of your score and the other weighing 45%. Both questions will assess you on multiple skills/concepts alike. There will be no investigative task this year.

The FRQs are designed to test your knowledge of statistics, and your ability to apply multiple skills and concepts in a question. There are four AP Stats skills that are tested on the exam.

Skills for AP Statistics:

• Skill 1: Selecting Statistical Methods (15-23% of exam)

• Skill 2: Data Analysis (15-23% of exam)

• Skill 3: Using Probability and Simulation (30-40% of exam)

• Skill 4: Statistical Argumentation (25-35% of exam)

All skills are based on the units you have learned in AP Statistics, and you have worked throughout the year to develop your argumentation and statistics skills to write FRQs with these skills.

The FRQs will test any knowledge from these AP Statistics units:

• Unit 1: Exploring One-Variable Data

• Unit 2: Exploring Two-Variable Data

• Unit 3: Collecting Data

• Unit 4: Probability, Random Variables, and Probability Distributions

• Unit 5: Sampling Distributions

• Unit 6: Inference for Categorical Data- Population

• Unit 7: Inference for Quantitative Data- Means

• Unit 8: Inference for Categorical Data- Chi Squared

• Unit 9: Inference for Quantitative Data- Slopes

Numbers 1-5 will test the following skills:

• One question will test skills associated with  collecting data

• One question will test skills associated with exploring data

• One question will test skills associated with probability and sampling distributions

• One question will test skills associated with inference skills

• One question will test 2 or more skill categories

 For 2020 OnlyUnits 8 and 9 will not be tested for the 2020 exam.

The total amount of time you will have on this section of the AP Statistics exam is 90 minutes, or one hour and 30 minutes. To break it down by section:

1 hour and 5 min. (Questions #1-5) + 25 min. (Question #6) = 1 hour and 30 min.

 For 2020 OnlySince there are only two FRQs, the timing is not the same. For question 1, you will have 25 minutes to respond and 5 minutes to submit your answer online. For question 2, you will have 15 minutes to respond and 5 minutes to submit your answer online. You will not be able to return to Question 1 after it is finished.

## How to Rock the FRQs - Rubric

The FRQ scoring for this AP Exam is different from other exams. Each question part will be based on ratings: essentially correct, partially correct, and incorrect. Depending on your rankings, each question will receive a score from 1-4.

Ratings

Essentially Correct: You have answered this part correctly showing all work.

Partially Correct: You were able to show the correct skill/content that was asked for, but one or two parts of your process were incorrect.

Incorrect: You did not show enough work or your answer did not align with the goal of the question.

After each part is rated, they will convert their ratings on a scale of 1-4. This depends on how many parts there are to each question, and varies for each question. Here is an example of how ratings are converted to scores from Question 1 of the 2018 AP Statistics Exam.

 For 2020 OnlyThere have been no changes to this rubric for the exam, so be sure to know how you will be graded to maximize your score.

## How to Rock the FRQs - The Process

Normally, the best way to rock the FRQ section of the AP Statistics exams is to tackle the questions in the following order:

1. Complete Number 1. This is generally an easier question in terms of difficulty and you can maximize points and “warm up” by completing this question first.

2. Read the prompts for 2-5 and identify any clear inference procedure questions. These are pretty predictable and you have likely seen questions like this more recently and practiced more questions like this. Again, you can maximize points by doing this problem.

3. Tackle the Investigative Task. Don’t spend too much time stressing on it, but you should spend about 25-30 minutes on this task at this point. Since this is worth a huge portion of this section of the exam, it can’t be skipped and needs to be answered to the best of your ability.

4. Fill in any gaps from 2-5. Expect to see a question on probability, designing studies along with some multi-skill tasks.

 For 2020 OnlyYou will not be able to jump back and forth from each question like an in-person exam. Be prepared to tackle the first question right away!

### Before you start writing

Because the FRQs will assess you on multiple skills and concepts, it’s important to pay attention to key verbs that the question has. In the AP Statistics Course/Exam Description, they have provided a list of verbs that are most common on the FRQ questions.

Verbs on the AP Statistics FRQs:

• Calculate: You will need to perform mathematical calculations to arrive at your final answer. Another way they may word this very is to ask to find “how many”, “how likely”, and etc.

• Compare: You will provide an explanation of similarities/differences. This often requires the same prompts as “describe” but involves doing it twice since there are two data sets.

• Construct/Complete: You will construct the data in a graphical/numerical manner.

• Describe: You will provide an explanation of any patterns you see in the data.

• Determine: You will provide a calculation or explanation of something the question wants to determine, such as “Is there evidence?”, “Does the data support?” and etc.

• Estimate: You will find an approximation of values for a function.

• Explain: You will use evidence/reasoning for a supposed claim, providing information on how or why this outcome/situation occurs.

• Give a point estimate or interval estimate: You will use models/representations to find approximate values for uncertain figures.

• Give examples: You will provide a specific example in the context of the question.

• Identify/Indicate/Circle: You will circle or indicate where a specific piece of information is based on the data or question.

• Interpret: You will be asked to provide context for a mathematical representation considering units also.

• Justify: Similar to explain, you will be providing evidence to support the answer you calculated

• Verify: You will most likely confirm a test is applicable to this problem, or test conditions for a given statistical test.

 For 2020 OnlyYou should spend about 2-3 minutes per question to find these key verbs. It’s important you know what the question is asking you to do so you don’t lose points or drop down ratings.

The very first thing you should do with any FRQ is to be sure you understand the question. Highlight or take note of anything the question is asking you to do, and potentially write down what tests or formulas you may need to use to help support your answer. If you are given a table or graph, be sure to take note of what is being measured and any relevant information that may be important for tests you will conduct. It is also valuable to identify if the data is categorical or quantitative. This can be found by seeing if we are dealing with proportions or means. This has huge implications as you work out the problem in terms of calculating test statistics (z or t score), how you check normality (Large Counts or Central Limit Theorem) and effects the outcomes of your response in several ways.

Example:

Tumbleweed, commonly found in the western United States, is the dried structure of certain plants that are blown by the wind. Kochia, a type of plant that turns into tumbleweed at the end of the summer, is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. Scientists are concerned that kochia plants are becoming resistant to the most commonly used herbicide, glyphosate. In 2014, 19.7 percent of 61 randomly selected kochia plants were resistant to glyphosate. In 2017, 38.5 percent of 52 randomly selected kochia plants were resistant to glyphosate. Do the data provide convincing statistical evidence, at the level of a = 0.05, that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate?

In 2014, 19.7 percent of 61 randomly selected kochia plants were resistant to glyphosate. In 2017, 38.5 percent of 52 randomly selected kochia plants were resistant to glyphosate.- This is the data that will help you construct your answer.

 Year % Resistant to Glyphosate Sample Size 2014 19.7% 61 2017 38.5% 52

Do the data provide convincing statistical evidence, at the level of a = 0.05, that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate? Let’s break down this question.

Verbs used= “provide consistent statistical evidence”. This indicates you will be performing some sort of statistical test.

You are given that alpha=0.05, so you will be performing a hypothesis test. Since you are given two years of data and comparing if there has been an increase in the proportion of all kochia plants resistant to glyphosate, you will be performing a Two-Proportion Z-Test.

Answering the FRQ

There are three important things you must ALWAYS do when answering the FRQs: define your variables , show your work, and put your answer in context.

Your FRQ score depends on how much work you show. It’s important to communicate to the reader that not only do you know the concepts and skills being tested, but also how you got to your answer and the depth of statistical knowledge you hold. Defining your variables is important to help provide context to the reader and your argument, and is essential in every rating a scorer provides.

Answer your questions chronologically, because one step of the FRQ may depend on an answer you had calculated earlier. Write any formulas/concepts/acronyms down that may help you answer the question, and show each step. Even if you messed up on a step, you may still be able to get partial credit because you followed through with your work! In addition, It’s important you know important calculator functions to help you calculate your answers. The most common functions on a graphing calculator are “stat”, and “dist” (2nd>>Distr), where you will be able to find functions to help calculate your answer. Answer each question to your best ability and explain your answer with complete sentences and thoughts if needed!

 For 2020 OnlyRemember, you have the formula sheet you can use for the AP Exam! Be sure to label formulas and what context they are used in. Write down any acronyms you have learned throughout the school year to help you answer specific questions. It’s important that you are able to communicate what you are doing to the reader through formulas, explanations, and more.

When you finish the question, it’s time to move on to the next question. Six FRQs seem like a lot, but if you are smart with how you tackle the questions and the information provided, you are on track to get a great score on the exam!

## Sample AP Stats FRQs

Here is a quick sample of numbers 1 and 2 from the 2017 exam. More past exam questions can be found with the links below.

STATISTICS SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam.

Percent of Section II score—75%

Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

1. Researchers studying a pack of gray wolves in North America collected data on the length x, in meters, from nose to tip of tail, and the weight y, in kilograms, of the wolves. A scatterplot of weight versus length revealed a relationship between the two variables described as positive, linear, and strong.

(a) For the situation described above, explain what is meant by each of the following words.

(i) Positive:

(ii) Linear:

(iii) Strong:

The data collected from the wolves were used to create the least-squares equation yˆ = -16.46 + 35.02x

(b) Interpret the meaning of the slope of the least-squares regression line in context.

(c) One wolf in the pack with a length of 1.4 meters had a residual of -9.67 kilograms. What was the weight of the wolf?

2. The manager of a local fast-food restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling the cup with water. The manager selected a random sample of 80 customers who asked for a water cup when placing an order and found that 23 of those customers filled the cup with a soft drink from the beverage fountain.

• (a) Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain.

• (b) The manager estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant \$0.25. Suppose that in the month of June 3,000 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink.

2016 AP Stats FRQs

2017 AP Stats FRQs

2018 AP Stats FRQs

2019 AP Stats FRQs

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