# AP® Statistics Multiple-Choice Questions

The multiple-choice section of the AP® Statistics exam makes up 50% of the total exam weight. So, scoring well in this section can give you an edge over other students because you can earn solid points for choosing the correct answer.

However, acing the MCQ section of AP Stats can be a little tricky, and you will need a few strategies to score well. In this guide, we will discuss all those key strategies and tricks that will help you analyze the questions, and pick the correct answers faster. This will help you manage your time efficiently on the exam day, so that you can also have some buffer time to revise your answers at the end of Section I.

**Format of AP Statistics MCQ section**

As you may already know, the **MCQ section** represents **50%** of the **composite score** on the AP Statistics exam. It also represents **50% of the total time** spent on the exam. The MCQ section includes **40 questions**, each with five possible options. The relative percentage of questions from each of the nine units of the course are listed below.

Units | Exam Weight |
---|---|

Unit 1: Exploring One-Variable Data |
15 - 23% |

Unit 2: Exploring Two-Variable Data |
5 - 7% |

Unit 3: Collecting Data |
12 - 15% |

Unit 4: Probability, Random Variables & Probability Distributions |
10 - 20% |

Unit 5: Sampling Distributions |
7 - 12% |

Unit 6: Inference for Categorical Data: Proportions |
12 - 15% |

Unit 7: Inference for Quantitative Data: Means |
10 - 18% |

Unit 8: Inference for Categorical Data: Chi-Square |
2 - 5% |

Unit 9: Inference for Quantitative Data: Slopes |
2 - 5% |

## How to Approach AP Statistics Multiple-Choice Questions?

The best way to prepare for the MCQ section is to practice. Beyond learning the material through class or on your own, going through many practice questions will help prepare you for the pace of the exam as well as the types of questions that will show up on the exam. For this reason, the best types of practice questions are high-quality ones that are similar to the types of questions that you will encounter on the AP Statistics exam.

Here are some tips for approaching the individual questions on the MCQ section of the AP Statistics exam:

**Read the question and answer choices thoroughly**The first thing you should do on any MCQ is carefully read the question. Then scan through the answer choices to see what form the answer will be in. For example, sometimes the question will include an integral and the answers will be numbers, requiring you to calculate the result of the integral. Other times, the answers will be in integral notation, so computing the integral will waste time.

**Underline important information**When reading through the question stem, underline things like vocabulary, given values, function definitions, and the actual quantity the question is asking for. This will help you key in on the important aspects of the question. When you hit a vocabulary word, stop and analyze what that means. For example, if the question says “median,” take a moment to think about what that means in calculus, like “dividing place between halves of a dataset,” “center of the dataset,” and so on.

**Eliminate answer choices**Sometimes you can immediately eliminate a choice because it does not fit in with what the question is asking. Cross out any such choices in your test booklet. For example, if the question asks you to interpret a p-value, you can eliminate choices that do not mention a null hypothesis.

**Keep moving**If you do not immediately know how to solve a problem, it’s OK to skip it and come back later. The AP Statistics exam is a timed test. Therefore, it is crucial to not waste time on questions you do not know until you’ve made sure to answer the ones you do know. Fold the corner of the page in your question booklet to mark the pages you need to come back to. You can even mark the ones you answered but aren’t sure of by folding the corner of the page in your question booklet. Then, if there is time, at the end of the exam, revisit all of the pages you marked to either try to answer the question or double-check your answer, unfolding the page corners as you revisit them.

**Read the question again**Sometimes, when you get into the thick of computing things, you tend to forget the gist of the question. Before answering, reread the question to find what you are supposed to calculate (if you underlined, it should be easy to find). Then compare it to help you ensure that you haven’t forgotten the final steps.

**Check before you bubble**Every time you answer a question, compare your answer sheet to the test booklet to make sure you’re answering the right question. This is especially important if you skip a question that you don’t know how to answer, but it is good practice regardless. If your answer sheet gets misaligned with the test booklet, you may end up missing points that you otherwise would have gotten.

## AP Statistics Multiple-Choice Examples

To give you a feel for the types of questions you will encounter on the AP Stats multiple-choice section, here are a few sample exam-like questions you’ll get to see:

A random sample of 200 video game players was selected, and the age of each player was determined. According to the boxplot below, what is the approximate interquartile range (IQR) of the ages?

- 20%
- 25%
- 35%
- 55%
- 60%

**Explanation:**

This is an “**interpret graphs**” question from Unit 1. There are a couple of things to note in this one:

- AP Statistics questions almost always include a context, so you’ll need to carefully read the question and pick out key information. Some information is important, but other information can be irrelevant or misleading. Notice in this question that the sample size (374 United States pennies) is not relevant, and the question can be solved without that information.
**Interpretation of graphs is very important**for statistics and is one of the key skills you will need to master to do well on the exam. You will definitely see a graph on the exam, so make sure you are familiar with each type of graph mentioned in the course.- A box plot is a graph of a distribution of data based on a five-number summary: minimum, first quartile (Q1), median (2nd quartile), third quartile (Q3), and maximum.
- Quartiles divide a distribution into four quarters, each holding about 25% of the data. Consider that quartiles may include outliers (data values outside the whiskers of a boxplot) as part of the distribution.

The interquartile range (IQR) measures the range of the middle 50% of the data in a distribution and is equal to the difference between the 3rd quartile (Q3) and the 1st quartile (Q1).

IQR = Q3 – Q1

On a boxplot, these two values form the outside edges of the “box.” The edges of the given boxplot are approximately 45 (Q3) and 20 (Q1), so the IQR is 45 − 20 = 25.

The approximate IQR of the ages is 25. Therefore, the **correct answer is (b) 25**.

A state is interested in knowing its citizens’ opinions on a proposed tax increase on tobacco-based products. The Department of Health Services surveyed a random sample of citizens whose highest level of education is a high school diploma, a bachelor’s degree, or a graduate degree. A total of 400 citizens responded with their highest level of education and whether they favor or oppose the tax increase. The results are shown in the table below.

Which of the following statements about a randomly chosen person from these 400 citizens is true?

- If a person favors the tax increase, he or she is more likely to have a bachelor’s degree as the highest level of education than to have only a high school diploma.
- If a person opposes the tax increase, he or she is more likely to have a postsecondary (bachelor’s or graduate) degree as the highest educational level than to have only a high school diploma.
- If a person opposes the tax increase, he or she is more likely to have a postsecondary (bachelor’s or graduate) degree as the highest educational level than to have only a high school diploma.
- The person is more likely to have only a high school diploma as the highest educational level than to have a postsecondary degree (bachelor’s or graduate).
- The person is more likely to favor the tax increase than to oppose the tax increase

**Explanation:**

Above is a “**contingency table**” question from Unit 2. Questions focused on contingency tables involve simple calculations and are more focused on concepts. Typically, it involves **navigating the difference between joint relative frequencies** (values in individual cells divided by the table total) and **conditional relative frequencies** (values in individual cells divided by row/column totals). You’ll need to carefully read the question and pick out key terms (“If…, then…”) that indicate particular types of relative frequencies or probabilities.

- The answer choices all require a comparison of the likelihood (probability) of two events from the given table. To find the probability P of an event, use the following formula:

- Analyze the probabilities of each choice to determine which statement is true. If two probabilities have the same number of possible outcomes, it is necessary to compare only the desired outcomes.
- Notice in the “favor” row that there are more people with bachelor’s degrees than with high school diplomas as their highest level of education.
- The number of people with a bachelor’s degree (42) represents a greater proportion of those who favor the tax increase (121) than does the number of people with only a high school diploma (30).

Therefore, **the correct answer choice is (a)**.

An insurance company surveyed each of its 130 employees to determine the proportion who donate to charitable organizations. Which of the following statements is true?

- The data from this survey should not be used because it is an observational study.
- It is necessary to use a confidence interval in order to estimate the proportion of employees who donate to charity.
- It is not necessary to use an inference procedure to determine the proportion of employees who donate to charity because the survey was a census of all employees.
- The result of this survey can be used to prove that working for the company causes employees to donate to charity.
- The sample of employees was not selected randomly, so the survey will not provide useful information.

**Explanation:**

This is a question from Unit 3. **Unit 3 questions** are unique in that they **do not involve calculations**. Instead, the important thing is to interpret the way data collection influences what can and cannot be said about a population. It is critical to know the vocabulary terms for concepts such as sampling methods and experimental designs. Here are a few steps to follow if and when you face questions like this in the exam:

- A population is all the individuals of a specific group (ex. US citizens, customers of an ice cream shop).
- A census collects data from an entire population in order to draw conclusions about the population. So any result from a census also describes the population. There is no need to make inferences about the population.

- It is known that the insurance company surveyed each of its 130 employees, so they conducted a census of all employees.

Therefore, the **statement that is true is (c)**: It is not necessary to use an inference procedure to determine the proportion of employees who donate to charity because the survey was a census of all employees.

A tutoring company prices lessons in groups of 10 lessons. The probability distribution of *X*, the number of lessons sold to a single customer, is summarized in the table below.

X = the number of lessons |
10 | 20 | 30 | 40 | 50 |
---|---|---|---|---|---|

Probability | 0.15 | 0.25 | 0.30 | 0.20 | 0.10 |

The expected value of the probability distribution of *X* is 28.5 and the standard deviation is 11.95. There is a fixed cost of materials and advertising for the lessons. The profit *Y*, in dollars, for a single customer can be predicted by *Y* = 25*X* − 50. What is the standard deviation of *Y* ?

- $248.75
- $298.75
- $348.75
- $662.50
- $700.00

**Explanation:**

**Unit 4 questions** tend to be on the opposite end of the spectrum from Unit 3 questions. These questions, like the one given here, are mostly pure mathematical type questions that you will see on the AP Statistics exam. All of the formulas from Unit 4 can show up on the exam, and there are several things to keep in mind for Unit 4 questions:

- Unit 4 questions allow the
**most creativity**. Typically, they can be solved in many ways. If you find one method that you know doesn’t work, try thinking about the question in another way. - Unit 4 questions are the most mathematical, and they
**require the most practice**. - Unit 4 questions are among the lowest scoring on the test, while Unit 4 also
**represents a large portion**of the test. Try doing as many practice questions as you can in order to be prepared.

Now, let’s try solving this problem with the help of a few pointers:

- A linear transformation of a random variable
*X*is a transformed random variable*Y*formed by multiplying every value of*X*by a constant b and then adding another constant a (*Y = a +bX*). - The standard deviation (SD) of a linearly transformed random variable
*Y*is equal to the SD of the original variable*X*multiplied by the absolute value of the constant b.

- It is given that the profit
*Y*, in dollars, for a single customer can be predicted by the equation*Y*= 25*X*− 50, so*Y*is a linear transformation of*X*with a multiplicative constant of 25. - Plug the value of
*b*(25) and the standard deviation of*X*(*σX*= 11.95) into the formula for the SD of a linear combination and solve for the standard deviation of*Y*(*σY*).

Therefore, **the standard deviation of Y is $298.75**. The correct answer is (b).

### How can I practice AP Statistics multiple-choice questions?

Use a reliable MCQ question bank to take timed practice tests and hone your time-management and precision skills. You can choose from the College Board® 's database of past question papers, as well as UWorld’s AP Statistics Exam Prep for best practice problems and tests. You get a free trial for 7 days. Try it and feel the difference!

## Frequently Asked Questions

### How many multiple-choice questions are there on the AP Stats exam?

There are 40 MCQs on the AP Statistics exam.

### How are the AP Stats multiple-choice questions graded?

The multiple-choice questions are scored by machines. Each question is scored based on whether the selected option is correct or not.

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

The time allotted for the multiple choice section of the AP Statistics exam is 1 hour 30 minutes (total ninety minutes).

### When can I get the AP Statistics past exam multiple-choice questions?

The College Board releases past exam questions where you can download FRQs from.