AP® Statistics Course And Exam Description
Are you thinking of taking the AP® Statistics exam? If so, this guide is a must-read. Although AP Stats might seem challenging, this article will help you build a strong foundation in the subject and set you up for success at the college level. We are breaking down the course description for AP Statistics to help you understand the course outline, units, topics, and key concepts.
Before we journey through the AP Stats curriculum, let us answer a few questions students often ask about AP Stats:
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Is AP Statistics a one-semester course or a dual-credit course in high school?
The AP Stats course is taught over one high school year and differs from a dual credit course in
high school.What college course is equivalent to the AP Statistics course?
AP Statistics is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. If your college accepts AP Stats scores to offer credit or advanced placement, you will be able to satisfy a credit for non-science majors. However, if you wish to pursue a field where statistics is important, you will usually need to take another introductory course.
How to Navigate AP Statistics: Understanding Units, Topics, and Key Concepts?
The AP Statistics course and exam description1 consists of two main elements: course content and course skills. As you progress through the course content, you will acquire the essential course skills required to pass the AP exam. Combined, these components will prepare you to build a solid foundation in stats and help you succeed in the exam. The course content is further divided into nine units. Each unit is based on the three big ideas that provide the foundation upon which the course is structured.
Before you start planning for the AP Statistics course, it is essential to understand the prerequisites needed to help you grasp the course successfully. As far as prerequisites are concerned, a basic knowledge of second-year Algebra is necessary to take AP Statistics. It would also be beneficial to have a bit of graphical literacy and mathematical reasoning to ease your way through the course.
Use our AP Statistics Exam Guide to explore the exam in detail.
What Are the Three Big Ideas of AP Statistics?
The curriculum for AP Stats involves three key concepts or Big Ideas that provide the foundation for the course. As you progress through the course, you will find that these big ideas spiral into the course units. Let's take a look at what these big ideas are:
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Big Idea 1: Variation And Distribution (VAR)
The first big idea teaches you how statistical methods based on probabilistic reasoning serve as the foundation for understanding this idea of variation.
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Big Idea 2: Patterns And Uncertainty (UNC)
This big idea will help you understand how statistical tools allow us to represent and describe patterns in data and classify departures from patterns. You will also learn to analyze simulation and probabilistic reasoning to anticipate data patterns and determine the likelihood of errors in inference.
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Big Idea 3: Data-Based Predictions, Decisions, And Conclusions (DAT)
The third big idea will teach you how statistical inference allows us to make data-based decisions. You will learn about data-based regression models that describe relationships between variables and serve as a tool for predicting response variable values.
As we will see shortly, these three big ideas are spread across nine units to help students understand each concept as efficiently as possible. As a result, both the big ideas and the course units form a template for the statistics course, similar to many college courses and textbooks.
The Nine Units of AP Statistics and Their Topics
The AP Statistics units contain the course material you'll learn throughout your AP classes. As we discuss each AP Statistics unit, we will also learn about the big ideas incorporated into that unit.
Each of the nine units comes with specific topics you'll learn during your course. Understanding how the AP statistics topics are classified will allow you to concentrate on specific topics in greater depth. It will also assist you in assessing your target areas and weaknesses to determine which unit and topic to focus on during your revision period. We have also included the relative exam weightage for every unit to get all the info in one place.
If you are curious to find detailed information about any particular AP Statistics unit, click on the unit widgets below to know more about them.
Unit 1: Exploring One-Variable Data
Exam Weightage: 15-23 % ｜ Class periods ~ 14-16
Unit 1 introduces students to data and the vocabulary of statistics. Students also learn to talk about data in real-world contexts. Statistics allow us to develop shared understandings of uncertainty and variation. In this unit, students will define and represent categorical and quantitative variables, describe and compare distributions of one-variable data, and interpret statistical calculations to assess claims about individual data points or samples.
As per College Board®, the big ideas explored in this unit are:
- Big Idea 1: Variation and Distribution (VAR) – How can we tell whether differences between measures are random or due to meaningful distinctions?
- Big Idea 2: Patterns and Uncertainty (UNC) – How certain are we that what seems to be a pattern is not just a coincidence?
In this unit, you will learn how to:
- understand a given data set and identify a problem to be solved: Topic 1.1.
- describe data presented numerically or graphically, construct numerical or graphical representations of distributions, and compare distributions within a distribution: Topics 1.2 – 1.6, 1.8 – 1.9.
- interpret statistical calculations and findings to assign meaning or assess a claim: Topics 1.7.
- determine relative frequencies, proportions, or probabilities using simulation or calculations: Topic 1.10
Unit 2: Exploring Two-Variable Data
Exam Weightage: 5-7% ｜ Class periods ~ 10-11
In Unit 2, you’ll learn about the correlation between variables and analyze patterns or randomness. With this training, you’ll be able to calculate and describe statistical values, such as a conditional relative frequency or the slope of a regression line. You’ll learn to use a linear model to predict the values of the response variable from the values of the explanatory variable. Lastly, you’ll be taught to interpret the least-squares regression line in context, analyze prediction errors (residuals), and explore departures from a linear pattern.
According to the College Board, these are the big ideas explored in this unit:
- Big Idea 1: Variation and Distribution (VAR) – Can two or more variables be related within a specific scenario?
- Big Idea 2: Patterns and Uncertainty (UNC) – How might you analyze and represent variables to help describe similarities and/or differences between the two data sets?
- Big Idea 3: Data-Based Predictions, Decisions, and Conclusions (DAT) – How can you determine the effectiveness of a linear model that uses the frequency of a certain event in a dataset to predict a specific phenomenon?
In this unit, you will learn how to:
- identify whether two or more variables can be related or random: Topic 2.1
- represent and identify the relationship between two quantitative variables. You’ll also learn how to read, analyze, and use linear regression models to calculate summary statistics, correlation, predicted response, and departures from linearity: Topics 2.2 – 2.4, 2.6 – 2.7, 2.9
- interpret statistical calculations and findings to assign correlation or assess a claim: Topic 2.5
- understand and analyze the correlation among data presented through the Least Squares Regression Line and assert a claim: Topic 2.8
Unit 3: Collecting Data
Exam Weightage: 12-15% ｜ Class periods ~ 9-10
In this unit, you will learn important principles of sampling and experimental design. You’ll be taught how to collect data and assess it to understand if the data set can be used to generalize findings or establish evidence of causal relationships.
The College Board explains the following big ideas in this unit:
- Big Idea 1: Variation and Distribution (VAR) – What does our data tell us?
- Big Idea 3: Data-Based Predictions, Decisions, and Conclusions (DAT) – Why can the collected data be insufficient to draw conclusions about an entire population?
In this unit, you will learn how to:
- interpret data, identify key information to solve a problem, collect data and approach random sampling. You will also learn how to identify potential problems with random sampling and thereby describe an appropriate method for gathering and representing data: Topics 3.1 – 3.4
- employ experimental design to draw an appropriate conclusion, and select an appropriate experimental design to support your claim: Topics 3.5 – 3.6
- interpret statistical calculations and findings to assign meaning or assess a claim: Topic 3.7
Unit 4: Probability, Random Variables, and Probability Distributions
Exam Weightage: 10-20% ｜ Class periods ~ 18-20
Unit 4 will focus on quantifying the likelihood of random events over the long run and making statistical inferences from that pattern. You will learn to understand simulated or empirical data distributions and fundamental principles of probability to represent, interpret, and calculate parameters for theoretical probability distributions for discrete random variables.
As per College Board, the big ideas explored in this unit are:
- Big Idea 1: Variation and Distribution (VAR) – How can an event be both random and predictable?
- Big Idea 2: Patterns and Uncertainty (UNC) – How do we use probabilistic reasoning to determine the likelihood of certain events?
In this unit, you will learn how to:
- assess the pattern or randomness of an event and to determine relative frequencies, proportions, or probabilities using simulation or calculations: Topics 4.1 – 4.3
- identify and analyze mutually exclusive events, conditional probability, events and unions of events: Topics 4.4 – 4.6
- determine parameters for probability distributions, mean and standard deviation of random variables, and combining random variables to describe probability distributions: Topics 4.7 – 4.9
Unit 5: Sampling Distributions
Exam Weightage: 7-12 % ｜ Class periods ~ 10-12
This unit applies probabilistic reasoning to sampling, introducing you to the ‘Sampling Distributions’ of statistics that you will use in Units 6 and 7. Simulating ‘Sampling Distributions’ will enable you to comprehend how statistics vary in repeated random samplings from populations with known parameters. The normal distribution probabilities are useful for justifying claims about populations that can never be directly measured. Reviewing these properties early in Unit 5 will help you understand why ‘Sampling Distributions’ enable statisticians to approximate parameters for the population of interest.
According to the College Board, the following big ideas are explored in this unit:
- Big Idea 1: Variation and Distribution (VAR) – How likely is it to get a value this large just by chance?
- Big Idea 2: Patterns and Uncertainty (UNC) – How can we anticipate patterns in the values of a statistic from one sample to another?
In this unit, you will learn:
- why do samples of the same data set vary in certain circumstances when collected by different statisticians? You will also revisit the normal distribution: Topics 5.1 – 5.2
- about the central limit theorem and biased and unbiased point estimates. You will be taught to determine parameters for probability distributions and sampling distributions for differences in sample proportions: Topics 5.3 – 5.6
- how to describe and determine sampling distributions for sample means and sampling distributions for differences in sample means: Topics 5.7 – 5.8
Unit 6: Inference for Categorical Data: Proportions
Exam Weightage: 12-15% ｜ Class periods ~ 16-18
Unit 6 is a critical chapter in the course where you will be introduced to ‘Statistical Inference,’ which will continue through the end of the course. You will learn to analyze categorical data to make inferences about ‘Binomial Population Proportions’. You will also be taught to interpret the two types of errors you can make in a significance test, their probabilities, and their possible consequences in context. Unit 6 is an important crux for the AP Statistics course, as you’ll acquire the skills that will be applied repeatedly in units 7 and 8.
The College Board explains the following big ideas in this unit:
- Big Idea 1: Variation and Distribution (VAR) – When can we use a normal distribution to perform inference calculations involving ‘Population Proportions’?
- Big Idea 2: Patterns and Uncertainty (UNC) – How can we narrow the width of a confidence interval?
- Big Idea 3: Data-Based Predictions, Decisions, and Conclusions (DAT) – How can we determine whether the results of a sample can be generalized to the population from which the sample was taken?
In this unit, you will learn how to:
- construct a confidence interval for a Population Proportion and justify a claim based on the confidence interval: Topics 6.1 – 6.3
- set up a test for a Population Proportion, identify null and alternative hypotheses, followed by developing an appropriate inference method for significance tests. You’ll also learn to verify the claim that inference procedures only apply in a given situation: Topic 6.4
- calculate a test statistic and find a p-value, provided conditions for inference are met: Topic 6.5
- conclude a test for a Population Proportion and identify and address potential errors when performing tests: Topics 6.6 – 6.7
- identify an appropriate inference method for confidence intervals for the difference of two proportions and justify a claim based on the confidence intervals: Topics 6.8 – 6.9
- set up and carry out a test for the difference of two Population Proportions: Topics 6.10 – 6.11
Unit 7: Inference for Quantitative Data: Means
Exam Weightage: 10-18% ｜ Class periods ~ 14-16
Unit 7 focuses on means, which shares many similarities with the conditions and procedures for proportions. In this unit, you will learn to analyze quantitative data to make inferences about ‘Population Means’. Since it is easy to confuse t-tests and z-tests, you’ll benefit from reviewing the underlying rationales each time conditions arise. You’ll also be taught to understand how and why conditions for inference with proportions and means are similar and different.
The following big ideas are explored in this unit as per the College Board curriculum:
- Big Idea 1: Variation and Distribution (VAR) – How do we know whether to use a t-test or a z-test for inference with means?
- Big Idea 2: Patterns and Uncertainty (UNC) – How can we make sure that samples are independent?
- Big Idea 3: Data-Based Predictions, Decisions, and Conclusions (DAT) – Why is it inappropriate to accept a hypothesis as true based on the results of statistical inference testing?
In this unit, you will learn how to:
- construct a confidence interval for a population mean and justify a claim about a population mean based on the confidence interval: Topics 7.1 – 7.3
- set up a test for a population mean and carry out a test for a population mean: Topics 7.4 – 7.5
- assess and analyze confidence intervals for the difference of two means and justify a claim about the difference of two means based on a confidence interval: Topics 7.6 – 7.7
- set up a test for the difference between two Population Means and carry out a test for the difference of two Population Means: Topics 7.8 – 7.9
- focus and revise the skills acquired in the previous topics. Skills include selecting, implementing, and communicating inference procedures: Topic 7.10
Unit 8: Inference for Categorical Data: Chi-Square
Exam Weightage: 2-5% ｜ Class periods ~ 10-11
Unit 8 builds on the concept of categorical data that you learned in Unit 6. However, in this unit, you’ll be introduced to chi-square tests, which can be used when there are two or more categories. As a learner, you will aim to assess categorical data and select from a variety of chi-square tests to reach the ‘Inference’. Your problem-solving approach should be similar to what you learned in the previous units: state the hypotheses in words, explicitly identify the correct procedure, verify conditions, calculate the test statistic and the p-value, and then draw a conclusion in a context that is directly linked to the p-value.
The College Board explains the following big ideas in this unit:
- Big Idea 1: Variation and Distribution (VAR) – How does increasing the degrees of freedom influence the shape of the chi-square distribution?
- Big Idea 3: Data-Based Predictions, Decisions, and Conclusions (DAT) – Why is it inappropriate to use statistical inference to justify a claim that there is no association between variables?
In this unit, you will learn how to:
- set up a ‘Chi-Square Goodness of Fit’ test and carry out the test: Topics 8.1 – 8.3
- determine relative frequencies, proportions, or probabilities using simulation or calculations: Topic 8.4
- set up a Chi-Square test for homogeneity or independence and carry out the respective test: Topic 8.5 – 8.6
- focus on the skills acquired: Selecting an appropriate inference procedure for categorical data: Topic 8.7
Unit 9: Inference for Quantitative Data: Slopes
Exam Weightage: 2-5 % ｜ Class periods ~ 7-8
In the concluding unit, you’ll discover that slope variability exists. The focus will be on constructing confidence intervals for and performing significance tests about the slope of a population regression line when appropriate conditions are met.
According to the College Board, these are the big ideas explored in this unit:
- Big Idea 1: Variation and Distribution (VAR) – How can there be variability in slope if the slope statistic is uniquely determined for a line of best fit?
- Big Idea 2: Patterns and Uncertainty (UNC) – When is it appropriate to infer the slope of a population regression line based on sample data?
- Big Idea 3: Data-Based Predictions, Decisions, and Conclusions (DAT) – Why do we not conclude that there is no correlation between two variables based on statistical inference for ‘Slopes’?
In this unit, you will learn how to:
- understand that there is variability in slope: Topic 9.1
- identify and construct confidence intervals for the slope of a Regression Model, and to justify a claim based on a confidence interval: Topics 9.2 – 9.3
- set up and carry out a test for the Slope of a Regression Model: Topics 9.4 – 9.5
- select an appropriate Inference procedure: Topic 9.5
After reviewing the big ideas and key concepts, we are ready to understand the skills you will acquire throughout the AP Statistics course.
Course Skills for AP Statistics
The AP Statistics Course Skills describe what a student should be able to do while learning the AP Statistics concepts. They serve as the foundation for the AP exam tasks. Each unit you learn will embed one or more of these skills and integrate them into the course content and topics. Let's look at what these course skills are.
Skill Category 1: Selecting Statistical Methods
This is the fundamental skill you will learn during the AP Stats course. You will also learn to identify critical information for solving a problem and describe an appropriate method for gathering and representing data.
Skill Category 2: Data Analysis
The second skill you will acquire will enable you to describe data presented numerically or graphically. You'll construct numerical or graphical representations of distributions and calculate summary statistics, relative positions of points within a distribution, correlation, and predicted response. Data analysis enables you to compare distributions or relative positions of points within a distribution.
Skill Category 3: Using Probability and Simulation
You'll learn to determine relative frequencies, proportions, or probabilities using simulation or calculations. Under this skill category, you will also learn to define parameters for probability distribution and describe probability distributions.
Skill Category 4: Statistical Argumentation
For the last skill category, you learn to make an appropriate claim or draw a reasonable conclusion. As you proceed through the units, ‘Statistical Argumentation’ will help you interpret statistical calculations and findings to assign meaning or assess a claim.
As you journey through the course units, remember to apply the skills you learned during your course. Developing a clear understanding of the concepts and mastering the skill of applying those concepts effortlessly is the key to unlocking that 5 on your AP Statistics exam!
References
1(2020). AP® Statistics Course and Exam Description. College Board. Retrieved on February 16, 2024, from https://apcentral.collegeboard.org/media/pdf/ap-statistics-course-and-exam-description.pdf.
Frequently Asked Questions
How many units are there for AP Statistics?
What is the hardest topic in AP Statistics?
According to students who have taken the AP Statistics exam in the past, the most challenging units were
- Unit 4: Probability, Random Variables, and Probability Distributions
- Unit 5: Sampling Distributions