AP Statistics Units: Full List

If you are studying AP Statistics, then you likely will have looked at the Course and Exam Description document produced by College Board. Although this is a comprehensive document, it is also over 270 pages long. There are nine units covered in the course. Each one contains a set of topics that you will study throughout the year. In this article, I will summarize the topics covered in each unit to help you organize your studies.

College Board AP Statistics Units

Unit 1: Exploring One-Variable Data

This unit introduces statistics by focusing on one-variable data. You are likely to be familiar with some of these topics already such as summary statistics and statistical graphs. 

However, there is one topic which you are unlikely to have explored previously, the normal distribution. Learning about the normal distribution is fundamental to further studies in a range of subjects such as Psychology and Biology. 

During this unit, you will learn how to:

• Calculate measures of center (mean, median, mode)

• Calculate measures of position (median, quartiles, percentiles)

• Calculate measures of variability (range, standard deviation)

• Identify outliers and skewness

• Use tables to represent categorical data

• Use graphs, such as bar charts, to represent categorical data

• Use graphs, such as histograms, to represent quantitative data

• Calculate and interpret the five-number summary

• Draw and interpret boxplots

• Model data using a normal distribution

• Calculate z-scores using a normal distribution

Unit 2: Exploring Two-Variable Data

This unit expands on the previous one by introducing two variables. You will explore the relationship between two variables using graphs and further statistical measures.

During this unit, you will learn how to:

• Interpret two-way tables

• Calculate relative frequencies and conditional frequencies from two-way tables

• Use graphs, such as mosaic plots, to represent two categorical variables

• Use scatterplots to represent two quantitative variables

• Calculate and interpret correlation coefficients

• Use linear models to predict values of a variable

• Calculate the least-squares regression line

• Calculate and interpret the coefficient of determination

• Linearize bivariate data using logarithms

Unit 3: Collecting Data

This unit gives you the practical skills most needed for your future career. Most organizations collect data regularly. To get the most out of the data, it is important that you use a well-designed survey.  

During this unit, you will learn how to:

• Use random sampling methods such as simple random sampling

• Use non-random sampling methods such as quota sampling

• Discuss the advantages and disadvantages of the different sampling methods

• Identify and explain types of bias

• Explain the features of a well-design experiment

• Use a completely randomized design

• Use randomized blocking and matched pairs designs

Unit 4: Probability, Random Variables, and Probability Distributions

In this unit, you will study how to use probability distributions to find the likelihood of events occurring. You use probability in your day-to-day life, and in this unit you will formalize your understanding of the topic so that it can be applied in more abstract settings.  

During this unit, you will learn how to:

• Estimate probabilities using data and simulations

• Calculate probabilities of single events and combined events

• Identify events that are mutually exclusive or independent

• Calculate conditional probabilities

• Use random variables and their probability distributions

• Calculate the mean and standard deviation of discrete random variables

• Calculate the mean and standard deviation of combined random variables

• Calculate probabilities using a binomial distribution

• Calculate probabilities using a geometric distribution

Unit 5: Sampling Distributions

This is the unit where you learn the foundations needed for making statistical inferences. The main idea is to use statistics from a sample to make predictions about unknown parameters of the population. 

During this unit, you will learn how to:

• Use the Central Limit Theorem

• Calculate unbiased estimates for the population mean and variance

• Describe the sampling distribution for the sample proportions

• Describe the sampling distribution for the sample means

• Describe the sampling distribution for the differences in the sample proportions

• Describe the sampling distribution for the differences in the sample means

Unit 6: Inference for Categorical Data: Proportions

Imagine you are playing a game, and the odds of winning are claimed to be 30%. However, after playing the game 20 times, you have only won 3 times. Does this mean that the stated 30% chance of winning is incorrect? These are the types of questions you will explore while studying this unit. 

During this unit, you will learn how to:

• Find critical values from a normal distribution

• Find p-values using a normal distribution

• Construct a confidence interval for a population proportion

• Set up a test for a population proportion

• Construct a confidence interval for the difference of two population proportions

• Set up a test for the difference of two population proportions

• Justify claims using confidence intervals or conclusions of hypothesis tests

• Identify Type I and Type II errors

Unit 7: Inference for Quantitative Data: Means

This unit is like the previous one, except instead of working with proportions, you will work with means. Imagine you take a random sample of 30 teenagers and calculate the mean time they spend on their phones each day to be 1 hour. You might then want to know what an appropriate interval would be, which is likely to contain the mean time that all teenagers spend on their phones each day. You will learn how to tackle these kinds of investigations. 

During this unit, you will learn how to:

• Find critical values from a t-distribution

• Find p-values using a t-distribution

• Construct a confidence interval for a population mean

• Set up a test for a population mean

• Construct a confidence interval for the difference of two population means

• Set up a test for the difference of two population means

• Justify claims using confidence intervals or conclusions of hypothesis tests

• Set up a paired test for the mean difference of two populations

Unit 8: Inference for Categorical Data: Chi-Square

In this unit, you will learn how to test to see whether a variable can be modeled by a given distribution. You will also learn how to test to see whether there is an association between two variables. To tackle both problems, you will need to study the chi-square distributions. 

During this unit, you will learn how to:

• Find critical values from a chi-square distribution

• Find p-values using a chi-square distribution

• Construct a contingency table for expected frequencies

• Calculate the degrees of freedom for the chi-square distribution

• Set up a goodness of fit test

• Set up a test for homogeneity or independence

• Justify claims using the conclusions of hypothesis tests

Unit 9: Inference for Quantitative Data: Slopes

When working with quantitative bivariate data, it is common to calculate the regression line for a sample. However, if you were to take a different sample, you are likely to get a different regression line. 

In this final topic, you learn how to investigate how the slope of a regression line from a sample can be used to estimate the slope of the regression line if the complete populations were used. 

During this unit, you will learn how to:

• Construct a confidence interval for a slope of a regression model

• Set up a test for a slope of a regression model

• Justify claims using confidence intervals or conclusions of hypothesis tests

What is Covered in the College Board AP Statistics exam?

There are two sections to your exam, the multiple-choice section and the free-response section. Both sections are weighted equally, and you have 90 minutes for each section. Topics from all nine units will be assessed in both sections. The weightings of each unit are shown in the table below.

Below is a two‐column table with 10 rows, including the header row as Row 1:

Section I: Multiple-choice questions

In this section, you will have 90 minutes to answer 40 questions. Each question contains five options to choose from. For some questions, you might be able to work out the answer directly. However, for some others, it might be quicker to eliminate options which you know are incorrect. My best advice to students is to always take a guess, as you have nothing to lose by getting the answer wrong. If you can eliminate one incorrect option, then your chances of guessing correctly go from 20% to 25%. 

Section II: Free-response questions

In this section, you will have 90 minutes to answer six questions. This is split into two parts, Part A and Part B. Part A consists of five questions, and you should spend 65 minutes on this part. Each of these questions is worth 15% of your total score for Section II. Part B has only one question, which is an investigation-style question. This could involve some unfamiliar topics; therefore, you should spend around 25 minutes on this question. It is also worth 25% of the Section II score. My advice would be to do Part B before Part A. If you have any time left, then prioritize checking Part B, as this one question contributes more to your score than any single question in Part A.

Study Resources for College Board AP Statistics

Hopefully, after reading my breakdown of the units above, you now feel ready to start studying for your exams. Here at Save My Exams, we have a set of concise study guides to help you master AP Statistics. The study guides include worked examples so you can see the best methods to use in your exams.

We also have some original, exam-aligned multiple-choice questions for you to practice. These come with student friendly model answers which explain how to arrive at the correct answer as well as the misconceptions which lead to the incorrect answers. Once you feel ready, you can tackle past free-response questions. The marking guidance is included so you can check how many points your answers would have been awarded.

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