AP Statistics:
Study Guide
AP is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this
product.
,Key Exam Details
The AP® Statistics course is equivalent to a first-semester, college-level class in statistics. The 3-
hour, end-of-course exam is comprised of 46 questions, including 40 multiple-choice questions
(50% of the exam) and 6 free-response questions (50% of the exam).
The exam covers the following course content categories:
• Exploring One-Variable Data: 15%‒23% of test questions
• Exploring Two-Variable Data: 5%‒7% of test questions
• Collecting Data: 12%‒15% of test questions
• Probability, Random Variables, and Probability Distributions: 10%‒20% of test questions
• Sampling Distributions: 7%‒12% of test questions
• Inference for Categorical Data: Proportions: 12%‒15% of test questions
• Inference for Quantitative Data: Means: 10%‒18% of test questions
• Inference for Categorical Data: Chi-Square: 2%‒5% of test questions
• Inference for Quantitative Data: Slopes: 2%‒5% of test questions
This guide will offer an overview of the main tested subjects, along with sample AP multiple-
choice questions that look like the questions you’ll see on test day.
Exploring One-Variable Data
On your AP exam, 15‒23% of questions will fall under the topic of Exploring One-Variable Data.
Variables and Frequency Tables
A variable is a characteristic or quantity that potentially differs between individuals in a group.
A categorical variable is one that that classifies an individual by group or category, while a
quantitative variable takes on a numerical value that can be measured.
1
, Examples of Variables
Categorical variables The country in which a product is manufactured
The political party with which a person is affiliated
The color of a car
Quantitative variables The height, in inches, of a person
The number of red cars that pass through an intersection in a day
It is important to recognize that it is possible for a categorical variable to look,
superficially, like a number. For example, despite being composed of numbers, a zip code is
categorical data. It does not represent any quantity or count; rather, it’s simply a label for a
location.
Quantitative variables can be further classified as discrete or continuous. A discrete
variable can take on only countably many values. The number of possible values is either finite
or countably infinite. In contrast, a continuous variable can take on uncountably many values.
An important characteristic of a continuous variable is that between any two possible values
another value can be found.
Graphs for Categorical Variables
A categorical variable can be represented in a frequency table, which shows how many
individual items in a population fall into each category. For example, suppose a student was
interested in which color of car is most popular. He collects data from the parking lot at school,
and his results are shown in the following frequency table:
Color Frequency
Black 14
Red 6
Blue 5
Silver 11
White 6
Green 3
Yellow 1
Grey 4
2
, A relative frequency table gives the proportion of the total that is accounted for by each
category. For example, in the previous data, 14 of the 50 cars, or 28%, were black. The full
relative frequency table is as follows:
Color Relative Frequency
Black 28%
Red 12%
Blue 10%
Silver 22%
White 12%
Green 6%
Yellow 2%
Grey 8%
Note that the percentages add up to 100%, since all of the cars were of one of the colors
represented in the table.
A bar chart is a graph that represents the frequencies, or relative frequencies, of a
categorical variable. The categories are organized along a horizontal axis, with a bar rising
above each category. The height of the bar corresponds to the number of observations of that
category. The vertical axis may be labeled with frequencies or with relative frequencies, as in
the following examples.
A bar chart representing data from more than one set is useful for comparing the
frequencies across the sets. For example, suppose that the day after collecting the initial data
on car colors, the student collected the same information from a parking lot at a nearby school.
The results can be compared using the following bar chart, which shows the relative
frequencies for each color, separated by school:
3
Study Guide
AP is a registered trademark of College Board, which was not involved in the production of, and does not endorse, this
product.
,Key Exam Details
The AP® Statistics course is equivalent to a first-semester, college-level class in statistics. The 3-
hour, end-of-course exam is comprised of 46 questions, including 40 multiple-choice questions
(50% of the exam) and 6 free-response questions (50% of the exam).
The exam covers the following course content categories:
• Exploring One-Variable Data: 15%‒23% of test questions
• Exploring Two-Variable Data: 5%‒7% of test questions
• Collecting Data: 12%‒15% of test questions
• Probability, Random Variables, and Probability Distributions: 10%‒20% of test questions
• Sampling Distributions: 7%‒12% of test questions
• Inference for Categorical Data: Proportions: 12%‒15% of test questions
• Inference for Quantitative Data: Means: 10%‒18% of test questions
• Inference for Categorical Data: Chi-Square: 2%‒5% of test questions
• Inference for Quantitative Data: Slopes: 2%‒5% of test questions
This guide will offer an overview of the main tested subjects, along with sample AP multiple-
choice questions that look like the questions you’ll see on test day.
Exploring One-Variable Data
On your AP exam, 15‒23% of questions will fall under the topic of Exploring One-Variable Data.
Variables and Frequency Tables
A variable is a characteristic or quantity that potentially differs between individuals in a group.
A categorical variable is one that that classifies an individual by group or category, while a
quantitative variable takes on a numerical value that can be measured.
1
, Examples of Variables
Categorical variables The country in which a product is manufactured
The political party with which a person is affiliated
The color of a car
Quantitative variables The height, in inches, of a person
The number of red cars that pass through an intersection in a day
It is important to recognize that it is possible for a categorical variable to look,
superficially, like a number. For example, despite being composed of numbers, a zip code is
categorical data. It does not represent any quantity or count; rather, it’s simply a label for a
location.
Quantitative variables can be further classified as discrete or continuous. A discrete
variable can take on only countably many values. The number of possible values is either finite
or countably infinite. In contrast, a continuous variable can take on uncountably many values.
An important characteristic of a continuous variable is that between any two possible values
another value can be found.
Graphs for Categorical Variables
A categorical variable can be represented in a frequency table, which shows how many
individual items in a population fall into each category. For example, suppose a student was
interested in which color of car is most popular. He collects data from the parking lot at school,
and his results are shown in the following frequency table:
Color Frequency
Black 14
Red 6
Blue 5
Silver 11
White 6
Green 3
Yellow 1
Grey 4
2
, A relative frequency table gives the proportion of the total that is accounted for by each
category. For example, in the previous data, 14 of the 50 cars, or 28%, were black. The full
relative frequency table is as follows:
Color Relative Frequency
Black 28%
Red 12%
Blue 10%
Silver 22%
White 12%
Green 6%
Yellow 2%
Grey 8%
Note that the percentages add up to 100%, since all of the cars were of one of the colors
represented in the table.
A bar chart is a graph that represents the frequencies, or relative frequencies, of a
categorical variable. The categories are organized along a horizontal axis, with a bar rising
above each category. The height of the bar corresponds to the number of observations of that
category. The vertical axis may be labeled with frequencies or with relative frequencies, as in
the following examples.
A bar chart representing data from more than one set is useful for comparing the
frequencies across the sets. For example, suppose that the day after collecting the initial data
on car colors, the student collected the same information from a parking lot at a nearby school.
The results can be compared using the following bar chart, which shows the relative
frequencies for each color, separated by school:
3
