AP Statistics Practice Quiz: Representing Two Categorical Variables
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 11 questions to check your progress.
Question 1 of 11
All Questions (11)
A) Segmented bar graph
B) Mosaic plot
C) Two-way table
D) Side-by-side bar graph
Correct Answer: C
A two-way table, also known as a contingency table, is a numerical representation that summarizes two categorical variables using frequencies or relative frequencies. The other options are graphical representations.
A) A cell frequency divided by its row total.
B) A cell frequency divided by its column total.
C) A row total divided by the table total.
D) A cell frequency divided by the total for the entire table.
Correct Answer: D
The definition of a joint relative frequency is a specific cell's frequency divided by the grand total for the entire two-way table.
A) A histogram
B) A scatterplot
C) A side-by-side bar graph
D) A stem-and-leaf plot
Correct Answer: C
Side-by-side, segmented, and mosaic bar graphs are used for representing the relationship between two categorical variables. Histograms, scatterplots, and stem-and-leaf plots are used for quantitative data.
A) To show the shape and spread of a single variable's distribution.
B) To compare the distributions of one variable across the categories of another or to determine if there is an association between them.
C) To calculate the exact frequencies and joint relative frequencies for each cell.
D) To identify outliers and influential points in a bivariate relationship.
Correct Answer: B
According to the provided content, graphical representations of two categorical variables are used to compare distributions or to determine if there is an association between the variables.
A) 0.125
B) 0.25
C) 0.875
D) It cannot be determined without the full table.
Correct Answer: A
A joint relative frequency is the cell frequency (25 seniors who drive) divided by the total for the entire table (200 students). Therefore, the calculation is 25 / 200 = 0.125.
A) A two-way table provides exact frequencies, while a segmented bar graph visually compares conditional distributions.
B) Both representations are numerical and show the exact count in each category.
C) A segmented bar graph is a numerical summary, while a two-way table is a graphical summary.
D) Both representations are graphical and are primarily used to show the shape of the data.
Correct Answer: A
A two-way table is a numerical representation that summarizes data with frequencies or relative frequencies. A segmented bar graph is a graphical representation used to compare distributions, which helps in visually assessing potential associations.
A) Two quantitative variables
B) One quantitative and one categorical variable
C) Two categorical variables
D) A single categorical variable
Correct Answer: C
The provided content explicitly states that a two-way table (contingency table) is used to summarize two categorical variables.
A) Frequencies are counts, while relative frequencies are proportions or percentages of a total.
B) Frequencies are used for graphical displays, while relative frequencies are used for numerical summaries.
C) Frequencies can only be used when there are two categories for each variable, while relative frequencies can be used for any number of categories.
D) There is no difference; the terms are interchangeable.
Correct Answer: A
A frequency is a raw count of occurrences within a category. A relative frequency is that count expressed as a proportion or percentage of a total (e.g., cell total, row total, or grand total).
A) All bars for all categories are of the same height.
B) The total number of observations is large.
C) The pattern of bar heights (representing the distribution of one variable) is different across the categories of the other variable.
D) The x-axis and y-axis have the same scale.
Correct Answer: C
An association between two categorical variables exists if the distribution of one variable changes across the categories of the other. In a side-by-side bar graph, this would be visually represented by different patterns of bar heights for each group being compared. If the patterns were the same, it would suggest the variables are independent.
A) Convert the table to joint relative frequencies and create a scatterplot.
B) Calculate conditional relative frequencies (e.g., by region) from the table and create a segmented bar graph.
C) Use the raw frequencies to create a histogram for each region.
D) Sum the row and column totals to create a single bar graph.
Correct Answer: B
A two-way table provides the numerical summary. To compare distributions graphically, one would use a display like a segmented or side-by-side bar graph. These graphs are most effective when they display conditional relative frequencies, which show the proportion of one variable's categories within a category of the other variable.
A) Dot plot
B) Box plot
C) Mosaic bar graph
D) Frequency polygon
Correct Answer: C
The provided content explicitly lists side-by-side, segmented, and mosaic bar graphs as graphical representations used for two categorical variables. The other options are typically used for quantitative data or a single categorical variable.