Mosaic Plot in AP Statistics

In AP Statistics, a mosaic plot is a graph of two categorical variables where bar widths show the marginal distribution of one variable and segment heights show conditional distributions, so each rectangle's area is proportional to the joint relative frequency of that cell.

What is Mosaic Plot?

A mosaic plot displays the relationship between two categorical variables. The CED (2.1.A.2) lists it alongside side-by-side bar charts and segmented bar charts as a way to show the frequency or relative frequency of each level of one variable for each level of the other.

Here's the easiest way to think about it. A mosaic plot is a segmented bar chart where the bars are allowed to get fat or skinny. Each bar's width shows how big that group is (the marginal distribution). The heights of the segments inside each bar show the conditional distribution of the other variable within that group. Multiply width by height and you get the area of each rectangle, which is proportional to that cell's share of the whole data set. Basically, it's a two-way table turned into a picture where you can see every cell at once.

Why Mosaic Plot matters in AP® Statistics

Mosaic plots live in Topic 2.1 (Tabular and Graphical Representations for the Distributions of Two Categorical Variables) in Unit 2. They support two learning objectives. AP Stats 2.1.A asks you to compare tabular and graphical representations of two categorical variables, and the mosaic plot is one of the three named graphs. AP Stats 2.1.B asks you to justify a claim using those representations (2.1.B.1), which in practice means reading the plot to argue whether an association exists, in context. This skill reaches beyond Unit 2. The same picture of "do the conditional distributions match?" is exactly what a chi-square test checks formally later in the course.

How Mosaic Plot connects across the course

Contingency Table (Unit 2)

A mosaic plot is a two-way table drawn as a map. Every cell in the table becomes a rectangle, and the rectangle's area matches that cell's joint relative frequency. If you can compute row or column percentages from a table, you can read a mosaic plot, and the reverse is true too.

Bar Chart (Units 1-2)

A bar chart shows the distribution of one categorical variable. A mosaic plot stacks a second variable inside each bar and lets bar width carry the group sizes. So you're going from one distribution to many conditional distributions shown side by side.

Chi-Squared Test (Unit 3)

The mosaic plot is the eyeball version of a chi-square test for independence. If the variables were independent, the horizontal dividers would line up straight across every bar. When a rectangle is much bigger or smaller than that "lined-up" picture predicts, that cell is where the observed count differs most from the expected count, and that difference is what the chi-square statistic measures.

Is Mosaic Plot on the AP® Statistics exam?

Mosaic plots appear in multiple-choice questions and FRQs. Typical MCQ stems ask you to do the following:

• Interpret unequal widths. If the first divisions have different widths, the groups of the explanatory variable have different sizes (different marginal proportions). Width says nothing about association by itself.
• Spot association. A stem might say the rectangle for SUVs with severe crashes is larger than expected under independence. That points to an association between vehicle type and crash severity, not proof that one causes the other.
• Compare representations. You may need to match a mosaic plot to a two-way relative frequency table, or choose the true statement comparing mosaic plots and segmented bar graphs.

On the free-response side, 2026 FRQ Q5 asked about a possible association among professional athletes between age-group and type of sport played (basketball, football, baseball). That's the classic setup. To justify a claim (2.1.B), compare the conditional distributions across groups, cite specific proportions, and write your conclusion in context. Saying "the segments don't line up" isn't enough. Name which groups differ and by roughly how much.

Mosaic Plot vs Segmented Bar Chart

Both graphs stack conditional distributions to 100% inside each bar, so the heights mean the same thing. The difference is width. In a segmented bar chart every bar is the same width, so you lose any information about how big each group is. In a mosaic plot bar width is proportional to group size, so you also see the marginal distribution, and rectangle area shows each cell's joint proportion. If a question asks which graph shows how many observations fall in each group, the answer is the mosaic plot.

Key things to remember about Mosaic Plot

• A mosaic plot displays the relationship between two categorical variables, and the CED names it next to side-by-side and segmented bar charts.

• Bar widths show the marginal distribution of one variable, so unequal widths mean the groups have different sizes.

• Segment heights within each bar show the conditional distribution of the second variable for that group.

• The area of each rectangle is proportional to the joint relative frequency of that cell in the two-way table.

• If the horizontal dividers line up across all bars, the variables look independent, and if they shift, there is evidence of an association.

• To justify a claim from a mosaic plot, compare specific conditional proportions across groups and state your conclusion in context, without claiming causation.

Frequently asked questions about Mosaic Plot

What is a mosaic plot in AP Stats?

It's a graph of two categorical variables where bar widths show group sizes (the marginal distribution) and segment heights show conditional distributions. Each rectangle's area is proportional to that cell's share of all observations. It's part of Topic 2.1 and learning objective AP Stats 2.1.A.

Do unequal widths in a mosaic plot mean the variables are associated?

No. Unequal widths only tell you the groups of the first variable have different sizes. Association shows up in the heights, when the conditional distributions differ across bars and the dividers don't line up.

How is a mosaic plot different from a segmented bar chart?

Both show conditional distributions that add to 100% in each bar. A segmented bar chart uses equal-width bars, while a mosaic plot makes each bar's width proportional to group size, so it also displays the marginal distribution and joint proportions.

How do you tell if there's an association from a mosaic plot?

Compare the segment heights across bars. If the conditional proportions are about the same in every group, the variables look independent. If they clearly differ, like a much larger severe-crash rectangle for SUVs than independence would predict, there's evidence of an association.

Are mosaic plots on the AP Statistics exam?

Yes. They appear in multiple-choice questions about reading widths, heights, and associations, and 2026 FRQ Q5 asked about an association between athletes' age-group and type of sport played. You'll need to compare conditional distributions and justify a claim in context.