A mosaic plot is a graph that displays the relationship between two categorical variables using rectangles whose areas are proportional to the frequency of each combination, so unequal rectangle widths or heights across groups signal a possible association.
A mosaic plot takes a two-way (contingency) table and turns it into a picture. Each rectangle represents one combination of categories, and the area of each rectangle is proportional to how many observations fall in that combination. The widths of the columns usually show how big each group is overall, and the heights within each column show the conditional proportions for the second variable.
Here's the intuition that makes it click. A mosaic plot is basically a segmented bar chart where the bar widths also carry information. In a segmented bar chart, every bar is the same width no matter how many people are in that group. A mosaic plot fixes that by making bigger groups wider. If the variables are unrelated, the rectangles line up in a neat grid because every group has roughly the same breakdown. If the variables are associated, the segments shift around and the grid looks uneven. That visual unevenness is your clue that something other than randomness might be going on.
Mosaic plots live in Unit 2 (Exploring Two-Variable Data), Topic 2.1, supporting learning objective 2.1.A, which asks you to identify questions about possible relationships in data. The essential knowledge behind that objective is a big deal in AP Stats: apparent patterns and associations in data may be random or not. A mosaic plot is one of the first tools you get for spotting a possible association between two categorical variables before any formal inference. It also sets up Unit 8, because the question a mosaic plot raises visually ("are these variables associated?") is exactly the question a chi-square test for independence answers formally. For the bigger picture of how Topic 2.1 frames relationships in data, check the 2.1 Introducing Statistics: Are Variables Related? study guide.
Keep studying AP Statistics Unit 2
Contingency Table (Unit 2)
A mosaic plot is a contingency table drawn as a picture. Every rectangle in the plot corresponds to one cell in the two-way table, and the rectangle's area matches that cell's count or proportion. If you can read one, you can read the other.
Chi-Squared Test (Unit 8)
The mosaic plot asks the question, and the chi-square test for independence answers it. An uneven mosaic suggests an association; the chi-square test tells you whether that pattern is too big to blame on random chance.
Bar Chart (Unit 1)
A bar chart handles one categorical variable, while a mosaic plot handles two. Stacking and proportioning the bars is what upgrades a simple bar chart into a two-variable display.
Categorical Data (Unit 1)
Mosaic plots only work for categorical variables. If both variables are quantitative, you need a scatterplot instead, which is a distinction MCQs love to test.
On the exam, mosaic plots show up in two ways. Multiple-choice questions ask you to read one (which group has the highest conditional proportion?) or to recognize when a mosaic plot is the right display, which means spotting that both variables are categorical. The 2026 FRQ Q5 is a good example of the territory: it asks about a possible association between age-group and type of sport played among professional athletes, which is exactly the two-categorical-variable setup a mosaic plot visualizes. Your job with a mosaic plot is always the same. Compare the conditional distributions across groups, decide whether they look similar (no association) or different (possible association), and remember the CED's warning that an apparent pattern may still be random.
Both displays show conditional proportions of one categorical variable across the levels of another, and they look almost identical. The difference is bar width. In a segmented bar chart, all bars are the same width, so you lose information about group sizes. In a mosaic plot, the width of each bar is proportional to the size of that group, so the area of every rectangle reflects the actual count. If a question emphasizes that one group is much larger than another, the mosaic plot is the display that shows it.
A mosaic plot displays two categorical variables using rectangles whose areas are proportional to the frequency of each category combination.
It's essentially a segmented bar chart where bar widths also show group sizes, so area carries the information.
If the rectangles form an even grid across groups, the variables look independent; if the segments shift between groups, there may be an association.
Mosaic plots support LO 2.1.A in Topic 2.1, where you identify questions about possible relationships between variables.
Any pattern you see in a mosaic plot might still be random chance, which is why the chi-square test for independence in Unit 8 exists.
Use a mosaic plot only when both variables are categorical; two quantitative variables call for a scatterplot.
It's a graph for two categorical variables where each rectangle's area is proportional to the frequency of that category combination. It appears in Topic 2.1 as a way to spot possible associations between categorical variables.
No. A mosaic plot can only suggest an association. The CED's essential knowledge for 2.1.A says apparent patterns may be random or not, so you need a chi-square test for independence (Unit 8) to formally decide.
In a segmented bar chart, every bar has the same width regardless of group size. In a mosaic plot, bar widths are proportional to group sizes, so every rectangle's area matches its actual count.
No. Mosaic plots are strictly for two categorical variables. For two quantitative variables, like height and weight, you'd use a scatterplot and tools like the correlation coefficient instead.
Compare the conditional proportions (segment heights) across the columns. If the breakdown looks roughly the same in every group, there's little evidence of association; if segments differ noticeably between groups, the variables may be related.