Segmented Bar Graph — Definition, Formula & Examples
A segmented bar graph (also called a stacked bar graph) is a bar chart where each bar is divided into colored segments that represent the proportion or count of subcategories within each group. The segments stack on top of each other so the full bar represents the whole group.
A segmented bar graph displays the distribution of a categorical variable across levels of another categorical variable by partitioning each bar into contiguous segments whose lengths correspond to the frequency or relative frequency of each sub-category. When every bar is scaled to a total height of 100%, the display is called a 100% segmented (or relative frequency) bar graph.
How It Works
Each bar corresponds to one group (for example, grade level or survey response). Within that bar, segments are stacked to show how the group breaks down by a second categorical variable. If you use counts, bar heights may differ; if you convert to percentages, every bar reaches 100%, making proportions easy to compare across groups. In AP Statistics, the 100% segmented bar graph is the standard way to investigate a possible association between two categorical variables.
Worked Example
Problem: A survey asks 200 students whether they prefer online or in-person classes. Results: Freshmen — 30 online, 50 in-person; Seniors — 80 online, 40 in-person. Construct a 100% segmented bar graph.
Step 1: Find each group's total. Freshmen: 30 + 50 = 80. Seniors: 80 + 40 = 120.
Step 2: Convert to percentages. Freshmen online: 30/80 = 37.5%, in-person: 62.5%. Seniors online: 80/120 ≈ 66.7%, in-person ≈ 33.3%.
Step 3: Draw two bars, each reaching 100%. Shade the lower segment for 'Online' and the upper segment for 'In-Person' using the percentages above.
Answer: The 100% segmented bar graph shows that seniors preferred online classes at a much higher rate (66.7%) than freshmen (37.5%), suggesting an association between class year and format preference.
Visualization
Why It Matters
On the AP Statistics exam, segmented bar graphs appear in free-response questions asking you to compare distributions of two categorical variables. They are also the go-to visual in fields like public health and market research whenever analysts need to show how subgroup compositions differ across populations.
Common Mistakes
Mistake: Using raw counts instead of percentages when groups have different sizes, then concluding the groups are similar because the segment lengths look alike.
Correction: When group totals differ, always convert to relative frequencies (percentages) before comparing proportions across bars. A 100% segmented bar graph makes this comparison valid.