Reading One 100% Bar for Each Group
A side-by-side bar chart places separate bars next to one another for each response category. A segmented bar chart instead shows one full bar for each group, divided into colored or patterned segments for the response categories. Each bar represents \(100\%\) of its group.
As in Side-by-Side Bar Charts for Two Groups, the goal may be to compare the distribution of a categorical response across groups. The important difference is how the comparison appears: in a segmented bar chart, the height of a response segment represents the percentage of that group in the response category. That is a conditional percentage, like those studied in the earlier tutorials on conditional distributions.
For example, if a bar represents 100 surveyed weekday visitors, a segment reaching \(35\%\) means that \(35\%\) of those weekday visitors fall into the segment’s response category. The denominator is the weekday group, not all visitors surveyed. The explanatory grouping variable identifies the bars; the categorical response variable identifies the segments.
A segmented bar chart is often called a 100% stacked bar chart. Its vertical scale usually runs from \(0\%\) to \(100\%\), and every bar reaches the \(100\%\) mark. The colors or patterns need a key that names the response categories. Use the same segment order in every bar so the same category can be tracked from group to group.
Read Segment Heights and Boundaries
If a segment is labeled with its percentage, read the label directly. Otherwise, use the vertical scale to estimate its height. The bottom segment starts at \(0\%\), so its height is its upper boundary. For a segment higher up the bar, find both its lower and upper boundaries: its height is the difference between them.
The boundaries are cumulative heights, not always the percentages of the individual categories. For example, if a segment stretches from \(40\%\) to \(75\%\) on the vertical scale, its height is \(75\%-40\%=35\%\), not \(75\%\). A common reading error is to report the top boundary as the segment’s value.
For each bar, check that the segment percentages add to \(100\%\). Small differences can occur if you estimate from a graph or round the values. When comparing groups, focus on the same response category in each bar. Subtract the two percentages to describe a difference in percentage points, as explained in Percent Versus Percentage Point Differences.
A Practical Reading Routine
Read the axis labels to find the groups, then use the key to identify the response category represented by each segment.
Confirm that the vertical axis is a percentage scale running from \(0\%\) to \(100\%\). Note its tick-mark spacing.
Use a direct label or estimate the segment’s height. For a segment above the bottom, subtract its lower boundary from its upper boundary.
State what percentage of the named group falls into the named response category. For a comparison, give both percentages and their difference in percentage points.
A segmented bar chart is designed to compare conditional distributions, not group sizes. Since every bar represents \(100\%\), bars for groups with very different numbers of individuals still have the same total height. The chart alone does not tell you how many people were in each group. If the sample sizes are provided elsewhere, use them when you need counts or when considering how much information each percentage represents.
Worked Example: Read Each Segment from Its Boundaries
Worked Example: Read Each Segment from Its Boundaries
A fictional survey asks beginning and experienced pottery students which workshop format they prefer: in person, hybrid, or online. Each bar in the segmented chart reaches \(100\%\). The category order from bottom to top is in person, hybrid, and online. The chart’s segment boundaries align with these percentages:
| Group | Bottom boundary | In-person / hybrid boundary | Hybrid / online boundary | Top boundary |
|---|---|---|---|---|
| Beginning students | 0% | 45% | 70% | 100% |
| Experienced students | 0% | 30% | 55% | 100% |
What percentage of each group prefers each format? For beginning students, the in-person segment runs from \(0\%\) to \(45\%\), so it represents \(45\%\). The hybrid segment runs from \(45\%\) to \(70\%\), so its height is \(70\%-45\%=25\%\). The online segment runs from \(70\%\) to \(100\%\), so it represents \(100\%-70\%=30\%\).
For experienced students, the in-person segment is \(30\%\). The hybrid segment is \(55\%-30\%=25\%\), and the online segment is \(100\%-55\%=45\%\).
Check the bars: \(45\%+25\%+30\%=100\%\) for beginning students, and \(30\%+25\%+45\%=100\%\) for experienced students. In this survey, the percentage preferring online workshops was \(45\%-30\%=15\) percentage points higher among experienced students than beginning students. The hybrid percentages are equal.
Worked Example: Compare a Response Category Across Groups
Worked Example: Compare a Response Category Across Groups
A fictional survey of apartment and house residents records how often they use a neighborhood tool-sharing cabinet: never, sometimes, or often. Each bar is divided from bottom to top in that order. In the apartment bar, the boundaries are at \(0\%, 20\%, 65\%,\) and \(100\%\). In the house bar, they are at \(0\%, 35\%, 75\%,\) and \(100\%\). What percentages use the cabinet sometimes, and how do those percentages compare?
For apartment residents, the sometimes segment lies between the \(20\%\) and \(65\%\) boundaries. Its percentage is \(65\%-20\%=45\%\). For house residents, the sometimes segment lies between \(35\%\) and \(75\%\), so it is \(75\%-35\%=40\%\).
In this survey, the percentage who sometimes use the cabinet is 5 percentage points higher among apartment residents than among house residents. This comparison concerns the share within each residence group. It does not mean that there were more apartment residents than house residents who sometimes used the cabinet; counts depend on the group sizes as well.
Check the other segments too: for apartment residents, never is \(20\%\) and often is \(100\%-65\%=35\%\); for house residents, never is \(35\%\) and often is \(100\%-75\%=25\%\). The resulting totals are \(20\%+45\%+35\%=100\%\) and \(35\%+40\%+25\%=100\%\).
Worked Example: Estimate from a Percentage Scale
Worked Example: Estimate from a Percentage Scale
A fictional community survey displays a segmented bar chart of how residents travel to a local market: walk, bicycle, or drive. The bars represent residents of two neighborhoods, and the categories are stacked from bottom to top in that order. The vertical axis is marked every \(10\%\). In Neighborhood East, the walk segment ends near \(25\%\), and the walk/bicycle boundary is near \(60\%\). In Neighborhood West, the corresponding boundaries are near \(15\%\) and \(50\%\). Estimate the percentages who bicycle and compare the neighborhoods.
Because the bicycle segment is above the walk segment, its height is found by subtracting the walk boundary from the walk/bicycle boundary. The scale gives estimates rather than exact values, so report the results as approximate.
The estimated percentage who bicycle is about \(35\%\) in both neighborhoods. The chart also shows that the walking percentages differ: about \(25\%\) in East compared with \(15\%\) in West. Since the two boundary readings were estimated from tick marks, it is best to describe these as approximate percentages, not exact measurements.
The driving segments can be estimated from the remaining heights: about \(100\%-60\%=40\%\) in East and \(100\%-50\%=50\%\) in West. Each estimated distribution totals \(100\%\): East has about \(25\%+35\%+40\%=100\%\), and West has about \(15\%+35\%+50\%=100\%\).
Common Mistakes and What a Strong Answer Says
- Reporting a cumulative boundary as a segment percentage. A boundary at \(70\%\) does not automatically mean the segment is \(70\%\). For a segment from \(45\%\) to \(70\%\), subtract: \(70\%-45\%=25\%\).
- Using the wrong denominator in the interpretation. A \(35\%\) segment means \(35\%\) of the group represented by that bar are in the response category. It is not \(35\%\) of everyone in the chart unless the question and data happen to make that true.
- Confusing segment colors or order. Check the key and follow the same response category across bars. A segment’s position alone does not tell you its meaning.
- Assuming equal bar heights mean equal group sizes. All bars reach \(100\%\), even if the groups contain different numbers of people. A segmented bar chart shows percentages, not the group counts.
- Calling a percentage-point difference a percent change. Subtract the two percentages and state the result in percentage points. For example, \(45\%-40\%=5\) percentage points.
- Claiming that the chart proves a cause. A chart describes distributions in the data. It does not, by itself, show that group membership caused a difference in responses.
A full-credit interpretation names the group, the response category, and the percentage. For a comparison, report both group percentages and the percentage-point difference. If values are estimated from the axis, say “about” or “approximately,” and do not report more precision than the scale supports.
Check Your Understanding
Use the bar’s group, the segment boundaries, and the scale when answering.
- A segment runs from \(30\%\) to \(68\%\) on the vertical scale. What percentage of its group does the segment represent?
- A bar’s three segment boundaries are at \(0\%, 25\%, 55\%,\) and \(100\%\), from bottom to top. Find the percentage represented by each segment.
- In a chart of meal choices, the “vegetarian” segment is \(32\%\) in Group A and \(41\%\) in Group B. State the difference in percentage points in context.
- Why can two bars of equal height represent groups with different numbers of individuals?
- A segment appears to be about \(18\%\) using a scale marked every \(10\%\). How should you communicate the reading’s precision?