Lesson 5 of 15 · free to read
Choose and interpret pie charts, bar graphs, and Pareto charts for categorical data, and recognize when pie charts are inappropriate.
A pie chart and a bar graph can show the same categories, yet one may mislead while the other clarifies. When do you choose which?
The idea
Pie charts, bar graphs, and Pareto charts each display qualitative data, but pie charts only work when categories are exclusive and percentages sum to 100%.
Tables organize data, but graphs often reveal patterns more clearly. For qualitative (categorical) data, the common choices are pie charts, bar graphs, and Pareto charts.
Vocabulary· 2 terms
Easily confused
Pie charts and bar graphs are interchangeable ways to show the same categorical data.
A pie chart requires that the categories be exclusive and that percentages sum to 100%; a bar graph does not.
A pie chart's wedges must represent parts of a whole, so overlapping or missing categories break it, while a bar graph simply compares bar lengths.
Definition
Pareto chart
Bars are sorted into order by category size, from largest to smallest.
A bar graph where the tallest bar comes first, then the next tallest, and so on.
Compare the two bars for each campus: at De Anza the full-time bar is shorter than the part-time bar, while at Foothill the gap is wider, showing the difference in proportions.
The bar graph above compares full-time and part-time enrollment at two colleges. It lets you see at a glance that Foothill has a larger share of part-time students than De Anza.
Sometimes percentages add to more than 100% (or less than 100%). This happens when students can belong to more than one category, or when some categories are missing. In such cases, a pie chart cannot be used because the wedges would not represent the whole. A bar graph is appropriate to compare the relative sizes of the categories.
De Anza College student characteristics (overlapping categories)
| Characteristic/Category | Percent |
|---|---|
| Full-Time Students | 40.9% |
| Students who intend to transfer to a 4-year educational institution | 48.6% |
| Students under age 25 | 61.0% |
| TOTAL | 150.5% |
The percentages add to 150.5% because a student can be in more than one category; a pie chart would be impossible here.
Definition
Other/Unknown
This category contains people who did not feel they fit into any of the ethnicity categories or declined to respond.
A catch-all group for respondents who don't belong to the listed categories or who skip the question.
When a table omits the 'Other/Unknown' category, the frequencies do not add up to the total number of students. In that situation, create a bar graph and not a pie chart.
Ethnicity of students at De Anza College (missing Other/Unknown)
| Ethnicity | Frequency | Percent |
|---|---|---|
| Asian | 8,794 | 36.1% |
| Black | 1,412 | 5.8% |
| Filipino | 1,298 | 5.3% |
| Hispanic/Latino | 4,180 | 17.1% |
| Native American | 146 | 0.6% |
| Pacific Islander | 236 | 1.0% |
| White | 5,978 | 24.5% |
| TOTAL | 22,044 out of 24,382 | 90.4% out of 100% |
The total is 22,044 out of 24,382, so 9.6% of students are unaccounted for; that missing slice is why a pie chart would mislead.
Read the bars from left to right: Asian is tallest, then White, Hispanic/Latino, Other/Unknown, and the small categories trail off, making the ordering obvious.
Including the 'Other/Unknown' category (9.6%) is important because it is large compared to some categories like Native American (0.6%) and Pacific Islander (1.0%). A Pareto chart sorts the bars from largest to smallest, making the graph easier to read and interpret.
Recap
Say each point to yourself, then tap it to check.
Always include 'Other/Unknown' when it exists.
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Adapted from Introductory Statistics 2e, © 2023 OpenStax, Rice University
Barbara Illowsky and Susan Dean
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