AP Statistics · Topic 1.4 · Unit 1
AP Stats 1.4: Graphs for Categorical Data
By Jude Wallis · Published
Bar charts and pie charts display one categorical variable. A bar's height is a category's count or proportion; a pie slice's area is its relative frequency, and the slices sum to 100%. Both can compare two or more data sets on the same variable.
AP Statistics: Unit 1 (topics 1.4). Topic 1.4 (Graphical Representations for One Categorical Variable) sits in Unit 1 of the redesigned AP Statistics course (effective Fall 2026, first exam May 2027). Unit 1 is the heaviest weighted unit at 20-30% of the multiple-choice section.
Bar charts and pie charts
Topic 1.4 turns the tables from topic 1.3 into pictures of one categorical variable. A bar chart, also called a bar graph, draws a bar for each category, and the height or length of each bar is the frequency (count) or relative frequency (proportion) for that category. Bars can run vertically or horizontally, and because categories have no natural order you can arrange them in whatever order reads best.
A pie chart draws a slice for each category, where each slice's area as a fraction of the whole circle equals that category's relative frequency. The slices together make up 1, or 100%, of the area. Because a category's angle is its relative frequency times 360 degrees, a pie chart is really a table drawn in a circle.
Justifying claims and comparing groups
A categorical graph is evidence. It reveals information you can use to justify a claim about the variable in context, such as which category is most common or how close the top two are. Say what the graph shows and tie it to the actual categories and counts.
Frequency and relative frequency tables, bar charts, and pie charts can also compare two or more data sets on the same categorical variable. When the groups differ in size, compare relative frequencies rather than raw counts, because proportions put every group on the same scale. See histogram vs bar graph to keep the categorical bar chart separate from the quantitative histogram.
Choosing between a bar chart and a pie chart
A bar chart and a pie chart hold the same information, so the choice is about readability. A bar chart makes it easy to rank categories and to read each value against a scale, and it stays clear even with many categories. A pie chart emphasizes each category as a share of the whole, which reads well when there are only a few categories and the point is the split of 100%.
Whichever you pick, label the categories and the axis or slices so the graph can stand on its own. A common error is treating a categorical bar chart like a quantitative histogram; the bars sit apart because the categories have no numeric order, and reordering them changes nothing about the data.
Turn relative frequencies into pie slice angles
In a class of 40 students, 18 prefer cats, 14 prefer dogs, and 8 prefer neither. Find each category's relative frequency and the central angle of its pie slice.
Check the total: .
Cats: relative frequency ; angle degrees.
Dogs: relative frequency ; angle degrees.
Neither: relative frequency ; angle degrees.
Check the angles: degrees, a full circle.
Cats take a 162-degree slice (0.45), dogs 126 degrees (0.35), and neither 72 degrees (0.20). The three angles add to 360 degrees, confirming the pie chart is complete.
Frequently asked questions
What is the difference between a bar chart and a histogram?
A bar chart shows a categorical variable, with a separate bar per category and gaps between bars. A histogram shows a quantitative variable grouped into numeric bins, and its bars touch because the axis is a number line.