Categorical Variable Displays

Unit 1 · Exploring One-Variable Data

What AP Stats asks here

Categorical data is summarized by category counts and proportions, then displayed with bar charts, pie charts, segmented bars, or tables. The two recurring AP traps: (1) drawing bars touching as if it were a histogram, and (2) using a pie chart when there are too many categories to compare slices visually.

Relative frequency

Proportion in a category

\text{rel. freq.} = \dfrac{\text{count}}{\text{total}}

Sum check

\sum \text{rel. freq.} = 1 = 100\%

Display choice by purpose

Compare frequencies, many categories

\text{bar chart}

Parts of a whole, few categories

\text{pie chart}

Compare composition across groups

\text{segmented bar chart}

AP Tip: Bar chart bars are separated; histogram bars touch. The gap signals 'distinct categories' rather than 'continuous bins'.

Caution: Pie charts work for 2–5 slices. With 12 thin slices, the human eye cannot compare angles accurately — a sorted bar chart wins every time.

Type 1

Frequency and relative frequency

Convert raw counts into proportions or read counts off a pie chart. The two summaries must sum to the total or 100%.

Example 1

A survey of 400 students asked their primary mode of transportation to school. A pie chart shows: Bus 50%, Car 30%, Bike 12%, Walk 8%. How many students bike to school? (A) 12 (B) 30 (C) 48 (D) 50

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Type 2

Choose the appropriate display

Match the display to the variable type and the question being asked. Histogram is a trap when the variable is categorical.

Example 2

A medical study records blood type (A, B, AB, O) for 200 patients. Which display is most appropriate? (A) Histogram with bars touching (B) Bar chart with gaps between bars (C) Boxplot of the four categories (D) Pie chart that omits 'O' to keep slices visible

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Type 3

Read or compare two-group displays

Compare two groups using comparison language and specific percentages. AP rubrics reward named subjects and named numbers, not vague claims.

Example 3

A survey asked 100 boys and 100 girls their favorite school subject: Math: 35 boys, 22 girls English: 18 boys, 31 girls Science: 28 boys, 25 girls History: 12 boys, 14 girls Art: 7 boys, 8 girls Which best describes a key difference between the two groups? (A) Boys liked some subjects more than girls. (B) Boys preferred Math (35% vs 22%) while girls preferred English (31% vs 18%); Science, History, and Art are similar. (C) Boys and girls had identical preferences overall. (D) Girls had a higher total because they preferred more subjects.

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