AP Statistics · Topic 1.3 · Unit 1
AP Stats 1.3: Categorical Tables
By Jude Wallis · Published
A frequency table shows the count in each category of a categorical variable; a relative frequency table shows the proportion. Proportions, percentages, and ratios all carry the same information: a category with 12 of 40 has relative frequency 0.30, or 30%.
AP Statistics: Unit 1 (topics 1.3). Topic 1.3 (Tabular Representation and Summary Statistics 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.
Frequency and relative frequency tables
Topic 1.3 is about organizing one categorical variable into a table so its pattern is easy to read. A frequency table lists each category of the variable alongside the number of observational units in it, and that count is the frequency. A relative frequency table replaces each count with the proportion of units in that category, found by dividing the count by the total number of units. A category holding 12 of 40 responses has frequency 12 and relative frequency .
The relative frequencies across all categories add to 1, which is a quick check that every unit was counted exactly once. A frequency table answers "how many," while a relative frequency table answers "what share," and the second is what you need when you plan to compare groups of different sizes.
Proportions, percentages, and ratios
Percentages, relative frequencies, and ratios all carry the same information as proportions, so you can move between them freely. A proportion of 0.30 is 30%, and it is the ratio 12 to 40, which reduces to 3 to 10. Which form you report is a matter of audience, not of content, since each is a rescaling of the same count.
Counts and relative frequencies both reveal information you can use to justify a claim about the variable in context. A claim like "most respondents chose option A" holds only if A's proportion is above 0.5, so the table itself is the evidence. Reading a table well means tying a specific number back to the category and setting it describes.
The table as a distribution
Taken together, the categories and their relative frequencies give the distribution of the categorical variable, the pattern of how observational units are spread across the categories. Describing that distribution with summary statistics means reporting the count and the share in each category and naming what each one refers to. A single category's proportion is itself a summary statistic, and the whole table is the variable's distribution.
Topic 1.4 turns these tables into bar charts and pie charts, which show the same distribution as a picture. Comparing the same categorical variable across two or more data sets also belongs to topic 1.4.
Build a relative frequency table
A survey of 50 students records how they get to school: 22 walk, 15 take the bus, 8 bike, and 5 go by car. Build the relative frequency table as proportions and as percentages.
Find the total: . This matches the stated sample size, so every student is counted once.
Walk: , which is .
Bus: , which is .
Bike: , which is .
Car: , which is .
Check the total: , or .
| Method | Count | Proportion | Percent |
|---|---|---|---|
| Walk | 22 | 0.44 | 44% |
| Bus | 15 | 0.30 | 30% |
| Bike | 8 | 0.16 | 16% |
| Car | 5 | 0.10 | 10% |
The proportions add to 1.00 (100%), confirming the table is complete.
Frequently asked questions
Do relative frequencies have to add up to 1?
Yes, up to rounding. Each observational unit falls in exactly one category, so the proportions across all categories sum to 1, or 100%. A sum that misses badly means a counting error.