AP Statistics - Unit 1 - Topic 1.3
Categorical Tables Counts, Percents, and Claims
Categorical data use labels instead of measurements. A good table turns those labels into counts and proportions so you can describe what is common, rare, or convincing in context.
Lesson Overview
Topic 1.3 is about one categorical variable at a time: make a table, compute proportions, then write a clear contextual sentence.
Frequency Table
A frequency table lists each category and the count of observational units in that category.
Relative Frequency Table
A relative frequency table lists each category and the proportion of observational units in that category.
Formula Box
Relative frequency = category count / total count
Percent = relative frequency x 100%
AP Big Idea
Counts tell how many. Relative frequencies, proportions, percentages, and ratios help you compare categories fairly.
Key Definitions
Use these words exactly and keep every answer tied to the real situation.
Categorical Variable
A variable whose values are labels or groups, such as eye color, class year, payment method, or favorite genre.
Category
One possible label for the variable. For the variable "favorite pet," categories could include dog, cat, fish, and none.
Distribution
The pattern of how observational units are spread across the categories of a variable.
Mode
The category with the largest count or relative frequency. A categorical variable can have more than one mode if categories tie.
Proportion
A part divided by the whole. Proportions are often written as decimals, fractions, or percents.
Ratio
A comparison of two counts. A ratio of 14 to 11 compares one category count to another category count.
AP Notation and Table Moves
These are the small calculations Topic 1.3 expects you to do without losing the context.
From Raw Counts to AP-Ready Summary
Suppose 40 students are asked how they usually get to school.
| Transportation | Frequency | Relative Frequency | Percent |
|---|---|---|---|
| Car | 14 | 14/40 = 0.350 | 35.0% |
| Bus | 11 | 11/40 = 0.275 | 27.5% |
| Walk | 8 | 8/40 = 0.200 | 20.0% |
| Bike | 5 | 5/40 = 0.125 | 12.5% |
| Other | 2 | 2/40 = 0.050 | 5.0% |
Check that 14 + 11 + 8 + 5 + 2 = 40.
Each relative frequency uses the same denominator, 40.
Say "35% of these students ride by car," not just "35% car."
Worked AP-Style Examples
Practice moving from a table to a conclusion that an AP reader can score.
Club Preference
A sample of 60 students chose one after-school club: Robotics 18, Art 12, Music 15, Debate 9, Other 6. Construct relative frequencies.
AP description: Robotics is the most common club choice in this sample, chosen by 30% of the 60 students.
Is a Majority Interested in Creative Clubs?
Using the club data, suppose someone claims that a majority of students prefer a creative club, defined as Art or Music. Does the table support the claim?
Work: Art + Music = 12 + 15 = 27 students. The proportion is 27/60 = 0.45 = 45%.
Conclusion: No. The data do not support the majority claim because only 45% of the sampled students chose Art or Music, which is less than 50%.
Snack Choice
In a class of 32 students, 10 chose fruit, 14 chose chips, 6 chose cookies, and 2 chose no snack.
- Frequency for chips: 14 students.
- Relative frequency for chips: 14/32 = 0.4375.
- Percent for chips: 43.75%, or about 43.8%.
- Ratio of chips to fruit: 14:10, which simplifies to 7:5.
AP warning: The ratio 7:5 is not the same as saying 70% chose chips. A ratio compares two category counts; a percent compares a category count to the total.
Common AP Mistakes
These are easy to fix once you know what an AP answer is looking for.
Forgetting the Total
Relative frequency needs a denominator. Always add the category counts and check that every category is included.
Mixing Up Count and Percent
A count such as 14 is not a percent. A percent such as 35% is not a count unless the total is known.
Using Ratio Like Proportion
A ratio compares two selected counts. A proportion compares a selected count to the whole group.
No Context
"0.275 are bus" is weak. "27.5% of the 40 surveyed students usually ride the bus to school" is AP-ready.
Overstating a Claim
Tables from a sample describe the sampled group unless the sampling method justifies a broader conclusion.
Rounding Too Early
Do calculations with fractions or extra decimals first, then round the final percent when you write the answer.
Flashcard Deck
Fifteen quick cards for Topic 1.3 vocabulary, formulas, and AP wording.
Multiple-Choice Practice
Answer one question at a time. You will get instant feedback and a review at the end.
FRQ-Style Practice
Prompt: A class collects data related to frequency tables and relative frequencies for one categorical variable. Write a free-response answer that uses the correct vocabulary and statistical reasoning.
- Identify the variable(s), population/sample, or study design feature requested.
- Choose or describe the appropriate table, graph, summary statistic, sampling method, or design decision.
- Write one contextual interpretation that uses statistical language rather than a vague everyday claim.
Scoring focus: Credit depends on precise vocabulary, context, and a justified choice or description.
Calculator and Technology Check
Output to read: Calculator or spreadsheet output gives n = 48, mean = 16.2, median = 15.4, IQR = 4.8, and one flagged high value.
How to interpret it: For frequency tables and relative frequencies for one categorical variable, connect the output to the context: compare resistant and nonresistant summaries, mention units, and decide whether the flagged value changes the story.
Source note: Aligned to AP Statistics Course and Exam Description, Effective Fall 2026.