AP Statistics · Unit 1 · Topic 1.2

Variables Study Lab

Data sets list individuals (rows) and the variables measured on them (columns). A categorical variable puts individuals into groups; a quantitative variable takes numerical values where arithmetic makes sense. Explore a class survey, then test yourself with the sorting game.

1. Classify the variable, then pick the graph

A variable is a characteristic that changes from one individual to another. Its type decides which summaries and graphs make sense.

Class survey data click a column

Each row is one individual (a student). Each column is one variable.

Variable type

Sensible summary

Good graphs

Sorting game: what kind of variable?

2. Key ideas

Data

Individuals and variables

Individuals are the people, animals, or objects described by a data set. A variable is any characteristic that can differ from one individual to the next.

Type 1

Categorical variables

Values are labels or groups, such as eye color or yes/no. Summarize them with counts and proportions. Some categorical variables use numbers as labels, like zip codes or jersey numbers.

Type 2

Quantitative variables

Values are numerical amounts, such as height or the number of siblings, where means and differences make sense.

Counts

Discrete

A discrete quantitative variable takes a countable set of separate values, usually whole numbers from counting: pets, goals, siblings.

Measures

Continuous

A continuous quantitative variable can take any value in an interval: time, weight, temperature. Rounding the recorded value does not make it discrete in the AP sense.

Why it matters

Type decides the tools

Categorical data get bar charts, pie charts, and proportions. Quantitative data get dotplots, histograms, boxplots, means, and standard deviations.

3. Quick reference

Match each type of variable with its summaries and graphs.

Type	Examples	Summarize with	Graph with
Categorical	Blood type, favorite subject, yes/no, zip code	Counts, proportions, percents	Bar chart, pie chart
Quantitative, discrete	Number of pets, goals in a game, siblings	Mean, median, SD, IQR, range	Dotplot, histogram, boxplot
Quantitative, continuous	Height, commute time, temperature	Mean, median, SD, IQR, range	Histogram, stemplot, dotplot, boxplot

4. On the FRQ

How to earn the points

When asked to identify a variable, name it in context and give its type: “Minutes of exercise per week is a quantitative variable.”
Justify the type: “It is categorical because each response places a student into a group.”
Choose graphs and summaries that match the type, and say why. A bar chart for a categorical variable; a histogram or boxplot for a quantitative one.
Identify the individuals explicitly when asked: they are the objects in each row, not the variables.

Common mistakes

Calling a variable quantitative just because its values are numbers (zip codes, jersey numbers, area codes).
Making a histogram of a categorical variable. Use a bar chart, with gaps between the bars.
Calling time or weight discrete because they were rounded. Measurements are continuous.
Confusing the variable (“height”) with its values (“170 cm”) or with the individuals (“the students”).

5. Practice questions

AP-style multiple choice. Pick an answer to see the explanation.

0 / 0 correct

6. Key terms

The vocabulary for topic 1.2. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.