1.2 The Language of Variation: Variables

Variables and Data

A variable is a characteristic that can differ from one individual to another (e.g., height, eye color). When you record a variable's value for each individual in a group, you get data. Statistics is fundamentally about studying variation — how and why data values differ.

Categorical vs. Quantitative

Categorical variables place individuals into groups or categories (e.g., favorite color, blood type). Quantitative variables take numerical values that represent counts or measurements and allow meaningful arithmetic (e.g., height, weight, age). Knowing the variable type determines which graphs and summary statistics are appropriate.

Distributions

The distribution of a variable shows all its possible values and how often each occurs. Distributions can be displayed with tables or graphs. Understanding a distribution means describing the pattern of variation — where values are concentrated and how they spread out.

Key terms

Variable

A characteristic that can take different values for different individuals.

Categorical variable

A variable that places individuals into categories or groups (e.g., eye color, brand preference).

Quantitative variable

A variable with numerical values representing counts or measurements that support arithmetic (e.g., age, weight).

Data

Recorded values of one or more variables for a set of individuals.

Distribution

The pattern of a variable's values, showing what values occur and how often each occurs.

Try an AP-style question

Which variable is categorical?

1. A student's number of siblings
2. A student's GPA
3. A student's height
4. A student's ZIP code