Categorical vs. Quantitative Variables
Distinguish categorical variables (labels or names) from quantitative variables (meaningful numerical values). Understand that the appropriate analysis depends entirely on the type of variable involved.
A lesson of AP Statistics, in Exploring One-Variable Data, about 10 minutes.
By the end of this lesson, you will be able to classify variables as categorical or quantitative, distinguish discrete from continuous, and explain why classification drives every analysis choice.
Why Classification Matters
Every statistical analysis starts here: what kind of data do I have? The answer determines which graphs, which summaries, and which inference procedures are valid.
Categorical Variables
Categorical variables place each individual into one of several groups or categories. Values are labels, not numbers — even when coded numerically, arithmetic is meaningless.
Examples: blood type, political party, eye color, pass/fail.
Appropriate summaries: counts, proportions, percentages. Appropriate graphs: bar chart, pie chart.
Ordinal categorical: categories have a natural order (agree/neutral/disagree) but gaps between them aren't necessarily equal.
Quantitative Variables
Quantitative variables record a numerical measurement for which arithmetic makes sense.
Examples: height (cm), SAT score, temperature, number of siblings.
Key property: differences have meaning. Being 180 cm tall is 20 cm more than 160 cm.
Discrete vs. Continuous
| Type | Definition | Examples |
|---|---|---|
| Discrete | Isolated values; counting | Number of pets, number of goals |
| Continuous | Any value in an interval; measuring | Height, weight, time |
Classification Practice
| Variable | Type |
|---|---|
| Jersey number | Categorical (a label) |
| Temperature (°F) | Quantitative, continuous |
| Number of AP exams | Quantitative, discrete |
| Letter grade | Categorical, ordinal |
| GPA |