Key takeaway: Categorical and quantitative variables are the two basic kinds of data: categorical variables sort individuals into groups by label, while quantitative variables record numerical amounts that can be added and averaged.
Grade 12 – AP StatisticsAP Statistics Unit 1Statistics and Data
Definition of Categorical and Quantitative Variables
Categorical and quantitative variables are the two kinds of characteristic recorded for each individual in a study, and they differ in what the recorded values mean. A categorical value is a label such as a team, a color or a yes-or-no answer. A quantitative value is a number with a unit that measures an amount, such as age or distance.
The distinction decides which graphs and summaries make sense. Percentages and bar charts suit labels; means, medians and histograms suit measured amounts. A number alone does not make a variable quantitative.
Notation
Variables are usually named with capital letters, such as \(X\) for age or \(Y\) for favorite sport. Quantitative ones are further split into two kinds:
- discrete: counts that can be listed, like 0, 1, 2 water bottles;
- continuous: any value in an interval, like 63.4 inches.
A quick test: if averaging the values would be meaningful, the variable is quantitative.
Key facts
- Numbers used as identifiers, such as bib numbers or ZIP codes, are categorical because arithmetic on them means nothing.
- Bar charts and pie charts display categorical data; histograms and box plots display quantitative data.
- Ordinal categories, like small, medium and large, have a natural order but are still categorical.
- Summaries for categorical data are counts and percentages, not means.
Categorical and Quantitative Variables example
A park ranger records, for each of 60 hikers: the trail chosen (Eagle Loop, Pine Ridge or Creek Walk), age in years, shirt color, number of water bottles carried, and bib number. Classify each variable.
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Trail chosen and shirt color are labels, so they are categorical.
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Age in years and number of water bottles are amounts that can be averaged, so they are quantitative (water bottles is discrete).
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Bib number only identifies a runner; averaging bib numbers has no meaning, so it is categorical.
Three variables are categorical (trail, shirt color, bib number) and two are quantitative (age and water bottles).
Common mistake
Watch out
A student computes the mean ZIP code of 40 customers, 80,214, and treats it as a typical customer location.
Why it is wrong
ZIP codes are labels for regions, not amounts. Their average does not point to any place. Treat them as categories and count customers per code. Sorting categorical and quantitative variables correctly comes before choosing any summary.
Related terms and lessons
Browse the glossary: A–Z list · AP Statistics vocabulary · Statistics and Data