Categorical and quantitative variables
Also known as: qualitative and quantitative variables
A categorical variable places each individual into a group or label, while a quantitative variable records a numerical measurement you can meaningfully do arithmetic with. The distinction determines which graphs and summary statistics are appropriate for a data set.
Every variable in a data set describes some characteristic of the individuals being studied, and each one is either categorical or quantitative. A categorical variable (also called qualitative) sorts individuals into groups: eye color, blood type, political party, or whether a student passed a course. A quantitative variable records an amount: height in centimeters, test score, number of siblings, household income.
The test is not whether the values look like numbers — it is whether arithmetic on them means anything. Jersey numbers and ZIP codes are written with digits but are categorical, because an average jersey number is meaningless. Quantitative variables split further into discrete variables, which take countable values such as the number of siblings, and continuous variables, which can take any value in an interval, such as weight or elapsed time.
The type dictates the analysis. Categorical data is summarized with counts, proportions, and percentages, displayed in frequency tables, bar charts, and pie charts, and compared across two variables using two-way tables and segmented bar graphs. Quantitative data is summarized with measures of center and spread — mean, median, standard deviation, interquartile range — and displayed with dotplots, stemplots, histograms, and boxplots, with relationships shown on a scatterplot. Asking for the mean of a categorical variable, or a bar chart of a continuous one, is a category error.
AP Statistics opens with this distinction and returns to it throughout the course. Unit 1 questions ask you to classify variables, choose an appropriate display, and explain why a given summary statistic is or is not suitable — and getting the classification wrong on a free-response question usually invalidates everything that follows.
Key takeaways
- Categorical variables assign individuals to groups; quantitative variables record numerical measurements.
- Numbers used as labels, such as ZIP codes or jersey numbers, are categorical because arithmetic on them is meaningless.
- Quantitative variables are discrete (countable) or continuous (any value in an interval).
- Categorical data uses counts, proportions, bar charts, and two-way tables; quantitative data uses center, spread, histograms, and boxplots.
- AP Statistics Unit 1 tests classifying variables and choosing the matching display and summary statistic.