Data are categorical when values identify groups or qualities, such as eye color, transportation type, or satisfaction level; they are quantitative when values represent numerical amounts or measurements on which meaningful arithmetic comparisons can be made. The classification requires distinguishing numerical labels or codes from measured quantities and recognizing that the variable type determines appropriate summaries, graphs, and statistical analyses, without requiring advanced treatment of measurement scales or specialized data types.
To classify a variable, ask:
A number is not automatically quantitative. Sometimes numbers are used only as labels or codes.
Example: A school survey records two pieces of information about each student:
The values and are codes for different transportation groups. They do not represent amounts. For example, transportation type is not “twice as much” as transportation type .
Therefore, transportation type is categorical data. We could summarize it by counting how many students use each type or make a bar graph.
The travel times are numerical measurements. Differences and averages are meaningful: a -minute trip is minutes longer than an -minute trip.
Therefore, travel time is quantitative data. We could calculate the mean travel time or make a histogram.
The key question is: Are the numbers labels for groups, or do they represent meaningful amounts?
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