Data are categorical when values identify groups or qualities, such as eye color or transportation type, and numerical when values represent counts or measurements for which comparisons and arithmetic summaries are meaningful. A number used merely as a label, such as a jersey or identification code, remains categorical; distinguishing these types supports choosing appropriate tables, graphs, and statistical summaries without treating category labels as quantities.
Data can be classified by asking:
Be careful: a number is not always numerical data. If it is only being used as a label, it is categorical.
Example: A teacher records the following information about students:
| Information recorded | Example value |
|---|---|
| Favorite type of music | Rock |
| Number of pets | 2 |
| Jersey number | 14 |
| Height |
Classify each type of data.
Favorite type of music is categorical because “Rock” identifies a group or category. It does not make sense to find the average of music types.
Number of pets is numerical because is a count. It makes sense to compare the numbers or find an average number of pets.
Jersey number is categorical, even though it uses numbers. The is only a label for a player, not a quantity. Adding jersey numbers or finding their average would not be meaningful.
Height is numerical because it is a measurement. Heights can be compared, and an average height can be calculated.
So, the classifications are:
When unsure, ask: Is this value a group or label, or is it a count or measurement?
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