Which type of variable has categories that cannot be rank ordered? NominalRatioOrdinalInterval

The type of variable that has categories that cannot be rank ordered is called a nominal variable.

Explanation:

1. Nominal Variables: These are categorical variables that represent different categories or groups without any inherent order. Examples include gender, ethnicity, or types of fruits (e.g., apples, oranges, bananas). The central characteristic is that the categories are simply different from one another without any ranking.

2. Ordinal Variables: These variables do have a meaningful order among the categories, such as rankings (e.g., education level: high school, bachelor's, master's).

3. Interval Variables: These are numeric variables where the distance between values is meaningful and consistent, but there is no true zero point (e.g., temperature in Celsius).

4. Ratio Variables: These variables also have consistent intervals and a true zero point, allowing for a full range of operations (e.g., height, weight).

In summary, since nominal variables consist of categories that cannot be ordered in a hierarchy or rank, they are distinctly classified as non-ordinal.