What type of variable is defined as having no meaningful ordering or ranking of the categories?

The concept of a variable having no meaningful ordering or ranking of the categories refers specifically to a nominal variable. Nominal variables categorize data without representing any kind of quantitative value or inherent order. Examples include gender, race, or city of residence—these categories simply classify observations without indicating any hierarchy or relationship.

In contrast, ordinal variables do have a defined order or ranking—such as a Likert scale measuring satisfaction—where one category signifies a greater amount of something than another. Quantitative variables are numerical and can be measured, allowing for meaningful arithmetic operations, while interval variables possess both order and equal intervals between values, but do not have a true zero point (like temperature in Celsius). Thus, the defining characteristic of nominal variables is their lack of meaningful order, making them unique among the types listed.