Which type of variable has two or more categories with no intrinsic ordering?

The correct choice is nominal variable, which is characterized by having two or more categories that do not possess any intrinsic order or ranking among them. For example, variables such as gender, hair color, or types of cuisine can be categorized, but there is no inherent order that suggests one category is higher or lower than another.

In contrast, ordinal variables do have an intrinsic order or ranking, even if the intervals between categories are not uniform. For example, a satisfaction rating (e.g., "very unsatisfied," "unsatisfied," "satisfied," "very satisfied") indicates a hierarchy in responses.

Interval and ratio variables are both quantitative and represent data that can be measured on a numerical scale. Interval variables have meaningful intervals between values but lack a true zero point (e.g., temperature in Celsius). Ratio variables, on the other hand, have both meaningful intervals and a true zero point, allowing for the comparison of absolute magnitudes (e.g., weight, height).

Nominal variables stand out as the only type without any inherent ordering or ranking, making this the defining characteristic that leads to the choice of this option.