Which type of data uses natural, ordered categories with unknown quantitative distances?

The correct choice is based on the characteristics of ordered categories, which are fundamental to understanding ordinal data. Ordinal data is a type of categorical data that can be arranged in a meaningful order or ranking, but the intervals between the categories are not defined or uniform.

For example, consider a survey that asks participants to rate their satisfaction on a scale of "very dissatisfied," "dissatisfied," "neutral," "satisfied," "very satisfied." While it is clear that "very satisfied" is considered better than "satisfied," and so on, the exact difference in satisfaction level between "satisfied" and "very satisfied" is not quantifiable. This uncertainty about quantitative distances is what distinguishes ordinal data from interval data.

In contrast, nominal data involves categories without a natural order (like gender or colors), interval data has defined intervals between values with no true zero point (like temperature in Celsius), and discrete data refers to countable quantities (like the number of students in a class). Thus, the unique trait of ordinal data is its ranking without precise measurements between those ranks, making it the correct choice.