Final answer:
A variable that categorizes elements without a numerical value is known as a qualitative variable, representing categories or labels like political affiliations rather than quantities.
Step-by-step explanation:
A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called a qualitative variable. Qualitative variables, also known as categorical variables, assign labels to categorize elements without a numerical value. For instance, political party affiliations like Republican, Democrat, and Independent would be qualitative, as there's no inherent order or numerical value assigned to these categories. Quantitative variables, on the other hand, represent data that can be quantified and are expressed as numbers, such as the weight of luggage or distance traveled. These can be further classified into discrete and continuous data, with discrete data resulting from counting like the number of books on a shelf, and continuous data resulting from measuring, such as the weight of luggage.