Which type of measurement identifies variables without a mathematical interpretation?

Nominal measurement is the type that identifies variables without a mathematical interpretation. This type of measurement classifies data into distinct categories that do not have an inherent order or value. For example, nominal variables include categories such as gender, race, or the brand of a product. Each category is simply a label, and while they can be counted or categorized, they do not allow for any form of quantitative comparison.

In nominal measurement, one cannot calculate meaningful statistical measures such as means or standard deviations, because the categories do not possess numerical significance. Instead, analysis typically involves counting the frequency of each category or looking at mode, which simply indicates which category is most common.

The other types of measurement—ordinal, interval, and ratio—each provide a deeper level of measurement. Ordinal measurements imply a rank order among categories, interval measurements provide meaningful intervals but lack a true zero point, and ratio measurements include a true zero and allow for all mathematical operations. These features introduce the ability to perform calculations that nominal measurement cannot support. Thus, nominal measurement stands out as the method that purely identifies variables without a quantitative framework.