Identify the nominal variables. A. Gender B. Annoyance level C. Caste D.…

Concept. A variable’s measurement scale is fixed by the mathematical relations its values can legitimately carry. On a nominal scale the values are only names or category labels: they support equality and difference alone, so they can be counted and cross-tabulated but never ranked, added or divided. On an ordinal scale the categories additionally carry a meaningful rank order, though the gaps between ranks are not equal. An interval scale adds equal gaps but places its zero by convention, and a ratio scale adds an absolute zero, so ratios of its values are meaningful.

Application. Apply that single test — “do these values carry an inherent order?” — to each listed variable:

• A. Gender: its values are category labels; no arrangement of them is higher or lower than another, so only equality and difference apply — nominal.

• B. Annoyance level: its values run from low to high on a graded scale of intensity, so they rank, but the step from “slight” to “moderate” is not a measured equal to the step from “moderate” to “severe” — ordinal.

• C. Caste: its values are social category names used for classification and counting; the categories themselves define no measured quantity or arithmetic order — nominal.

• D. Temperature in Kelvin: degrees are equally spaced and 0 K is an absolute zero, not a convention, so 300 K is genuinely twice 150 K — ratio (and therefore a fully quantitative, not categorical, variable).

• E. Economic status: its values — lower, middle, upper — are ranked bands of standing, so they order but do not carry equal measured intervals — ordinal.

Cross-check. Read the classification back as a table and confirm that exactly the entries with no inherent order survive the nominal test:

Result. Only Gender and Caste are unordered category labels, so the nominal variables are A and C only. Note the standard exam convention applied here: economic status is treated as ordinal because it is reported as ranked bands, and Kelvin temperature is a ratio scale precisely because its zero is absolute rather than conventional — the point that separates it from a Celsius reading.