Which statement is NOT true of a nominal scale?

Which statement is NOT true of a nominal scale?

• A. It is possible to determine the mean of nominally scaled variables.
• B. It has a true zero point.
• C. It assumes equal intervals between values.
• D. It supports meaningful arithmetic operations like averaging.

Answer: (A)

Nominal scales are purely categorical; they assign cases to named groups without any inherent order or numeric meaning. The numbers you might use as labels are just identifiers, not quantities with measurable distances or ratios. Because of that, there isn’t a meaningful way to compute an average or mean—the kind of arithmetic that relies on numeric distance between values is inappropriate for nominal data. In practice, with nominal data you’d summarize with counts or proportions and identify the most frequent category (the mode). You’d use nonparametric methods to compare groups rather than any arithmetic on the values themselves. The ideas of a true zero point and equal intervals imply numeric, quantitative relationships between values, which nominal data do not have, and arithmetic like averaging would be misleading if applied.

Nominal scales are purely categorical; they assign cases to named groups without any inherent order or numeric meaning. The numbers you might use as labels are just identifiers, not quantities with measurable distances or ratios. Because of that, there isn’t a meaningful way to compute an average or mean—the kind of arithmetic that relies on numeric distance between values is inappropriate for nominal data.

In practice, with nominal data you’d summarize with counts or proportions and identify the most frequent category (the mode). You’d use nonparametric methods to compare groups rather than any arithmetic on the values themselves. The ideas of a true zero point and equal intervals imply numeric, quantitative relationships between values, which nominal data do not have, and arithmetic like averaging would be misleading if applied.