Match List - I with List - II. List - I — Scale of Measurement List - II —…

Concept

The four levels of measurement form a hierarchy, and each level is defined by the properties it supports. A nominal scale only labels and classifies: its values are unordered categories. An ordinal scale adds rank order, but the gaps between consecutive ranks are not equal or quantitatively meaningful. An interval scale adds equal, meaningful intervals, yet its zero point is fixed by convention rather than by absence of the attribute, so ratios of its values carry no meaning. A ratio scale adds a true, absolute zero that denotes complete absence of the attribute, so a statement such as “twice as much” is valid.

Application

Test each variable in List - II against those defining properties:

• Caste is a classification label with no inherent ranking and no arithmetic — categories only, so it sits at the nominal level.

• Rank of army personnel is strictly ordered (Lieutenant below Captain below Major), but the gap between two consecutive ranks is not a fixed measurable quantity, so it sits at the ordinal level.

• Time of day has equal intervals — one hour spans the same duration anywhere on the clock — while its zero, midnight, is a convention rather than the absence of time; 14:00 is not “twice” 07:00, so it sits at the interval level.

• Height of students has equal intervals and an absolute zero, since zero height means no height at all; 180 cm is genuinely twice 90 cm, so it sits at the ratio level.

Cross-check

Apply the two discriminating tests in reverse. Only height survives the absolute-zero test, which fixes the ratio pairing. Of the remaining variables, only time of day has equal spacing, which fixes the interval pairing. Between the last two, rank carries order while caste carries none, which separates the ordinal pairing from the nominal one.

The matching therefore reads (A)-(III), (B)-(IV), (C)-(II), (D)-(I).