Measurement Scale Matching Solution

This question requires matching the four types of measurement scales (Nominal, Ordinal, Interval, Ratio) listed in List I with their appropriate statistical measures or properties from List II.

A. Nominal Scale Matching

Nominal Scale data consists of categories without any intrinsic order. The only measure of central tendency that can be meaningfully calculated for nominal data is the Mode (the most frequent category).

• A matches with IV. Mode.

B. Ordinal Scale Matching

An Ordinal Scale involves data that can be ranked or ordered, but the intervals between the ranks are not necessarily equal. Non-parametric measures like Kendall-Tau (a rank correlation coefficient) are suitable for ordinal data.

• B matches with I. Kendall-Tau.

C. Interval Scale Matching

An Interval Scale has ordered data with equal intervals between values, but it lacks a true zero point (e.g., temperature in Celsius). Statistical measures like the Mean can be calculated because the intervals are consistent.

• C matches with II. Mean.

D. Ratio Scale Matching

A Ratio Scale has all the properties of an interval scale but also includes a meaningful, absolute True zero point (e.g., height, weight). This allows for ratio comparisons (e.g., 'twice as heavy').

• D matches with III. True zero.

Final Matching Summary

The correct matching, based on the properties of each scale, is:

• Nominal scale (A) corresponds to Mode (IV).
• Ordinal scale (B) corresponds to Kendall-Tau (I).
• Interval scale (C) corresponds to Mean (II).
• Ratio scale (D) corresponds to True zero (III).

Therefore, the correct option is a-iv, b-i, c-ii, d-iii.