Correct option is C
(A) Nominal scale → Mode (IV) – Correct
The nominal scale is the simplest level of measurement, used for categorizing data without any order (e.g., gender, race, religion).
Mode (most frequently occurring category) is the most appropriate measure of central tendency for nominal data.
(B) Ordinal scale → Kendall-Tau (I) – Correct
The ordinal scale ranks data in order (first, second, third, etc.) but without equal intervals (e.g., socioeconomic status: low, middle, high).
Kendall-Tau is a statistical test that measures the correlation between two ranked variables, making it suitable for ordinal data.
(C) Interval scale → Mean (II) – Correct
The interval scale has equal intervals between values but lacks an absolute zero (e.g., temperature in Celsius, IQ scores).
The mean is the best measure of central tendency for interval data, as it considers all values.
(D) Ratio scale → True zero (III) – Correct
The ratio scale has equal intervals and a true zero point, meaning zero represents the complete absence of the quantity (e.g., weight, height, income).
True zero is what distinguishes ratio data from interval data.
Thus, the correct matching is A - IV, B - I, C - II, D - III, making option 3 the correct answer.
Measures of Central Tendency:
-Mode: Used for nominal data (e.g., most common blood type).
-Median: Best for ordinal data (e.g., ranking in a race).
-Mean: Used for interval and ratio data (e.g., average temperature).
Statistical Tests for Different Scales:
-Nominal Data: Chi-square test, mode calculation.
-Ordinal Data: Spearman’s rank correlation, Kendall-Tau test.
-Interval & Ratio Data: Pearson correlation, t-tests, ANOVA.
Importance of True Zero:
-Ratio scales allow for meaningful ratios (e.g., 100 kg is twice as heavy as 50 kg).
-Interval scales lack true zero, meaning ratios cannot be interpreted (e.g., 20°C is not twice as warm as 10°C)
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