Given below are two statements:

Statement I: In a ratio scale, zero point is arbitrary

Statement II: The nominal scale allows ordering/ranking of data

In the light of the above statements, choose the most appropriate answer from the options given below:

The correct option is Both Statement I and Statement II are false.

Let us analyze each statement step-by-step to understand why they are incorrect:

Analysis of Statement I: "In a ratio scale, zero point is arbitrary"
A ratio scale is the highest level of measurement. It possesses all the properties of nominal, ordinal, and interval scales, with the addition of a true (absolute) zero point. A true zero point indicates the complete absence of the property being measured (for example, zero weight means no weight, and zero income means no income). This allows us to compare the ratios of measurements (e.g., 10 kg is twice as heavy as 5 kg). Because the zero point in a ratio scale is absolute and not arbitrary (unlike in an interval scale, such as the Celsius temperature scale where 0°C does not mean the absence of heat), Statement I is false.

Analysis of Statement II: "The nominal scale allows ordering/ranking of data"
A nominal scale is the simplest level of measurement, used solely for labeling or categorizing data into mutually exclusive groups (e.g., gender, eye color, or political party affiliation). It does not imply any quantitative value, order, or ranking among the categories. The scale that allows ordering or ranking of data is the ordinal scale (e.g., first place, second place, third place). Since the nominal scale does not allow for any ordering or ranking, Statement II is false.

Therefore, both Statement I and Statement II are false.