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How are variables classified in a nominal scale?

1. Based on their size and amount

2. Based on their categorical information

3. On a linear numerical scale

4. Using descriptive statistics

The correct answer is: Based on their categorical information

Variables classified in a nominal scale are categorized based on distinct groups or categories that do not have a specific order or ranking. This classification focuses on qualitative differences rather than quantitative measures. For instance, nominal data may consist of categories such as gender, ethnicity, or types of employment, where each category is unique and does not inherently carry a numerical value or a hierarchy. The other classifications do not apply to nominal scales. Variables cannot be based on size and amount, as that would suggest a continuous scale. Similarly, classifying variables on a linear numerical scale relates to ordinal or interval scales where order matters. Using descriptive statistics is also more relevant to summarizing data rather than classifying it; nominal data is often described using frequency counts and percentages rather than mean or standard deviation, which are applicable to other types of scales. Therefore, the classification based on categorical information is the defining characteristic of a nominal scale.