Which data scale is characterized by a true zero and permits multiplication and division operations?

Which data scale is characterized by a true zero and permits multiplication and division operations?

• A. Nominal level
• B. Ordinal level
• C. Ratio level
• D. Interval level

Answer: (C)

The key idea is that a ratio scale has a true zero, meaning zero represents the absence of the quantity and relative comparisons (multiplication and division) are meaningful. With a ratio scale you can say one value is a certain multiple of another, such as twice as long or half as heavy. Because zero truly means “none,” arithmetic can extend beyond addition and subtraction to include multiplication and division. In contrast, an interval scale has equal intervals but its zero point is arbitrary (like Celsius temperature), so you can add and subtract but not meaningful multiply or divide. Nominal scales are just categories without order, and ordinal scales have order but not equal spacing, so they don’t support arithmetic ratios either. Therefore, the data scale described is the ratio level.

The key idea is that a ratio scale has a true zero, meaning zero represents the absence of the quantity and relative comparisons (multiplication and division) are meaningful. With a ratio scale you can say one value is a certain multiple of another, such as twice as long or half as heavy. Because zero truly means “none,” arithmetic can extend beyond addition and subtraction to include multiplication and division.

In contrast, an interval scale has equal intervals but its zero point is arbitrary (like Celsius temperature), so you can add and subtract but not meaningful multiply or divide. Nominal scales are just categories without order, and ordinal scales have order but not equal spacing, so they don’t support arithmetic ratios either.

Therefore, the data scale described is the ratio level.