Which measurement level is necessary for mathematical operations including addition, subtraction, multiplication, and division?

Which measurement level is necessary for mathematical operations including addition, subtraction, multiplication, and division?

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

Answer: (C)

The ability to perform addition, subtraction, multiplication, and division meaningfully requires a measurement level that has a true zero point and equal intervals. That is the ratio level. With a true zero, numbers can represent actual magnitudes, so you can compare amounts by multiples (twice as much, half as much) and still add or subtract in a meaningful way. Interval data have equal intervals but lack a true zero, so you can add and subtract but not interpret ratios in a meaningful way. Nominal data are just categories, and ordinal data indicate order without consistent intervals, so arithmetic isn’t appropriate. Therefore, performing all four arithmetic operations in a meaningful way points to ratio data.

The ability to perform addition, subtraction, multiplication, and division meaningfully requires a measurement level that has a true zero point and equal intervals. That is the ratio level. With a true zero, numbers can represent actual magnitudes, so you can compare amounts by multiples (twice as much, half as much) and still add or subtract in a meaningful way. Interval data have equal intervals but lack a true zero, so you can add and subtract but not interpret ratios in a meaningful way. Nominal data are just categories, and ordinal data indicate order without consistent intervals, so arithmetic isn’t appropriate. Therefore, performing all four arithmetic operations in a meaningful way points to ratio data.