Questions: Levels of Measurement

Question 1

A researcher asks participants to identify their preferred study location from four options: library, dorm room, café, or coffee shop. What is the most statistically appropriate measure of central tendency for this variable?

• A. Mean
• B. Median
• C. Mode
• D. Standard deviation

Answer: (C)

Study location is a nominal variable — it consists of unordered categories with no numeric meaning. You cannot rank, add, or average category labels. The only appropriate measure of central tendency for nominal data is the mode (the most frequently chosen category). Standard deviation is a measure of spread, not central tendency.

Question 2

Because Celsius temperature has equal intervals between degrees, it is meaningful to say that 40°C is twice as hot as 20°C.

• T. True
• F. False

Answer: False

Celsius is an interval scale, not a ratio scale, because it lacks a true zero point — 0°C does not mean 'no heat.' Ratio statements (twice as much, half as much) require a true zero. On the Kelvin scale, which has an absolute zero, 400K would indeed be twice 200K. The equal intervals of Celsius allow subtraction (40°C is 20° warmer than 20°C), but not ratios.

Question 3

Why does a true zero matter for ratio-level measurement?

Model answer: A true zero means the absence of the measured property, which makes ratio comparisons meaningful — you can say one value is twice or half another.

Without a true zero, ratios are mathematically undefined. Reaction time measured in milliseconds has a true zero (0ms = no time elapsed), so 400ms is genuinely twice 200ms. IQ, by contrast, lacks a true zero — an IQ of 0 doesn't mean 'no intelligence,' so saying someone is 'twice as intelligent' is not meaningful. The true zero is what licenses multiplication and division across measurements.