Identify the scale of measurement that is being used in each of the following ca
ID: 3043552 • Letter: I
Question
Identify the scale of measurement that is being used in each of the following cases. Provide a brief explanation for your choice.
Q2-1: The New Democratic Party, The Conservative Party of Canada, the Liberal Party of Canada, and the Green Party are categorized on the voters’ ballot with the numbers: 1, 2, 3, and 4. [0.5 point]
Q2-2: The pages of a term paper are numbered 1 through 20. [0.5 point]
Q2-3: The prices of the three items were $5.00, $10.00, and $12.00. [0.5 point]
Q2-4: Geologists have established a “hardness” scale for classifying the difference between rocks, called the Mohs’ scale. The hardest rock (diamond) has a value of 10 and will scratch all others. The second hardest rock will scratch all but the diamond, and so on, down to a rock such as talc, with a value of 1, and can be scratched by any other rock. A fingernail, a truly handy field-test instrument, has a value of between 2 and 3. [0.5 point]
Q2-5: The volumes of three different cubes are 40, 64, and 65 cubic inches. [0.5 point]
Q2-6: Six different highways in the Montreal region are identified by their numbers: 15, 20, 30, 40, 520, and 720. [0.5 point]
Explanation / Answer
(1) Nominal scale, because the parties have been numbered only on the basis of their names. The numbers don't have any numerical value or relationship.
(2) Interval scale, because the page numbers here tell us the difference between the pages but not the ratio between them.
(3) Ratio scale, because the prices here have an absolute (and meaningful) zero value and ratios of differences can be expressed using these prices.
(4) Ordinal scale, because the hardness values have an ordering among themselves and can be sorted accordingly.
(5) Ratio scale, because ratios of differences can be expressed using these volume values and these ratios are meaningful.
(6) Nominal scale, because the numbering of these highways has been done only on the basis of the names and the numbers don't have any significance or relationship.
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