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# Levels of Measurement Worksheet - Solutions

Data can be classified into the levels of nominal, ordinal, interval and ratio. Each of these levels of measurement indicates a different feature that the data is showing. Read the full description of these levels, then practice sorting through the following. You can also look at a version without answers, then come back here to check your work.

Indicate which level of measurement is being used in the given scenario:

1. The teacher of a class of third graders records the height of each student.

2. SOLUTION: This is the ratio level of measurement. There is a starting point (0 feet, 0 inches) and it makes sense to say that 6 feet is twice as long as 3 feet.

3. The teacher of a class of third graders records the eye color of each student.
4. SOLUTION: This is the nominal level of measurement. Eye color is not a number, and so the lowest level of measurement is used.

5. The teacher of a class of third graders records the letter grade for mathematics for each student.
6. SOLUTION: This is the ordinal level of measurement. The letter grades can be ordered with A as high and F as low, however differences between these grades are meaningless. An A and a B grade could be separated by a few or several points, and there is no way of telling if we are simply given a list of letter grades.

7. The teacher of a class of third graders records the percentage that each student got correct on the last science test.
8. SOLUTION: This is the ratio level of measurement. The numbers have a range from 0% to 100% and it makes sense to say that one score is a multiple of another.

9. A meteorologist compiles a list of temperatures in degrees Celsius for the month of May
10. SOLUTION: This is the interval level of measurement. The temperatures can be ordered and we can look at differences in the temperatures. However a statement such as ``A 10 degree day is half as hot as a 20 degree day'' is not correct. Thus this is not at the ratio level.

11. A meteorologist compiles a list of temperatures in degrees Fahrenheit for the month of May
12. SOLUTION: This is also the interval level of measurement, for the same reasons as the last problem.

13. A meteorologist compiles a list of temperatures in degrees Kelvin for the month of May
14. SOLUTION: Careful! Even though this is another situation involving temperatures as data, this is the ratio level of measurement. The reason why is that the Kelvin scale does have a absolute zero point from which we can reference all other temperatures. The zero for the Fahrenheit and Celsius scales is not the same, as we can have negative temperatures with these scales.

15. A film critic lists the top 50 greatest movies of all time.
16. SOLUTION: This is the ordinal level of measurement. The rankings are ordered from 1 to 50, but there is no way to compare the differences in rankings. Movie #1 could beat #2 by only a little, or it could be vastly superior (in the critic's eye). There is no way to know from rankings alone.

17. A car magazine lists the most expensive cars for 2012.
18. SOLUTION: Prices can be compared at the ratio level of measurement.

19. The roster of a basketball team lists the jersey numbers for each of the players.
20. SOLUTION: Even though there are numbers associated with this data set, the numbers serve as alternate forms of names for the players and the data is at the nominal level of measurement. Ordering the jersey numbers makes no sense, and there is no reason to do any arithmetic with these numbers.

21. A local animal shelter keeps track of the breeds of dogs that come in.
22. SOLUTION: This is the nominal level due to the fact that dog breeds are not numeric.

23. A local animal shelter keeps track of the weights of dogs that come in.
24. SOLUTION: This is the ratio level of measurement. Zero pounds is the starting point for all weights and it makes sense to say ``The 5 pound dog is one quarter the weight of the 20 pound dog.

Courtney Taylor