Identify which level of measurement is represented by the following data.
Years covered in European History 101: 1066–1492
Annual income of students in Statistics 101 class: $0–$15,000
Course grades in English 101: A, B, C, D, F
Student gender: male, female
Solution
The years 1066 to 1492 represent interval data. No natural zero occurs (no “year zero”; the calendar goes from 1 b.c. to a.d. 1). Also, division () does not make sense in terms of years, so that the data are not ratio data. However, subtraction does make sense, in that the course covers .
Student income represents ratio data. Here, division does make sense. That is, someone who made $4000 last year made twice as much as someone who made $2000 last year. Also, some students probably had no income last year, so that $0, the natural zero, also makes sense.
Course grades represent ordinal data, because (a) they may be arranged in a particular order, and (b) arithmetic cannot be performed on them. The quantity A 2 B makes no sense.
Student gender represents nominal data, because the data cannot be ordered in a natural or obvious way. Also, no arithmetic can be performed on student gender.