The grade point average: A moment of solemn reflection
In the main text of this chapter we observe that the conventional letter-grade scale of academic achievement—A, A—, B+, B, B—, etc.—is only an ordinal scale of measurement, and that translating the letter grades into numerical "quality points" does not make it anything other than an ordinal scale. Now for a moment of solemn reflection. If the quality point scale is not an equal interval scale, and if it is only equal interval scales that readily permit the kinds of mathematical operations required for calculating an average--what, then, shall we make of that venerable academic institution known as the grade point average? In case you are unacquainted with the details of this average (also known by its acronym GPA), it is simply the sum of all a student's quality points divided by the number of course units on which those quality points are based.
Thus, a student who at the end of her first semester has accumulated the grades of B+, C+, B, and A— would have a GPA of
(3.3+2.3+3.0+3.7)/(4 course units) = 3.1
which conventional academic wisdom would take to represent "about a B average." (This illustration is based on the quality point schedule described in the main text of the chapter: A = 4.0, A— = 3.7, B+ = 3.3, B = 3.0, and so on.)
As a card-carrying member of the professoriate, I will have to admit that the grade point average does have a kind of utility. If two students at the same institution have taken approximately the same kinds of courses, it is a fairly safe bet that the student with the 3.6 GPA has an overall level of academic achievement rather higher than that of the student with a GPA of 2.0. It is even a fairly safe bet that the 3.6 GPA represents a higher level of academic achievement than a 3.0 GPA.
But what about the difference between 3.6 and 3.4? Or between 3.6 and 3.5? Could you legitimately conclude that the student with a 3.6 GPA has a higher level of academic achievement than the one who has only a 3.5? Or consider the same question from the opposite direction. If two students each end up with a 3.6 GPA, could you legitimately conclude that they both have precisely the same level of academic achievement? It is probably fairly obvious to you intuitively that the answer to both of these questions is no. Even if there were no problem with the validityof letter grades as a comparative measure of academic achievement (a question to be examined in a later SideTrip), conclusions of this sort would be warranted only if the scale of grade points were an equal interval scale. But of course it is not. Grade points belong to a scale that is merely ordinal, and taking their average will not make them anything more than ordinal. Grade point averages are at best ordinal measures that allow one to draw coarse-grained distinctions among students, but not fine-grained distinctions.