Dear Data Scientist,
Do any students actually graduate with a 4.00 GPA?
– Sharon, English Department
Yes, but not many.
How many?
One way to compute how many is to begin with the population of all students who graduated. Let’s further restrict it to only undergraduates. Over the 11-year period from June 2004 to May 2015, of 22,513 graduating undergraduate students, only 99 made it with a perfect 4.00 grade-point average ‑ about 1 out of every 227 graduating students.
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The event is even more exceptional if we use a prospective approach by beginning with the population of students who enroll as first-time degree-seeking students. For first-time students who began in the fall from 2000 to 2010, on average one of 1,327 students graduated with a 4.00 GPA.
Personally, I was surprised to find out how rare the pristine GPA is. Considering the rate of one per 1,327, we will average one to two of these accomplishments from each incoming class of first-time students. If I teach four classes of 25 new first-time students each fall semester, on average I would see a future-4.00-GPA student in the fall semester about once every thirteen years. By teaching spring semesters also, my chances increase. In a thirty-five-year teaching career here, I might teach about five such students. I’m putting aside the thought that my memory makes it hopeless that I would remember who they were.
Professors who teach only upper-division courses are more likely to encounter a future 4.00 superstar, because more transfer students enroll in those classes. Because the GPA at graduation for transfer students is based solely on their courses at St. Cloud State, not on courses at prior transfer institutions, transfer students are more likely to graduate with a 4.00 GPA, even though we admit more first-time students than transfer students. Of the 99 students that graduated with 4.00 GPAs, only 22 entered here as first-time students, while 77 entered as transfers.
Table 1
The only way a student can achieve a perfect 4.00 is by earning a grade of A or A+ in each class counting toward the grade-point average. I had heard indirectly that one recent statistics major had a 4.00 GPA, but as her adviser I looked at her academic record, and she had an A- in a first-year sociology course. That got me wondering whether it is possible to achieve a 4.00 GPA in spite of getting an A- in a course.
An A- adds 3.67 quality points per credit, whereas an A+ is equivalent to an A since both add 4 quality points for each credit. If a student graduates with 120 credits, but receives an A- for just one credit, perhaps in a one-credit seminar class, the GPA calculation turns out to be 3.99725. If this number is rounded to two decimal places, the number would be 4.00. Unfortunately for the student, GPAs are not rounded: the decimals are truncated after two places. So the GPA on the transcript would be 3.99. You have to be perfect to achieve a 4.00 GPA! Over the last 11 years, 16 students have graduated with a 3.99 GPA. Of course, a student always has the option of retaking that one course in hopes of raising the A- to an A.
What do these students major in?
Nine of the 99 students with perfect GPAs had double majors, for a total of 108 majors from 32 departments. Every school and college at St. Cloud State is represented. Twelve of the 99 students majored in Community Psychology, the most common major among students with perfect GPAs.
What else do we know about these students?
The 4.00 students are much more likely to be female, 70 of the 99 in this case.
The geographic origins are widely dispersed, with no single high school accounting for more than three of these students. Brainerd and Sartell each had three, while other tallies for central Minnesota high schools include two each from Albany, St. Cloud Cathedral and St. Cloud Tech, and one from Foley and St. Cloud Apollo. Among the others, two have been home schooled, and one had a GED. Six have come from international high schools.
The circles in Figure 1 represent the home counties of students who have earned a 4.00 GPA. The largest circle illustrates that the most students were from Stearns County. Home counties for one student from California, one student from Iowa, and one student from southern Wisconsin are not shown.
Figure 1
How does a student’s GPA change over time?
Table 2
The overall picture of GPAs across the university is clouded by opposing tendencies that complicate the analysis. On one hand, GPAs tend to rise over the course of a student’s college years (Table 2). For a student who hopes to finish with a perfect record, getting through the first few years unscathed is key.
At the same time, the percentage of all undergraduate students who are holding 4.00 GPAs is influenced by other factors.
Many students start their college careers with all A’s, only to eventually fall short in one or more courses later on. So we might think that the percentage of students holding the 4.00 GPA should be falling over the years. But other factors partially counteract this pattern. During the early years, many students with low GPAs leave school for a variety of reasons, but students with a 4.00 GPA are less likely to leave. As a result, the percentage of students with a 4.00 would be raised from these changes. Transfer students entering as sophomores or juniors might get off to a good start with 4.00 GPAs in their first one or two semesters, also providing a lift to the sophomore and junior GPAs. The cumulative effect of these different changes is that the 4.00 GPA percentage holds fairly steady through the first three years. But in the senior year, fewer students transfer out or drop out, and fewer transfer students enroll. So we see the percentages of students with 4.00 GPAs dropping from the 90 credit mark until graduation (Table 3).
Table 3
In spite of creeping grade inflation over the years, the 4.00 GPA is still something to be valued as a significant achievement. I wonder how it will be viewed 50 years from now?
About the data scientist: David Robinson is a Professor of Statistics and is Faculty Director of Analytics Projects in the Office of Strategy, Planning and Effectiveness at St. Cloud State University.
