Student-to-faculty ratio is a trick invented by universities to conceal the actual size of their lectures.

Back when I was doing college research, I was obsessed with one statistic: the student-to-faculty ratio. Consequently, I was very impressed with CU, as I browsed the Columbia College website, which boasts a “6:1 student to faculty ratio among undergraduates.” 6:1! In my naïve little mind, I pictured myself going to classes with fewer than 10 students in them.

In reality, I have to sit in an enormous lecture hall this semester for two back-to-back lectures, one with 300 students while the other has a staggering 400+. Engulfed by body heat and the pungent smell of sweat, I ask myself: why on earth are there so many people in my class? Is the faculty-to-student ratio just a lie?

The answer is: yes and no.

If you think about it, this ratio does not reflect the actual class size at all. Suppose University A has four faculties and four students. We further suppose each faculty offers one course per semester, while the students are required to take four. Accordingly, the four students have no option but to take all four classes offered by the university. Though the student-to-faculty ratio is 1:1, the class size is in fact four.

The key takeaway is that the class size is dependent on the number of classes students enroll in on average. Applying this logic, I have derived a nice little formula. (Don’t worry about the reasoning; just trust me.)

Class size = [Number of Students × Number of classes students take] / [Number of Faculties] = [Student-faculty ratio] × [Number of classes students take]

In the case of Columbia, we already know the student-faculty ratio. Normally, a student takes either four or five classes per semester. We take the number in between, 4.5, as the average number of classes they take (very sophisticated, I know). Plugging in the numbers, we find the class size should be around 27.

Now you might say, “Hmm, this number still feels way too small.” Congratulations, your intuition is absolutely right.

Firstly, the student-to-faculty ratio does not tell the whole story tell. When counting the number of undergraduates, the university conveniently leaves out the GS students. Take 2020 for example. Without factoring in GS students, the ratio is close to 6:1; after taking them into account, however, the ratio rises to 8.7:1.

Moreover, we must not forget about Barnard students, whom the university completely omits in their database. Even if Barnard students only take one class at Columbia per semester, the 3008 undergrads can still impact the mean significantly.

With all this new information, let’s crunch the numbers again.

Class size = (8842 Columbia Students × 4 classes + 3008 Barnard Students × 1 class) / (1017 professors) = 38

Now that is more like it.

But not all classes have the same number of students. The Columbia College website claims that “over 70 percent of classes [are] with fewer than 20 students.” With so many small classes, the other 30 percent must be filled with students. Indeed, using frequency to find the mean of the rest 30 percent, we find Average size = (38-20×0.7)/0.3=80.

And that is why your classes are packed like sardines.

Note: As a math major, I feel obliged to clarify two things. Firstly, my formula is merely an approximation. It is based on the assumption that all full-time professors only offer one course per semester. In reality, some professors may be on sabbatical, while others teach more than one course.  Secondly, students’ experiences of class size vary drastically from person to person. Enrollment in a class depends on many factors, such as the popularity of the major (Computer Science), and the level of the course (intro level classes that are major requirements are much larger than advanced electives.)

Classroom via Bwog Archives