# Class Size Paradox

A lot of freshman college students have probably experienced the ‘Class size paradox’, without even knowing it. This paradox is called the Class Size Paradox, but it is applicable to many other aspects of life, not just class sizes.

### The paradox itself

Colleges and universities tend to boast of small average class sizes, usually 10 to 15 students per class. But, most freshman are often surprised to find that their class size is a lot bigger than 15 students and are frequently complaining of being stuck in gigantic classes. However, university administrators keep reporting that most of their classes have relatively few students in them.

Both the students and the administrators are correct in their claims, so what is the source of this inconsistency in their reports?

Well, the reason for this discrepancy can be described in two lines:

The number of students who enjoy a small class is small, but the number

of students in a large class is large.

This might sound confusing at first, so let’s look at an example.

Suppose a college has 70 classes. There are 30 classes which hold 5 students each, another 20 classes which hold 10 students each, and remaining 20 classes hold 30 students, each.

If you asked the dean for the average class size, he would calculate it like this:

students per class

This average class size comes from the dean’s point of view, so let’s call this the *observed* average class size.

But, if you survey a group of students, ask them how many students are in their classes, and compute the mean, you would think the average class was bigger. Let’s see why.

Suppose all the students from the college come together to report their class sizes. You would have 150 students reporting a class size of 5, 300 students reporting a class size of 10, and 400 students reporting a class size of 20.

This is what the students experience, so let’s call these numbers the *experienced* class sizes. We will now compute the mean for these numbers, or the average experienced class size:

students per class

We multiply each class size by the number of students that observe that class size, and divide that result by the total number of students at the college.

And as you can see, the ‘experienced’ average class size is quite bigger than the observed average class size.

This is caused by the fact that there are a lot more students experiencing and reporting a large class size, than those experiencing and reporting a smaller class size. This happens because larger classes have more students in them, and consequently, we will have more reports from those larger classes.

So, while college students keep complaining about being stuck in large classes, deans keep reporting that most of their classes have relatively few students in them. Both groups are correct in their claims, and this is called the class size paradox.

Failure to understand this concept leads to plenty of controversy and confusion.

If you still couldn’t fully understand this paradox, don’t worry. Try watching this video, which explains the concept in detail. It was of immense help to me.

Do you have any questions?

Ask your questions in the comments below and I will do my best to answer.

Did I miss something or make a mistake somewhere?

Let me know in the comments below.