## Sunday, January 27, 2008

According to the powers that be, one of the lab classes I'm currently taking is graded on a curve. This means that a person's grade is determined by how well the class as a whole scores. Whatever the average score, whether it is high or low, it is assigned a B.

The lab notebook makes an odd suggestion that grading curves are justified because the laws of statistics are the "laws of common sense". It also suggests that the grading curve is an excellent example of an application of statistics. So let's analyze it!

The equation for a student's gpa* is as follows:
gpa = 3 + (x-m)/σ
Where x = the student's score
m = the average score of the entire class
σ = the standard deviation of the class's scores, a measure of how variable the scores are

Luckily, they gave us the mathematical tools to know exactly how accurate a grading curve is. If we have a class of 20 students, then the uncertainty of m is equal to σ/sqrt(20). That comes out to an uncertainty in gpa of about 0.22. That's almost a third of a letter grade!

If you're a student like me, the words "grading curve" inspire a nebulous fear--what will happen if the whole class is above average? Now, I can tell precisely how inaccurate my grade is. Thanks, statistics!

Another justification they used is that this how real life works. Maybe so, but I'm betting that real life has a sampling size larger than 20.

*gpa is the grade point average. A gpa of 4 is an A, a gpa of 3 is a B, and a gpa of 2 is a C.

#### 1 comment:

DeralterChemiker said...

Forget the curve. Just follow these three rules:
Rule 1. Never make any mistakes.
Rule 2. If Rule 1 fails, at least get the highest grade in the class.
Rule 3. If both Rule 1 and Rule 2 fail, chalk it up to experience. It's called education.