The "curve" (grading system) can mean a ton of different things

glennmagusharvey

Grading "on a curve" almost never involves a curve (unless you visualize things in a funny way), and takes many, many different forms.

My first encounter with a "curve" was in my high school calculus class.  All section test and term exam grades were "curved" to an average of 88 if the average is below 88, capping at 100 unless you got a natural 100.  This means that the mean score m on the exam is calculated, then 88 is subtracted from m, and if 88 - m is positive then 88 - m is added to everyone's scores, except those whose scores are between 100 - m and 100, exclusive, which just become 100.  In other words, let's say the average is a 77, so the curve is 11, and people who get a 70 now have an 81, people who get an 84 now have a 95, people who get a 94 now have a 100, and people who get a 100 now have a 111.

Later, I encountered a "curve" that was...just a simple grading system.  In my organic chem class, I think the grading system was 85~100 = A, 70~84 = B, 55~69 = C, 40~54 = D, <40 = F.  Scores were "curved" to this.  What that meant, other than "score means corresponding letter grade", I have no idea.

And even later, in various chemical engineering classes, I noticed that whatever the average was turned out to be a B or C roughly.  People would routinely get miserable scores on exams (we're talking 40s, 50s, 60s...if you got above a 70 you were considered a local genius), but people with average grades would get Bs and Cs.  This was referred to as a "curve" as well, though all this seemed to be was the profs deciding grades based on the distribution of scores.

I presume that the term "curve" actually originally meant that the instructors would fit the distribution of scores to some sort of probability distribution curve, such as a normal distribution.  Except it seems that the word is thrown around willy-nilly.  When I first heard that scores in a particular class in college/university would be "curved", I used to think that that would be a really good thing for my grades in case I sucked.  Then I learned that the word bore no inherent meaning anymore, and could be used to mean just about anything.

RedEyedAbyss

"Then I learned that the word bore no inherent meaning anymore, and could be used to mean just about anything."

Actually, it seems more like you don't understand the meaning. Maybe no one bothered explaining it to you, but it's really a matter of statistics.

"And even later, in various chemical engineering classes, I noticed that whatever the average was turned out to be a B or C roughly. People would routinely get miserable scores on exams (we're talking 40s, 50s, 60s...if you got above a 70 you were considered a local genius), but people with average grades would get Bs and Cs. This was referred to as a "curve" as well, though all this seemed to be was the profs deciding grades based on the distribution of scores."

This is precisely what curved grading is. It's based on the Gaussian distribution, otherwise known as the "normal distribution", which is generally regarded as a reliable model for predicting probability events such as student grades. The whole idea of 50 percent getting B might seem arbitrary to you, but really, a 50% in a high-level Physics course is very different from a 50% in Electrical Engineering, namely because the former is much harder. Thus, it's better to consider the relative performance of the class rather than the absolute performance.

I believe your first example may functionally serve the same purpose, though I don't see the point as it's less intuitive to grasp.

"Later, I encountered a "curve" that was...just a simple grading system. In my organic chem class, I think the grading system was 85~100 = A, 70~84 = B, 55~69 = C, 40~54 = D, <40 = F. Scores were "curved" to this. What that meant, other than "score means corresponding letter grade", I have no idea."

I suspect it's similar to your first example. Though it might just be based on historical averages, which, as my Math 100 professor explicity stated, is not curved grading.

glennmagusharvey

A probability distribution such as a normal distribution is precisely what I mentioned in my last paragraph.  I figure that the original idea is that the instructor probably fits the scores to a curve and gives grades based on, say, standard deviations from the mean.

That said, this assumes that the scores are actually normally distributed.  If you're going to just assign cut-off points based on these calculations, you might end up with strange numbers of people getting various grades if the scores are not normally distributed.

I guess you could alternatively use the "X% of the people in the class get Y grade" method, which I've never personally encountered and so can't say whether people refer to that as a "curve".

Alternatively, if the scores aren't normally distributed, I guess you could use the median and quartile (or whatever-ile, such as quintile, sextile, septile, etc.) numbers.  But you're no longer using a curve anyway.

And then you have my calculus class's thing, which only looks at the mean and roughly brings up the mean to a given minimum.  But just because you're working with a mean doesn't mean that you're working with a particular distribution.  Not to mention that bringing up the mean by adding a fixed amount is...well, shockingly linear for something called a curve.  (My original, very early misunderstanding of "curve" was actually that people would have their scores "curved" toward the desired average--so that people who got a 70 on a test would get a bigger bonus than those who got an 80, for example.)

RedEyedAbyss

"I guess you could alternatively use the "X% of the people in the class get Y grade" method, which I've never personally encountered and so can't say whether people refer to that as a "curve"."

That's actually my university's grading standard, as one of their pages nicely points out. In any case, grading based on distributions is going to be an approximation.