Assuming professors' curves are not auto-spikers but normalizers, what's the average distribution?

Factual Questions
1

So I remember reading Malcolm Gladwell’s Outliers, which said that someone with an 105 IQ can probably get through college alright, and most people with IQs just above 115, if their talents are properly exercised, can enroll and perform well in a Ph.D program. Now Ph.D programs’ difficulty obviously differ tremendously by discipline and by institution, but I’m not the one making the generalized statement.

After thinking about some things for a while, I began to wonder, 105 isn’t rare among the general population, and most people seeking college degrees are members of a group that has probably undergone some self-selection, so that they tend to possess more of the characteristics that facilitate academic excellence (e.g., diligence), so obviously IQ isn’t the only determining contributor. Maybe that explains why the number is 105 instead of 100 (unless I’m talking nonsense, in which case let me know).

My real question is (turns out the prelude isn’t the controlling context, but it’s there), what would a normal distribution look like for college grades and GPAs? That is, what percentage of people would ideally emerge with 4.0s (assuming 4.0 is the maximum), with 3.95s, and with each of the next gradations? Individually, in a class, how many people would ideally receive As?

However, just as Ph.D programs differ by institution and by discipline, undergraduate programs do too. Maybe upscaled rigor adjusts for this adequately, but if not, please consider other factors’ influence, then make a calculated estimate.

My earlier point about a 105’s frequency is that, Gladwell obviously leaves “get through college just fine” open to interpretation. How rare is a 4.0, for example, and how common is a 3.5?

2

I don’t know the answer to this question, but there’s one thing that’s going to mess up the numbers - differing grading scales and determinations of “passing”. In most of my school, 90% is an A, 60% a D, and D’s (1 point per credit) count as passing. In the nursing program, however, 92% is the lowest A, 78% is the lowest C (2 points per credit), and C’s or better are required to advance in the program. So a “regular” student could graduate with a 1.0, but a nursing student will never graduate with less than a 2.0 - and were the grading scale the same as the regular classes, it would be worth a 3.0.

3

miragesyzygy writes:

> So I remember reading Malcolm Gladwell’s Outliers, which said that someone
> with an 105 IQ can probably get through college alright, and most people with
> IQs just above 115, if their talents are properly exercised, can enroll and
> perform well in a Ph.D program. Now Ph.D programs’ difficulty obviously differ
> tremendously by discipline and by institution, but I’m not the one making the
> generalized statement.
>
> After thinking about some things for a while, I began to wonder, 105 isn’t rare
> among the general population, and most people seeking college degrees are
> members of a group that has probably undergone some self-selection, so that
> they tend to possess more of the characteristics that facilitate academic
> excellence (e.g., diligence), so obviously IQ isn’t the only determining
> contributor. Maybe that explains why the number is 105 instead of 100 (unless
> I’m talking nonsense, in which case let me know).

When you ask why the number isn’t 105 instead of 100, it appears to me that you’ve completely misunderstood what Gladwell is saying. Pretend for a second that I.Q. is actually an accurate measure of something that we’ll call intelligence. Pretend for a second that intelligence is the only thing that would determine one’s ability to succeed in college. (Yes, I know why each of these statements is shaky. I know. Really. I’m just assuming them for a second to simplify what I’m about to say. Don’t argue them with me.) What Gladwell is saying that anyone with an I.Q. above 105 is intelligent enough to succeed at college. He is not saying that the average I.Q. of people who are intelligent enough to succeed at college is 105. It appears to me that that’s what you think he is saying. If that’s not what you think he’s saying, why are you asking why the number is 105 instead of 100? If he were saying that the average I.Q. of people who are intelligent enough to succeed at college was 100, that would be equivalent to saying that everybody is intelligent enough to succeed at college. For that matter, if he was saying that the average I.Q. of people who are intelligent enough to succeed at college was 105, that would mean that nearly everyone was intelligent enough to succeed at college.

4

The OP’s question is totally tangled, as pointed out just above.

Let’s talk for a minute not about college but rather high school where we’ll assume 100% of the populace attends. **If **as assumed above, IQ is both a meaningful measure & an accurate predictor of expected academic results, then we’d see a Gaussian (normal) distribution of academic results.

Switching to college we’d drop a bunch of people from the sample population. More from the “dumb” end than the “smart” end, but some smarties & even super-geniuses won’t attend college.

So our distribution of academic potential is no longer Gaussian. It really doesn’t matter whether the coursework is harder or not. The academic results will no longer be Gaussian. And that’s about the end of what we can say. Without detailed knowledge of the IQ distribution of the college students we’re out of data.
Now above here I carefully said “academic results”, not “academic grades”. And that difference is a confounding issue which utterly swamps the others.

Pretend for a minute that all the colleges in our sample use the exact same grading techniques throughout all their courses. Then the academic grades we get in our sample depend almost totally on those techniques, not on the students’ academic results.

If the colleges all normalize to obtain a Gaussian distribution of A, B, C, D, F grades, then that’s what we’ll see.

If the colleges all normalize to obtain 60%As, 30% Bs, 8% Cs, 1.5% Ds and 0.5%Fs (not uncommon at some instuitutions today) then that’s what we’ll see.

Even if they use an apparently non-normalizing system like all grades are based solely on universally standardized tests per class subject which are graded as “>90% correct = A, >80% = B, >70% = C, >60% = D, else F” there is still the meta-normalization that somebody had to decide how hard to make the test. And that decision controls the grade distribution outcome at least as much as the students’ efforts do.

Add in the real-world factors that IQ measures something very different from college success, there is no standardization of class teaching, class evaluating or class grading systems at any level, and you’re left with nothing but silliness.
It seems to me the OP’s question amounts to “Tree leaves are basically green. And some are bigger than others. What is the color distribution of the pretty ones in the forest?” Damn if I know. Or even know how to start to parse the problem to do the research to find out.

5

You also can’t say, a priori, how many students “should” get As, or how many should get Bs, or whatever. To do that, you’d have to already know what distribution you wanted for grades. And the way such distributions are usually established in the first place is by some teacher or department head deciding how many students should get As, and so on.

Also be aware that the 90-80-70-60 grading scheme is far from universal, especially once you get to college. There’s a good argument to be made that a well-designed test will have an average of 50%, and I’ve had classes where the top grade (which got an A) was 25 or 30%.

6

You couldn’t test my class since I only give As, Bs, and Fs.

7

This isn’t always true. In a large lecture class with a couple hundred students that’s graded out of 1000 points, the distribution of points earned will generally look pretty close to Gaussian. As you point out, that doesn’t mean that grades the will, but it’s not correct to say that everything’s completely non-Gaussian.

8

As an addendum to this post, (a) what percent of students make the “Dean’s List”, or “honours”, or “cum laude” or whatever they call the top performers at your institute of choice, and (b) what was the cut-off criteria?

That should give an idea of the upper level of the distribution.

Many years ago, when York University first started up in Toronto… The Ontario government at the time would pay 5/6 of the tuition of any student. York U would accept anyone who passed high school but would flunk out the incapable in the first or second term… no matter, they got the full student subsidy for the year.

I think of college as like a filter. You are not guaranteed smarter, but the odds are that there is something above average if you actually make it through. I believe what Gladwell is saying is the IQ equivalent of “you must be this tall to ride this ride.” If not, you’ll probably fall off and hurt yourself.

What convinced me that higher degrees did not really mean much - when the “Cold Fusion” debacle came along, the number of disagreements over relatively basic science; is the energy-in energy-out being measured accurately, are we confusing a simple hydrogen explosion for something more? I would assume clever people would not make such public, fundamental, mistakes?

9

While I’d agree with the first sentence, I’d opinion that the second scenario is stupid. I’ve had a class or two like that. Test problems so hard nobody could do em. Rampant and random partial credit to get numbers even that high. Who got the A and who got a C or F was more a crap shoot rather than any actual indication of who actually knew what.

10

If we assume the distribution matches IQ generally and we pretty much chop off the lobe “below 105” then it will NOT be Gaussian. However, there’s a lot of assuming in this…

11

I don’t think thats true but I am not sure how to explain it.

12

I TAed a class just like that, and we structured the assignments to strongly encourage those on the very bottom of the curve to drop the class. We then structured the distribution of grades to not penalize the very bottom of the new distribution. Except for the few students who didn’t get the hint.

13

I don’t know if it is still true, but Harvard was know for rampant grade inflation. The University of Chicago was not. My daughter reports that when someone from Harvard came to Chicago to talk about the grade inflation problem, he got booed. :smiley:

I never graded papers at MIT, but got graded plenty, and pretty much all tests I remember were on curves with lots of long questions with partial credit. Many of the tests were designed to distinguish those who really got the material from those who did not, and none of it involved memorizing anything. MIT had no Deans List or cum laude, I suppose because we were psycho enough already without the need for anything else to increase the pressure.

The Illinois CS department, which I did grade for, had a fairly similar system, perhaps because CS majors were also self selecting.

When I taught in Louisiana students expected the 90 = A grading system, and expected multiple choice instead of essay type questions. It was quite a culture shock. I suspect that distribution looked a lot more normal than in the other places I had been.

14

It’s a nice story, but I’m telling you what I and others have seen in actual classes at elite universities, where you can be comfortable that the average IQ is above 105.

Edit: The reason that this happens is because 1000 points is enough for central limit-type behavior to kick in, and we would expect to see a Gaussian.

15

A well designed test is not meant to make it so hard that it’s a crap shoot. That’s a poorly designed test.

A test is used to measure skill or knowledge. Tests should be reflective of what the student is expect to know, not what the professor knows. A 100 level class shouldn’t be tested at the 300 level unless that’s clearly outlined. (If it is, then that’s grade inflation beyond reason, which I disagree with 3,000 per cent.)

You can design a test so that there really is a cutoff between those who know and don’t know. If your classes are thematic and continue to expand on prior knowledge, then yes, not only can you create appropriate tests, but you’re probably a good teacher as well.

//disclaimer: biased teacher

16

Uhhh, I think thats kinda what I was complaining about…

17

Quoth billfish678:

You’ll note that I didn’t actually say that the second scenario (high scores of 25%) was a good thing, just that it happens. The specific case I was thinking of was a new professor who, at the time, lacked the experience to write a well-crafted test. His averages have since gone up considerably.

18

Well, yes, if the lower end cut-off is 105, then I suspect the average will be above 105, except in the Harvard class where “Our Friend the Beaver” is the assigned essay.

Of course, if the lowest IQ you can hope to make it through on is 105, then odds are a lot of 105-115 will choose alternate paths to success. Then, elite colleges tend to admit based on test scores that will weed out a lot of the lower end of the acceptable range whose father was not a big-shot alumni. This may or may not be balanced out by those who are more than qualified scholastically but not financially for ivy league. Regardless, the bottom lobe will be truncated. For every high-grade genius in third-year math, one hopes there is not a special needs student to balance the distribution.

19

And I’ll agree that you didnt imply the second scenario was a good one :slight_smile: And I am sorry if I implied that you thought so.

My experience with the couple of classes I had like that was the exact opposite of yours though. These guys had been teaching this stuff for so long “everything was easy”. Teach all this X level stuff. Then test at the X plus something level because its the obvious next step. :rolleyes:

20

I have no idea what you’re trying to say here.