Real class sizes

College Search & Selection
1

<p>When universities report class sizes, they report them based on the percentage of total classes that are a certain size. Yet, since large classes have many more students than small classes, having 4% of students in classes over 100 can really mean that 20% of the average student's classes will have more than 100 people.
To illustrate: imagine a very small school, with say, 200 students, each taking only one class. Say that there are 11 classes, 1 with 100 students, and 10 with 10 students each. Though only 9% of classes would have 100+ students (and 91% would have 10 students), 50% of the students would be in a 100 student class, while an equivalent 50% would be in a 10 student class.
Using the principle above and info from the common data set, I calculated the "real" class size ranges at three elite private research universities (Yale, Princeton, Stanford), 3 elite LACs (Amherst, Williams, Swarthmore), 2 elite tech schools (Caltech, and MIT), and 3 elite public research universities (Berkeley, Michigan, and Virginia).
In making my calculations, I used the common data set listings of number of classes in certain size ranges. I assumed that classes with 2-9 students would average 5, classes with 10-19 students average 15, 20-29 produces an average of 25, 30-39 makes an average of 35, 40-49 makes an average of 45, and 50-99 makes an average of 75. For classes with more than 100 students, I assumed an average of 150 at small schools (below 10,000 undergrads) and an average of 200 at large schools (above 10,000), since these large classes are generally lower-division introductory classes that are larger at larger schools (ie, all psych majors take intro to psych at both Berkeley and Princeton, but there are a lot more psych majors at Berkeley, so the class will be bigger). I calculated the approximate number of students in each class size range at a university, added these together to produce total student-classes. I divided by the number of undergrads to make sure these results were reasonable (when they did not seem to be, I have made a note). I then divided number of student-classes in each size range by total student-classes to produce the following percentages:</p>

<p>Yale
2-9: 7.25%
10-19: 32.03%
20-29: 12.37%
30-39: 5.86%
40-49: 5.65%
50-99: 16.27%
100+: 20.56%
Total: 99.99%</p>

<p>Stanford (note: produces a large number of classes/student, so may be off)
2-9: 8.10%
10-19: 22.35%
20-29: 8.34%
30-39: 7.07%
40-49: 8.26%
50-99: 20.19%
100+: 25.70%
Total: 100.01%</p>

<p>Princeton
2-9: 5.58%
10-19: 29.80%
20-29: 8.70%
30-39: 7.78%
40-49: 5.00%
50-99: 17.76%
100+: 25.37%
Total: 99.99%</p>

<p>MIT (note: produces a surprisingly large number of classes/student, so may be off)
2-9: 6.69%
10-19: 13.32%
20-29: 13.20%
30-39: 7.45%
40-49: 8.10%
50-99: 27.31%
100+: 23.94%
Total: 100.01%</p>

<p>Caltech (uses 2005 data, the latest CDS I found) (further note: produces a surprisingly large number of classes/student, even more than MIT so may be significantly off)
2-9: 7.07%
10-19: 18.94%
20-29: 15.57%
30-39: 16.50%
40-49: 5.30%
50-99: 21.46%
100+: 15.15%
Total: 99.99%</p>

<p>Williams
2-9: 11.65%
10-19: 30.46%
20-29: 18.93%
30-39: 13.65%
40-49: 7.23%
50-99: 9.47%
100+: 8.61%
Total: 100.00%</p>

<p>Amherst
2-9: 5.69%
10-19: 35.39%
20-29: 21.68%
30-39: 12.94%
40-49: 8.32%
50-99: 13.86%
100+: 2.13%
Total: 100.01%</p>

<p>Swarthmore (produces a number of classes per student that seems low, may be off)
2-9: 11.21%
10-19: 38.95%
20-29: 25.72%
30-39: 11.21%
40-49: 1.52%
50-99: 8.85%
100+: 2.53%
Total: 99.99%</p>

<p>UC Berkeley
2-9: 5.27%
10-19: 12.57%
20-29: 11.65%
30-39: 6.95%
40-49: 5.19%
50-99: 17.91%
100+: 40.44%
Total: 99.98%</p>

<p>University of Michigan
2-9: 1.78%
10-19: 12.48%
20-29: 16.15%
30-39: 8.37%
40-49: 4.70%
50-99: 20.03%
100+: 36.49%
Total: 100%</p>

<p>University of Virginia
2-9: 2.27%
10-19: 13.13%
20-29: 14.49%
30-39: 9.25%
40-49: 8.85%
50-99: 18.69%
100+: 33.33%
Total: 100.01%</p>

<p>Note: I'm well aware that I don't have accuracy to two decimal places (numbers probably vary by up to 10% of the value provided, ie 100+ at UVA is between 30 and 36%, most likely). I calculated this way to ensure that my numbers added up right, and I don't feel like rounding, so I left as is.
Further note: Obviously, these numbers do not mean one university is "better" than another because of class size numbers. As vicissitudes pointed out in another thread, large class sizes have many advantages.</p>

2

<p>Wow, that's a lot of work, but you make a good point.</p>

<p>As they say, there are lies, damn lies and statistics. </p>

<p>The real point here though should be that people shouldn't fret about class size and that going to schools that advertise their small class sizes doesn't mean they'll never have a huge class. Likewise going to a huge university also doesn't mean that every class is going to be ginormous. I think most college students will tell you they've had a couple really big classes and a couple really small classes. The big classes tend to be lower level, and once you get to upper level classes in your major the size really drops off (unless it's one of those required classes for your major that they only offer once a year).</p>

3

<p>Its true, dont believe any crap about student to professor ratio. All the schools have the same ratio in reality anyway.</p>

4

<p>I created total scores for class size. I gave 4 points for each percentage point of 2-9 classes, 3 for each percentage point of 10-19 classes, 1 for each percentage point of 20-29 classes, no points for 30-39 and 40-49, -1 points for 50-99, and -2 points for 100+.
The results for these 11 schools were:
Swarthmore: 173.5
Amherst: 132.49
Williams: 130.22
Yale: 80.07
Princeton: 51.29
Caltech: 48.91
Stanford: 36.20
MIT: 4.73
Virginia: -22.39
Berkeley: -28.35
Michigan: -32.3</p>

<p>These scores seem to indicate that the LACs (particularly Swarthmore) do have substantially lower class sizes. It's probably accurate enough to say Yale is between the LACs and Princeton/Caltech/Stanford, which have smaller classes than MIT, which has smaller classes than the three state schools. Beyond that, my numbers aren't accurate enough to distinguish further (ie, Virginia and Michigan, or Princeton and Stanford, are effectively the same). I would say Swarthmore has definitively smaller classes than W+A, except that the classes/student number I calculated for Swarthmore seemed too low, implying that I was underestimating its class sizes. Caltech, Stanford, and MIT both seem to have class sizes overestimated (from my classes/student data), but the gap between MIT and those above it is probably big enough (particularly considering two of those schools may have had their class sizes overestimated) to make it safe to say that it has larger classes than P/M/S.</p>

<p>I went ahead and calculated numbers for the rest of the Ivy League (Harvard and Penn don't have their common data sets online).
Brown (not the common data set, so different ranges)
1-10: 4.52%
11-20: 20.61%
21-50: 28.70%
51-100: 18.40%
101-150: 10.5%
151-200: 7.97%
201-250: 3.15%
250+: 6.13%
Total: 99.98%
Score (approximate): 15.58 (assumes 1/3 of 21-50 are between 20 and 29).</p>

<p>Cornell (uses 150 avg for 100+, even though over 10,000 students because it produces more accurate classes/student)
2-9: 3.52%
10-19: 19.28%
20-29: 11.23%
30-39: 8.29%
40-49: 6.12%
50-99: 25.67%
100+: 25.89%
Total: 100.00%
Score: 5.70</p>

<p>Dartmouth (suspiciously low number of classes/student may skew numbers)
2-9: 3.80%
10-19: 28.67%
20-29: 16.39%
30-39: 8.68%
40-49: 11.88%
50-99: 20.99%
100+: 9.60%
Total: 100.01%
Score: 77.41</p>

<p>
[quote]
The real point here though should be that people shouldn't fret about class size and that going to schools that advertise their small class sizes doesn't mean they'll never have a huge class. Likewise going to a huge university also doesn't mean that every class is going to be ginormous. I think most college students will tell you they've had a couple really big classes and a couple really small classes. The big classes tend to be lower level, and once you get to upper level classes in your major the size really drops off (unless it's one of those required classes for your major that they only offer once a year).

[/quote]

True, but it seems that there still are significant differences. And at the small LACs, you won't have very many large classes. But, in general, this is good advice. You'll find both large and small classes everywhere, it's only the proportions that differ.</p>

5

<p>svalbardlutefisk, would assuming that no one student is taking more than one 100+ class distort the numbers? Or does this model take that into consideration (i.e. 45,000 student-classes, even though there are ~24,000 undergrads, so about two 100+ classes per semester per undergrad)? I'm not quite sure about this.</p>

<p>
[quote]
Cornell (uses 150 avg for 100+, even though over 10,000 students because it produces more accurate classes/student)

[/quote]
</p>

<p>Um, aren't you supposed to be basing your perceptions on the statistics, rather than shifting the numbers to fit your perceptions?</p>

6

<p>kyledavid, my numbers do not assume that no one takes more than 1 100+ student class. They simply find the total number of students in 100+ classes (it does not look at how many 100+ classes any individual takes). </p>

<p>With the Cornell thing, I made the adjustment because assuming that Cornell 100+ classes averaged 200 produced a number of classes per student that seemed too high. I checked the classes/student number at every university. At Michigan, Virginia, and Berkeley I did not have the same problem I had at Cornell.</p>

<p>Incidentally it seems that I underestimated the average size of 100+ student courses at Berkeley. I looked at the average for the first 23 (about 10% of the total) 100+ student classes, listed alphabetically, and found an average cap of 383 students (and most of them were near full, average enrollment around 350). Perhaps I will have to adjust my numbers to take this into account (though, kyledavid, it will only result in numbers you like even less).</p>

7

<p>
[quote]
With the Cornell thing, I made the adjustment because assuming that Cornell 100+ classes averaged 200 produced a number of classes per student that seemed too high. I checked the classes/student number at every university. At Michigan, Virginia, and Berkeley I did not have the same problem I had at Cornell.

[/quote]
</p>

<p>It seems your methodology is inconsistent. If it produces logical results for one, and illogical results for another, you change numbers to make them logical. The fact is, you don't have enough data on the 100+ class sizes, and that distorts every percent since that changes the denominator.</p>

<p>
[quote]
I looked at the average for the first 23 (about 10% of the total) 100+ student classes, listed alphabetically, and found an average cap of 383 students (and most of them were near full, average enrollment around 350). Perhaps I will have to adjust my numbers to take this into account.

[/quote]
</p>

<p>What? 10% is an accurate sampling size?</p>

<p>Before, I was going to point out (something that would help both Berkeley's and Stanford's numbers) something that someone on another thread said: are you going to notice a difference between 300 and 400? Or 300 and 500? Or, if you do, does it really matter? Beyond a certain point, it doesn't matter how many people are in the class. That's why I was going to suggest using simply 100 for all the schools (no, not because it helps Berkeley's numbers -- the difference in the # classes is insignificant to an undergrad). That would, however, suggest that once the class size has reached about 100, the size doesn't matter much. That's arbitrary, I suppose, so you can disagree.</p>

8

<p>
[quote]
It seems your methodology is inconsistent. If it produces logical results for one, and illogical results for another, you change numbers to make them logical. The fact is, you don't have enough data on the 100+ class sizes, and that distorts every percent since that changes the denominator.

[/quote]
</p>

<p>Look, it's true I don't have data on the exact numbers, and this could lead to problems in results. The goal is to get as accurate as possible for each college. Since the average number for 100+ student classes is the most likely to be wrong, if I end up with more classes per student that seems reasonable, the most likely source of error was an incorrect assumption about that average. So I adjust it. It's imprecise, but it is more accurate than not making the adjustment.</p>

<p>
[quote]
What? 10% is an accurate sampling size?

[/quote]

It's a pretty large sample. I would use the numbers from it as my average, but it's good enough to imply that 200 is an estimate far to the low end. </p>

<p>
[quote]
Before, I was going to point out (something that would help both Berkeley's and Stanford's numbers) something that someone on another thread said: are you going to notice a difference between 300 and 400? Or 300 and 500? Or, if you do, does it really matter? Beyond a certain point, it doesn't matter how many people are in the class. That's why I was going to suggest using simply 100 for all the schools (no, not because it helps Berkeley's numbers -- the difference in the # classes is insignificant to an undergrad). That would, however, suggest that once the class size has reached about 100, the size doesn't matter much. That's arbitrary, I suppose, so you can disagree.

[/quote]

I agree that it doesn't matter if your class has 300 or 500 students, but that's not the reason the average needs to be as close as possible (rather than just 100). Imagine a really simple scenario (so I can use exact numbers). Ten classes, one with 200 students, 9 with 10. That means that 200/290 of the total student classes have more than 100 students (69%). If, however, we bump the 200 student class up to 300, suddenly 300/390 students are in 100+ student classes (77%). So the percent of students in 100+ classes increases if the average size of 100+ classes increases. It doesn't mean that each class is worse for the student, but it does mean that more students are in huge classes. If I just used 100 as the average, it would significantly bias the results (by implying that far fewer students are in 100+ classes then is actually the case).</p>

9

<p>Well, perhaps there's data (I don't know of it, but it might be available somewhere) on the average class size, from which we could deduce the average 100+ class size.</p>

10

<p>
[quote]
I would say Swarthmore has definitively smaller classes than W+A, except that the classes/student number I calculated for Swarthmore seemed too low, implying that I was underestimating its class sizes.

[/quote]

[quote]
I assumed that classes with 2-9 students would average 5

[/quote]
Williams is noted for its tutorial</a> system, in which class size is capped at 2. It seems reasonable to suppose that a significant percentage of Williams classes in the "2 to 9" class size category are tutorials, and that Williams has an unusually high number of classes with only 2 students. So the assumed average of 5 for the "2 to 9" category may be an overestimate in this case.</p>

11

<p>Corbett, that's an excellent point. I'm not sure exactly how I should consider it (perhaps use 3 or 4 as the average for Williams).</p>

<p>kyledavid, when they report the average class size, schools use the "fake" class size number (ie, they don't control for the fact that more students are in 100+ classes than the percentage of classes over 100 would indicate). It would, however, be nice, if they reported either the number of classes taken by an average student (which would let me check some of my estimates) or if they broke down the 100+ category into multiple groups (as Brown does in its data).</p>

12

<p>
[quote]
Before, I was going to point out (something that would help both Berkeley's and Stanford's numbers) something that someone on another thread said: are you going to notice a difference between 300 and 400? Or 300 and 500? Or, if you do, does it really matter? Beyond a certain point, it doesn't matter how many people are in the class. That's why I was going to suggest using simply 100 for all the schools (no, not because it helps Berkeley's numbers -- the difference in the # classes is insignificant to an undergrad). That would, however, suggest that once the class size has reached about 100, the size doesn't matter much. That's arbitrary, I suppose, so you can disagree.

[/quote]
</p>

<p>This isn't a judgement on teaching, this is a reality-izing of class size date. If 400 people take a class and 100 people take a class, they are both 1 class, however a kid is more likely to be in the 400 kid class. This is what lutefish was getting at. Considering more people will be in the bigger class, a larger percentage of actual students classes will be of the 400 student variety than the 100 student one.</p>

13

<p>I'm aware that the probability of being in a 400-person class is higher than being in a 100-person class. However, there's little difference in experience.</p>

<p>Here's another question to use to supplement the data:</p>

<p>Beyond what size are classes not supplemented with small discussions/labs?</p>

14

<p>kyle - did you completely ignore the points in my post?</p>

<p>His percentages change based on there being more students in the classes than he thought. That was the point. Not some difference in quality.</p>

15

<p>
[quote]
Beyond what size are classes not supplemented with small discussions/labs?

[/quote]

I take it you mean "beyond what size" on the small end. I don't know where I would get this data, but it would be interesting if some universities have sections for 40 student classes while other schools only have sections for 100+ student classes. 70 students with smaller sections is certainly a different experience from 70 students without sections.
Do different universities have significantly different policies in this regard?</p>

16

<p>That's what I'm wondering. vicissitudes said they'd probably be the same, so it wouldn't be helpful in comparison, but I think it would -- why else would they report subsections? There probably are different policies. I'm pretty sure most, if not all, 100+ courses will have smaller subsections, and probably many of the 50-99 ones. Beyond that, I don't know. The only way I can see subsections as being useful for 30-50 classes is if the subsections have <10. I'm not sure, though.</p>

17

<p>
[quote]
His percentages change based on there being more students in the classes than he thought. That was the point. Not some difference in quality.

[/quote]
</p>

<p>I'm aware. I don't need comprehension help, but thanks.</p>