<p>Class size is one (among many) comparisons that people make between various colleges/universities, in particular between small liberal arts colleges (LACs) and national universities, and also among various universities. But Ive been frustrated by the slipperiness of the data provided in the headline statistics. A summary measure is provided in US News tables, where they give (1) the % of classes of 50 or more, (2) the % of classes of 20 or less, and (3) the median class size. For instance, Stanford has 10% of its classes over 50 students. But this doesnt mean that the average Stanford student will be in a class of over 50 students only 10% of the time actually, they will have a class over 50 students almost 50% of the time.</p>
<p>Why the difference? Intuitively, its because there are a lot more students in a large class than a small one, and therefore the large classes carry a lot more weight than smaller classes in the overall experience of the student body. The US News indicators do not perform such a weighting. So what Ive done below is to show summary results below obtained by appropriately weighting class size data (from the Common Data Set for each institution; Harvards is from their viewbook data based on Fall 2006 courses). Ive presented the results for some colleges and univs below, and followed with some more details on the rationale and methodology (and in case Ive made some mistakes, any comments or corrections are welcome).</p>
<p>The numbers below present answers to the following questions:
What % of an average students classes would be over 50 students? Below 20 students? And what would be the average class size encountered? (although I think the averages are less useful than the >50 or <20 questions)</p>
<p>Some top LACs:
Swarthmore: 9% >50, 48% <20, avg. 27
Pomona: 5%, 50%, 24
Carleton: 5%, 42% 25
Grinnell: 0%, 43%, 22
Amherst: 16%, 49% 33
Oberlin: 13%, 44%, 33
Wesleyan: 20%, 36%, 38</p>
<p>HYPS:
Yale: 40%, 38%, 74
Princeton: 47%, 33%, 85
Stanford: 49%, 31%, 83
Harvard: 55%, 26%, 120</p>
<p>An explanation of the rationale/methodology: For a simplified example, assume that a college has 50 classes with 2 students in each class (i.e. total of 50<em>2=100 student experiences) and 10 classes with 90 students each (i.e. total of 90</em>10=900 student experiences). So there are a total of 1000 student experiences, of which 90% are in classes of 90 and 10% in classes of 2. In other words, the average student will have a 90% chance of being in a class above 50, a 10% chance of being in a class below 20. This is in contrast to the US News manner of presenting the numbers: they would say that only 17% of the classes were above 90 (i.e. 10 out of 60 classes) and 83% below 20. While their statement is true, I dont think it is as useful as the other way of looking at the data.</p>
<p>Another way to think about this is that if each student has for example 10 classes (and hence there are 100 students), you could think of each student having, on average, 9 classes of 90 students each and 1 class of 2 students. And so the weighted average class size encountered by each student would be approx 81.</p>
<p>You can also calculate weighted average medians if you prefer those to the mean (in doing so, you should also interpolate the results so that you dont have large discontinuities).</p>
<p>btw one assumption I had to make was for the average class size above 100 (since the CDS just says greater than 100). I assumed 150 for the LACs and 200 for the national univs (200 was Harvard's average class size above 100).</p>