Top 5% Math Methodology

A handful of readers will no doubt be curious how I arrived at the list of universities with the most students in the top 5% on standardized math testing. Below is my methodology, hopefully explained well enough to be easily followed by all who are interested; if you have suggestions on how to improve it, I’d welcome them. If you represent a university, though, what I’d welcome even more is the exact number as calculated by you, which I would be happy to use to replace my estimate and indicate that I’ve done so.

The reason I chose Math instead of Reading is because the numbers reported by colleges in their Common Data Sets are for students with scores above 700 on the SAT and above 30 on the ACT, and these scores are roughly equivalent for the Math section. This is not true for the Reading section.

The calculations for this list do make some assumptions, including that all institutions report data in the same manner. The same assumptions were made for all schools, though, so the order should be close to accurate.

All calculations used the 2019-20 Common Data Set (CDS) for each university, with a couple of exceptions that were footnoted. Numbers used are from Sections B and C of the Common Data Set. The former has data for the numbers of students at each university, while the latter has testing data for those schools. To make it easier to follow what I’m talking about, I’ve included the numbers used for the University of Michigan so you can see where in the CDS the numbers are coming from.

Because the testing data provided is for degree-seeking, first-time, first-year freshmen, the first step was to add up the total number of these students from section B1 of the CDS. For Michigan’s 2019-20 CDS, that number is 6830.

The next task was to figure out the percentage of freshmen with an SAT Math score of 700 or above or an ACT Math score of 30 or above, using the data in section C1 of the CDS. Of these two groups, whichever reported percentage was higher (percentage with SAT 700+ or percentage with ACT 30+) I multiplied by the percentage of students submitting scores from that test. At Michigan, 84.5% of ACT takers scored 30 or above on the Math section, and only 67.1% of SAT takers scored 700 or above. Thus, I multiplied .845 by .48, which was the percentage who submitted ACT scores; the result was .4056. Since I used ACT scores for 48% of the students, I needed to use SAT scores for 52% of the students. Thus, I multiplied .671 by .52, yielding .34892. Adding .4056 and .34892 resulted in a total of 75.452% of Michigan students with a standardized math test score in the top 5%.

Multiplying this percentage by 6830 leaves us with 5153 Michigan freshmen with a Math section SAT or ACT score in the top 5%. I rounded this score–as well as those for all other universities–to the nearest 100 for the list, since I’m not trying to provide a definitive list of exact numbers, but rather to make a point that there are many extremely capable students in places folks might not expect to have such high numbers.