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. There are other approaches that could have been used, but I believe those I’ve used yield the most accurate results possible given the data available. 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.
Top 5% Math Methodology
First, 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.
All calculations for the list of universities with the most students in the top 5% on standardized testing in math used the 2018-19 Common Data Set (CDS) for each university. 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 Ohio State (OSU) so you can see where in the CDS the numbers are coming from.
Because testing data in the CDS is reported only for degree-seeking, first-time freshmen, my first step was to figure out what percentage of the overall student population should be used. To do this, I went to Section B and added up all of the degree-seeking, first-time freshman (both full- and part-time) plus all of the other first-year, degree-seeking students. This gives us the total number of degree-seeking, first-year students (8746 at OSU). I then divided just the degree-seeking, first-time freshman (7944 at OSU) by this total number to get the percentage reflected in the testing data (.9083 for OSU).
Next, I multiplied this percentage by the total number of degree-seeking students from all years (45,769 at OSU) to arrive at the number of students in the total student body that should be included in the calculation (41,572 at OSU). This makes the undesirable assumption that all years have the same percentages, but since the same assumption is made for all schools and any trends that might exist are likely similar for all schools, the numbers are probably not far enough off to make much, if any, difference in the final order in which the schools appear on the list. By the way, I decided that using Common Data Sets from previous years would not yield a more accurate result, due to not knowing which first-year students from those years were still in attendance.
The next task was to figure out the percentage of students with an SAT Math score of 700 or above or an ACT Math score of 30 or above. Of these two groups, whichever reported percentage was higher (SAT 700+ or ACT 30+) I multiplied by the percentage of students submitting scores from that test. At OSU, 59% of SAT takers scored 700 or above on the Math section, and only 44% of ACT takers scored 30 or above. Thus, I multiplied .59 by .35, which was the percentage who submitted SAT scores; the result was .2065. Since I used SAT scores for 35% of the students, I needed to use ACT scores for 65% of the students. Thus, I multiplied .44 by .65, yielding .286. Adding .286 and .2065 resulted in a total of 49.25% of OSU students with a standardized math test score in the top 5%.
Multiplying this percentage by 41,572 leaves us with 20,474 OSU students 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.