When Counts and Percents Contradict

I’m requesting an immediate dispatch of the Numeracy Police to Phoenix Sky Harbor Airport, Terminal 4, downward escalator to baggage claim—code 319: material contradiction between count and percent, in progress:

The sign says:

1,732 ASU freshmen graduated in the top 10 percent of their high school class. That’s more than Harvard, Princeton, Stanford or Yale. And one more reason to choose ASU.

ASU is Arizona State University. Despite its many merits, ASU is rarely grouped with these other elite schools. So how does it happen here?

According to Wikipedia, ASU has 48,955 undergraduates. That compares to the other colleges mentioned as follows (again, with numbers from Wikipedia):

College	Undergraduates
ASU	48,955
Harvard	6,655
Stanford	6,654
Yale	5,300
Princeton	4,365

I could not quickly find the numbers for each college’s freshman class. So for the sake of simplicity, let’s say that 25% of undergraduates at each college are freshmen. That would be 12,239 freshmen at ASU and an average of 1,436 freshmen at the others.

Recall that the sign said 1,732 ASU freshmen graduated in the top 10% of their high school class. That outnumbers any of the other schools’ entire freshman class. So even if the elite schools’ freshmen classes were entirely comprised of top-10% high schoolers—which is probably close to true—they would each still lose this comparison to ASU, where 14% of the freshmen (1,732 divided by 12,239) are top-10% high schoolers.

The trick is, ASU is using a count but implying a percentage. That’s bad practice if the percentage contradicts what you’re claiming with the count, as is the case here. To illustrate, if we restate the sign using a percentage...

14% of ASU freshmen graduated in the top 10 percent of their high school class. That’s more than Harvard, Princeton, Stanford or Yale. And one more reason to choose ASU.

...it would be false, by a wide margin.

I doubt ASU’s advertising people thought twice about this; they simply wanted a catchy sign. However, I’d like to think that many of this year’s top 10% high schoolers will not be persuaded.