Students gather for lunch in the foyer of the School Without Walls in the District in 2011. It was the top-ranking high school from Washington, D.C. on the America’s Most Challening High Schools list in 2015. (Marvin Joseph/Washington Post)

1. How does the America’s Most Challenging High Schools list work?

We take the total number of Advanced Placement, International Baccalaureate and Advanced International Certificate of Education tests given at a school each year and divide by the number of seniors who graduated in May or June. I call this formula the Challenge Index. With a few exceptions, public schools that achieved a ratio of at least 1.00, meaning they had as many tests in 2014 as they had graduates, were put on the national list. We rank the schools in order of ratio, with the highest (20.44) this year achieved by BASIS Oro Valley, in Oro Valley, Ariz., which takes over as the top-ranked school after the American Indian Public Charter in Oakland, Calif., held the position for two years.

I think 1.00 is a modest standard. A school can reach that level if only half of its students take one AP, IB or AICE test in their junior year and one in their senior year. But this year, just 11 percent of the approximately 22,000 U.S. public high schools managed to reach that standard and earn placement on our list. On our list, the top 220 schools are in the top 1 percent nationally, the top 440 in the top 2 percent, and so on.

2. Why do you count only the number of tests given, and not how well the students do on the tests?

Some schools brag about their high passing rates on AP or IB, meaning the percentage of test-takers who scored 3, 4 or 5 on the 5-point AP exam or 4, 5, 6 or 7 on the 7-point IB exam. Passing scores make students eligible for credit at many colleges and universities.

I decided not to count passing rates in this way because I found that many high schools kept those rates artificially high by allowing only top students to take the courses. AP, IB and AICE are important because they give average students a chance to experience the trauma of heavy college reading lists and long, analytical college examinations. Research has found that even low-performing students who got a 2 on an AP test did significantly better in college than similar students who did not take AP.

On the list, we also give readers a sense of how well each school’s students are doing on the tests by posting the Equity and Excellence rate, which is the percentage of all graduating seniors, including those who never took an AP course, who had at least one score of 3 or above on at least one AP test sometime in high school. The nonprofit College Board, which oversees the AP program, invented this metric. It found that the average Equity and Excellence rate in 2014 was 21.6 percent.

3. Why don’t I see famous public high schools such as Stuyvesant in New York City or Thomas Jefferson in Fairfax County on the list?

We do not include any magnet or charter high school that draws such a high concentration of top students that its average SAT or ACT score exceeds the highest average for any normal-enrollment school in the country. This year, that meant such schools had to have an average SAT score below 2000 or an average ACT score below 29 to be included on the main list.

The Challenge Index is designed to identify schools that have done the best job in persuading average students to take college-level courses and tests. It does not work with schools that have no, or almost no, average students. We put those schools on our Public Elites list.

4. If I think my school qualifies for the list but I don’t see it there, what should I do?

E-mail Jay Mathews at If we find that the school qualifies, we will add it to the list.