During a call with reporters in conjunction with the announcement of the Race to the Top Round 2 finalists, Education Secretary Arne Duncan touted the 26-point increase in average scores since the first round.

Between the two rounds of competition, he said, “The movement we saw in terms of reform was extraordinary.”

Just how extraordinary was it?

Well, to figure that out, we need to first figure out how the Education Department calculated this 26-point average increase. Officials there clarified for me that the 26-point average Duncan referred to was arrived at by comparing the average score of all Round 1 applicants with the average score of all of the Round 2 applicants. So the two groups aren’t the same, because some states applied in Round 1 but not Round 2 (e.g. Minnesota) or vice versa (e.g. Maryland.)

On a grading scale of 500 points, a 26-point increase average amounts to a 5 percent average jump. Is that a dramatic increase, especially given that we should expect applications to get better between Rounds 1 and 2, since applicants had the benefit of reading the judges comments? (I’m not sure, which is why I’m asking.)

It’s also important to note that averages can be greatly influenced by outliers, or those states that showed dramatic swings in their scores. Which brings me to Arizona, the comeback state that made it into the Round 2 finals after placing next-to-last in Round 1.

We know that Arizona scored 240 points in Round 1. We know that for Round 2, all finalists scored above 400. So that means Arizona, at a minimum, saw a whopping 160-point increase in scores.

Now that’s bound to have an effect on the average increase. But how much? Using some intermediate math skills, and assuming that Arizona got a score of 400 points in Round 2, we figured out that Arizona’s dramatic uptick drove up the average by about 3 1/2 points.

In addition, the Education Department told me that slightly more than half of the Round 2 finalists saw double-digit increases in their scores. Of course, that means half didn’t.

We’ll be able to scrutinize the scores much more deeply once they’re released alongside the winners later this month or in early September. In the meantime, it seems like there was “extraordinary” movement concentrated in some states, but certainly not all.