Tuesday, January 31, 2017

About averages

Radio Commentary

There is a tendency in the media to overuse the word “average” and misrepresent what it really means.
Take, for example, “average” test scores. As we all know, to get an average, you add up all the scores and then divide by the total number of scores. It is often the case that no individual score actually falls at the average.
An average isn’t a median or midpoint. It doesn’t mean that half the scores fall above and below that point. In fact, you could conceivably have a situation where ALL scores fall ABOVE the average, except for one score that is so very low, it pulls down the average.
This helps explain the seeming paradox with test scores. For many years the average SAT scores were down — but scores were up for every subgroup that took the test.
That included Hispanics, Asians, blacks, whites, etc. — and scores were up for every academic level represented — “A” students, “B” students, and “C” students.
If test scores rose for every academic level, how could the overall average be down?
It is because far more C students are now taking part. And even though scores rose for students who are still learning English, far more of those students have also been taking the test, too.
So when you disaggregate the tests and look at every group that took them, you see a success story. But when you aggregate the tests and look only at the overall average, the picture is very different.
This is a critical concept in assessing what needs to be “fixed” in our schools. Sadly, it is always easier to deal with simple rhetoric than with complicated facts.