The Fallacy of Average Class Size

The average person has one ovary and one testicle! 

If you think that’s ridiculous, then you’ll understand the folly of using average class size data in educational decisions. Statements that are mathematically correct can still be blantantly wrong.

Averages are attractive. In uncertain situations they provide a concrete anchor for understanding our world.

Data from the 2000 United States census indicate that the average household size in the United States is 2.59. Does that describe your family?

I didn’t think so, .59 of a person doesn’t exist.

You would call me a fool if I believed everyone has one ovary and one testicle, or even if I spent my days looking for the extra .59 person that should be living in the house next door. But somehow, when the average looks like something that supports our agenda, it becomes a valid measure of reality.  Kind of like average class size data.

Modern educators are familiar with the “power of zero” discussion. It goes like this: if a student has scores of 100, 100, 100, 100, and 0, they have an average of 80; a ‘B-’ for most, a ‘C’ for some. According to the argument, an 80 does not reflect the achievement of the student, the zero has an undue effect on the “average.” A move to standards-based grading indicates a desire to measure a child’s true achievement that can’t be measured with an average.  So averages aren't good indicators of student acheivement, but it's o.k. to use them as an indicator of how well a system is staffing.

Let’s assume that a school has ten teachers. Four of the teachers have a low class size of say twelve students. Perhaps they teach students who need more support, or they have a class that just met the minimum number for a section. The remaining six teachers each have classes of twenty-nine students. That school has an average class size of 22.2.

What if we looked at a different set of statistics? At this school with an average class size of 22.2, seventy-eight percent of the students are in classes with twenty-eight other students. Sixty percent of the teachers have classes of twenty-nine students. The average class size of 22.2 doesn’t look quite as successful.

What if this small model school were a high school? Each teacher has six classes. We would find six teachers at this school with a load of one-hundred seventy-four students and four teachers with a load of seventy-two student. The average teacher would have one-hundred thirty-three students, but in reality, sixty percent of the staff is teaching one-hundred and seventy-four students. Seventy-eight percent of the students at this school are 1 out of 174 to all of their teachers.

Honestly, we know better. Averages mean very little when divorced from their source, yet we continue to let them drive and/or support our positions. No amount of compiled information can substitute for looking closely at it’s individual parts and an uncritical acceptance of data is a recipe for poor decision-making.

Recently, I presented the following problem to my students:

Three truck drivers went to a hotel. The clerk told them that a room for three would cost $30. Each driver gave the clerk $10, and went to their room. After checking registrations the manager realized he had over-charged the drivers. The cost of the room should have been $25, so the manager gave the clerk $5 and told him to return the difference to the three drivers. On the way to the room, the clerk decided that since the drivers did not know they had been overcharged, he would return $1 to each of them and keep $2 for himself. Now each driver had paid $9 for the room and the clerk kept $2. 9 times three is 27 plus the 2 kept by the clerk totals 29. Where did the extra dollar go?

Just because the data are accurate and the numbers add up doesn't mean they reflect reality.  Sometimes we need to get out of the statistics and into people to find the answers.

Have you're experiences ever been misrepresented by "the average"?