Math CentralQuandaries & Queries


Question from Ray, a student:

It's about average test scores over a three year span. If the scores were:

2005- 52.6%
2006- 42.5%
2007- 45.5%

What is the average amount they changed each year in three years?

Hi Ray.

Between 2005 and 2006, the scores decreased 10.1 percentage points.
Between 2006 and 2007, the scores increased 3.0 percentage points.

Between 2005 and 2007, the scores decreased 7.1 percentage points.

Since this 7.1 percentage point decrease is over two years you might be tempted to say the scores decreased on average 7.1/2 = 3.55 percentage points per year. But this gives the wrong impression. The scores dropped by 10 percentage points and then rose 3 percentage points.

Stephen La Rocque and Harley Weston

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