I recently read about the failure of Japanese students to answer 5 questions posed by the Mathematical Society of Japan. After much searching, I was able to track down one of questions used:

I don’t know if it’s the translation or a fault of the original text, but as it stands the wording of this question has a lot of problems that make it (in my opinion) a poor gauge of a student’s understanding of statistics.

I will focus on just one of these problems: the use of the word “average”. This was the same mistake made by the Swedish national test for 9th graders a few years ago. They had a problem asking for the “*genomsnitt*” (average). I spend a lot of time explaining to my students that one of the strengths of mathematics is its ability to be precise with definitions. And in particular that the word average has no precise mathematical meaning. If you want the mean, ask for the mean, if you want the median, ask for the median. Yes, in common language “average” usually means “the mean”, but this has no place in a national math test in any language.

There are of course a number of other problems with the text in this question …

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