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Chi-squared Faker

Age 16 to 18
Challenge Level

Why do this problem?

This problem gives students an insight into the fact that data can be manipulated to give conflicting results and a glimpse of the more difficult issues surrounding the study of statistics. It contains a good mathematical problem solving element and draws students into the workings of the Chi-squared test, resulting in a greater understanding of the mechanics of the test.

Possible approach

Key to this task is the realisation that the Chi-squared test requires grouping of data classes when individual classes contain few elements and, in this case, that there are a variety of equally sensible ways of grouping the data. Students might realise this individually or this might emerge through classroom discussion.

Key questions

  • Can you think of a convincing explanation for the expected distribution of weights?
  • What choices are there to be made in a Chi-squared calculation?
  • How would you group classes to most increase the Chi-squared statistic?

Possible extension

If students have access to a spreadsheet, they might try to invent their own set of data which exhibits this type of behaviour.

Possible support

Rather than try to work out which would be the best grouping before performing a calculation, suggest that different students cluster the data categories individually and then perform the standard Chi-squared test. The students could then compare results and hopefully then realise that the grouping can significantly affect the character of the result.