### 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.