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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Why do 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.
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.
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?
If students have access to a spreadsheet, they might try to invent their own set of data which exhibits this type of behaviour.
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.
Chi squared tests
Estimation of areas under curves
Maths Supporting SET
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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Millennium Mathematics Project