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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# David and Goliath

### Why do this problem?

This problem encourages students to engage with a data set, pose
their own questions about it, and perform some statistical analysis
to try to answer their questions. The real-life sporting context
provides a 'hook' to draw students in to speculation and discussion
about how to compete on a level playing field.

### Possible approach

### Key questions

### Possible extension

Consider other athletic events where attributes such as height or
weight might confer an advantage. Collect some data and analyse it
to see whether there is a case to be made for some sort of
'handicapping' system.

### Possible support

Make it clear to students that there are no right or wrong answers
in this task, but that you are looking for answers with good
statistical justifications.

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Age 14 to 18

Challenge Level

- Problem
- Getting Started
- Teachers' Resources

Display the data (or hand out this
worksheet) and ask students to discuss with their partner any
questions that it provokes. Then take some time to share these
questions with the whole class.

If no questions are forthcoming, it is suggested in the
problem that there might be a link between weight of competitor and
distance thrown; this is one line of enquiry that could be pursued.
Other ideas (which will need more data to be collected) could
involve height, comparisons between men and women, comparisons
between junior and senior shot putters...

Stage 4 students could use statistical techniques such as
averages, range/IQR, and scatter graphs to test any hypotheses they
make. Stage 5 students might calculate standard
deviation, correlation coefficients or a suitable
t-test.

Students could be invited to work in small groups on their
chosen line of enquiry. If computers are available, the tables of
data are contained in this spreadsheet, and
more data from the IAAF on shot putting can be found
here.

Once students have analysed the data and answered the
questions they posed, they could present to the rest of the class,
either as a presentation with time for questions or by preparing a
poster explaining their work.

Do any data points jump out at you?

Does weight confer an advantage to shot putters?

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Like all sports rankings, the cricket ratings involve some maths. In this case, they use a mathematical technique known as exponential weighting. For those who want to know more, read on.