### High Jumping

How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...

### Sport Collection

This is our collection of favourite mathematics and sport materials.

### Speed-time Problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

# 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

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.

### Key questions

Do any data points jump out at you?
Does weight confer an advantage to shot putters?

### 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.