Planning tool

Students:

• can represent frequency data in many different displays
• can work with multiple datasets of the same type side by side
• make comparisons between dataset displays, such as back-to-back stem-and-leaf plots
• analyse, evaluate and interpret results when making comparisons of data displays
• use the language of statistics to describe spread, distribution, outliers, frequency, bi-modal and symmetry.

Some students may:

• not make distinctions between bar charts, which are used for categorical data, and histograms, which  are used for numerical data.
• not realise that when comparing back-to-back histograms, the leaves of histograms are ordered smallest to largest from the left of the stem.
• compare distributions using displays with different scales or class intervals.
• confuse negative and positive skews, as these are confusing without a useful memory technique.
• automatically revert to bar graphs rather than choose from a diverse range of displays.
• find it difficult to select appropriate class intervals on histograms.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning to represent the distribution of runs in each innings of a cricket test match on comparable displays.
• We will compare these distributions to gain deeper insights into the result of the match.

Why are we learning about this?

It is often said that the Australian test cricket captain is our second-most important leader, behind the prime minister. Unlike the football codes, which vary in popularity from state to state, cricket is a sport that unites us all. And, more than in any other sport, cricket fans are obsessed with stats.

Cricket datasets are as old as the game itself, with pages bursting out of home libraries the world over. Looking back over old scorecards tells a story about the game, but coaches and analysts need to dig deeper to find out how history can help their sides improve. Let’s get a feel for their work using cricket stats.

What to do

1. Select any past cricket test match and find the scorecard online. (If cricket isn’t your cup of tea, I’d recommend basketball, netball, soccer or any sport where there are multiple team players per match. Choose a famous match to make it easier to find the scorecard.)
2. Going back to the cricket example, use different columns on a spreadsheet, list the runs of each batter in ascending order for each innings. 
3. Create a histogram to display each innings. Make sure you use the same class interval (bin size) for each batter. Label the graphs clearly and display them side by side.
4. Comment on the shape of each distribution. What does the distribution tell you about the performance of the team during the innings? Was it a team effort or did one batsman carry the team? Are there any outliers present? 
5. Based on the shape of the distribution, determine whether it would be more useful to calculate the median or mean for each innings. Carry out these calculations.
6. Compare the measures of centre of the displays to the result of the match. Does your analysis suggest the actual result?
7. Imagine you are the team analyst. Write a short set of notes for the coach of the losing team suggesting improvements for a better performance next match.

Success criteria

• I can present multiple datasets on comparable displays.
• I can compare these datasets to gain useful insights.