Charting success

7735 /www/nrich/html/content/id/7735/ 1 2011-08-16T15:24:12 <mdoxml version="1.0"> Some say every picture tells a story... and that a picture is worth a thousand words... Below are some graphs, charts and diagrams created by sports statisticians, trainers or competitors to help them to analyse performance, inform training programmes or improve motivation. For each diagram, consider the following questions: <ul> <li>What information can you deduce from each diagram?</li> <li>Are the diagrams effective in communicating the information?</li> <li>Are there any diagrams where you think the data are not represented clearly or effectively? How could you improve them?</li> <li>Are there any diagrams where information is missing? Can you think of a way of presenting the data that would include that information in a clear and effective way?</li> <li>Who might have created each diagram, and for what purpose do you think they created it? Can you think of others who might be interested in using the same data in a different way?</li> </ul> Scatter plot showing Federer's first serve landing points <mdo:image src="Federer%20serve.png"></mdo:image> League positions of teams in a football league during a season <mdo:image src="football%20league.png"></mdo:image> Average speed and altitude of the terrain for a runner's 14 minute workout <mdo:image src="running4.png"></mdo:image> "Worm Graph" showing runs scored by two sides in a game of cricket<mdo:image src="worm%20graph.png"></mdo:image> "Wagon-wheel" chart showing where runs were scored in the first part of a cricket game <mdo:image src="wagon%20wheel.png"></mdo:image> EXTENSION Send us examples of particularly good (or bad) representations of sports data, together with your explanation of what makes them good (or bad). </mdoxml> <mdoxml version="1.0">The Pythagoreans from All Saints School in Dagenham analysed and commented on four of the diagrams: <h4>Scatter plot showing Federer's first serve landing points:</h4> The Tennis diagram shows where the ball bounced, you can see that the tennis player did well but it doesn't show the speed the served ball was travelling at. The bounced balls could also be labeled better (e.g make the graph bigger and maybe add a few colours to the bounces that were close to each other). It could also show serves that went out, because we don't know what percentage of serves were out. <h4>League positions of teams in a football league during a season:</h4> We do not like this graph! It is all over the place. The colours of the lines are confusing: when the lines intersect you can't see where they carry on because the colours are too similar. There is no key so we don't know which colour represents which team. There is too much information on the graph and so it is not clear. To improve it they could have separated the graph into a top half of the table and the bottom half, or a top six (European places) and bottom three (relegation zone). <h4>Average speed and altitude of the terrain for a runner's 14 minute workout:</h4> This graph is very well presented as it clearly shows the terrain that the runner is running on and the time the runner is taking to run it. The terrain is represented by a light grey colour which is also shown on the label of the axis representing the altitude of the ground in feet. The minutes per mile is shown on the graph by a fluorescent green colour as is the label on the axis representing the minutes/mile. The graph shows that when the height of the terrain dropped the runner must have been going downhill as the speed of the runner increased. The only concern about the graph is that it's written in minutes/mile instead of miles/minute and the scale decreases rather than increases. This is unnecessarily confusing. If the scale was miles/minute the vertical axis would have increased as it went up rather than decreased. <h4>Worm Graph:</h4> This graph shows how many runs each team scored and the number of balls each team faced. We could tell from the graph which team won and we could also tell when one team was ahead in the run rate. We could tell that the blue team scored very quickly at the beginning of the game but then started to score fewer runs, perhaps because they lost some of their wickets. The only thing that we can't see is who bowled first. We also can't see when each team lost their wickets. To improve the graph it should include crosses to tell you when they lost their wickets.</mdoxml> <mdoxml version="1.0"> <h3>Why do this problem?</h3> When processing and representing data, it is important to consider the audience and purpose of the representation. In this problem, students are invited to consider some examples of representations from the world of sport, to make sense of the stories they tell, and to analyse whether the right representation has been chosen for the purpose. <h3>Possible approach</h3> Hand out <a href="/content/id/7735/Charting%20Success.pdf">this worksheet</a> with the five questions from the problem. Give each pair of students some of the graphs to work on - all five graphs are available on <a href="/content/id/7735/Charting%20Success2.pdf">these worksheets</a>. "For each graph or diagram you have been given, try to tell the story about the sporting event it represents or the information it conveys. Then have a go at answering the questions on the sheet." As the class are working, circulate and listen out for particularly insightful and detailed descriptions of the sporting events or clear analysis of the advantages and disadvantages of particular representations. Bring the class together, and for each graph or diagram ask those students who worked on it to tell the story and share their answers to the questions. The questions and graphs are available to display as a powerpoint <a href="/content/id/7735/Charting%20success.ppt">here</a>. <a href="/7759">Charting More Success</a> offers some more charts that can be analysed in a similar way. <h3>Key questions</h3> What are the advantages of each representation? What are the disadvantages? <h3>Possible extension</h3> Invite students to search for other examples of graphs or diagrams used in sport, or in wider contexts, and ask them to prepare a short presentation on why particular representations are suitable or unsuitable for different purposes. (Newspapers are a great source of both good and bad representations of data.) <h3>Possible support</h3> Choose one of the graphs to go through together in the class, and model the sort of response each question requires. </mdoxml> <mdoxml version="1.0"> Some of the diagrams have labelled axes - what information can you deduce from these? Try to identify who would be interested in each graph. Then put yourself in their shoes and imagine how they might want to use the data. </mdoxml> <mdoxml version="1.0"> http://www.guardian.co.uk/football/chalkboards wagon wheel </mdoxml> 2 3 0 0 1 1 0 Charting success Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians? Handling, Processing and Representing Data Interpreting data Handling, Processing and Representing Data Processing and representing data Using, Applying and Reasoning about Mathematics Visualising Using, Applying and Reasoning about Mathematics Representing