Medals

TINKERPLOTS – OLYMPIC MEDALS Introduction A good definition of statistics is ‘numerical detective work’. Just like any other form of detective work, to be successful at statistics you need to practise. This exercise provides practice in a range of techniques involved in statistical work and is written around using TinkerPlots. Your report will be completed in Word and will include graphs with numbers and percentages. To put a copy of one of your plots in your report : (a) In Tinkerplots, click somewhere on the plot (b) On the EDIT Menu, select COPY AS PICTURE. (c) Go to your Word document and position the cursor where the plot will go. (d) On the EDIT Menu, select PASTE. The plot will be added to your document. (e) The plot may need resizing – click and drag one of the corners of the picture until the desired size is obtained. Work with a partner/group, so that you have someone with whom you can discuss the questions. Olympic medals data The Olympic Games were most recently held in Beijing, China. At the conclusion of the Games, many statements were made by various people about the number of medals – gold or total – won by athletes from their own or other countries. We will use Tinkerplots to examine some of these claims. First, we need a listing of all the medals won by competing countries in Beijing. We will load data from http://sports.espn.go.com/oly/summer08/medals Open a new Tinkerplots worksheet. Open the web page. Drag the URL onto the Tinkerplots worksheet, and wait. The data will be loaded into the worksheet the “medals collection” as shown in the figure below.

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Unfortunately the information does not load completely correctly from this site (other sites that have been tried have worse problems with labels and amount of data downloaded). To correct this problem is easy. First, to correct the labels, double click in each attribute heading and change to those shown in the figure below.

The USA results do not load into the cases file, so we will need to add them in. Click on the LEFT arrow next to “case 1 of 86”. This brings up a new case (numbered 87).

Click in the “Value” space next to Country and start adding the information as shown in the figure below, moving from one value field to the next by pressing TAB.

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Population Data Now click on the “” label and enter the label Population. Second, we need population values for all countries that won medals. We can use data from http://en.wikipedia.org/wiki/List_of_countries_by_population or from http://www.worldatlas.com/aatlas/populations/cytpopls.htm (or any other source you trust). Open the web page simultaneously with the Tinkerplots worksheet. For each country in the Tinkerplots worksheet, find the population value in the web page and enter it in the Medals Collection, rounded to the nearest 100 000 or 10 000 (whichever is appropriate).

Save the completed worksheet. Preliminary Investigation Click on and drag a PLOT from the toolbar to the worksheet. Click on the attribute name “Country” and drag it onto the plot to the middle of the side until a thick edged rectangle appears. Release the mouse and the axis will be labeled “Countries”. Click on the attribute name “Total” and drag it onto the plot to the middle of the left vertical side until a thick edged rectangle appears. Release the mouse and the axis will be labeled “Total”. This plot is almost incomprehensible as there are 87 countries that have won medals, and unless we have a very wide screen, we will not be able to see them all. We will need to cut down the amount of data we plot to be able to clearly see what is happening. Tinkerplots has a FILTER function that enables us to restrict the quantity of data being examined at any one time. We will also need to use formulae to calculate parameters for comparison. medals

Country Circle Icon

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Filter Use With the plot selected, on the PLOT Menu, select ADD FILTER. In the window that opens, click on the triangle next to Attributes to open up the list, and double click on “Total” to select it. Click on “>” and type in (or click on) 20 to set a lower limit. Click OK to activate the filter. The plot will change, and the filter formula in use can be seen at the bottom of the plot. medals

Country Circle Icon

Total > 20

The number of points on the plot has diminished, but all the country names still appear at the bottom of the screen, so the individual countries are difficult to identify. By clicking on a particular point, we then see its data card selected, and can see its values. To change a Filter, double click on the Filter formula at the bottom of the plot window. The Filter window will appear, and it can be modified, rewritten anew or deleted. Delete any Filter settings before the next step.

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Formula Use Some of the arguments raging about the end of the Olympics concerned the number of medals won per head of population (or equivalent). We can use Formulae to carry out a number of calculations. We will calculate the number of medals won per million population of every medal-winning country. On the Cases table, click on “”, label it “TotalMhead” and press ENTER. Click and drag the bottom right corner of the Cases table until the column headed “Formula” appears. Click on the formula button in the TotalMhead row. The window that appears is identical to the Filter window and is operated in the same way. Enter the calculation Total × 1000000 and click OK. Population medals

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TotalMhead Circle Icon

Click on the attribute name “TotalMhead” and drag it onto the plot to the middle of the bottom side until a thick edged rectangle appears. Release the mouse and the axis will be labeled “TotalMhead”. From the plot, we see that most countries are below 1 medal per million people. If we click on the data point with the highest value (approximately 6), we see that it is the Bahamas, who won two medals with a population of just over 300 000 people. By clicking on the other data points, we can see that the majority of the other top performers by this criterion are countries with small populations. From this start, we can now proceed to a number of Activities, as outlined on the next page.

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Activity One Draw up a table listing the top ten (twenty?) countries as ranked by this measure. Include in the table their calculated ratio value as well as the total number of medals and their population. How does this list compare with the Total Number of Medals Won list ? Activity Two Use a Filter to place limits on the population, and see how this affects the results. A suggested starting point is a limit of 5 000 000. Compare a Top Ten listing of countries ranked by this measure for populations below 5 000 000 as compared to countries with populations above 5 000 000. Do countries with smaller populations have an advantage by this measure ? Activity Three Trial other population limits. If you want select a group in the range say, 5 000 000 to 50 000 000, you will need to use the “and” logical operator (Population < 5 000 000 and Population > 50 000 000). Compare your Top Ten lists for each population grouping you create. Activity Four Calculating the cost of each medal to the country that won it is a tricky process, given the different ways in which countries support or encourage their athletes. For countries like Australia which have a specific sports grant allocation, this is easy. For countries like the USA where athletes can be in the College system or performing as professional athletes, this cost is harder to determine. One possible way is to take the number of medals won and divide it by the total wealth of the country (multiply the GDP per capita (Wikipedia or World Bank or United Nations are useful sources) by the population). Given the size of the numbers generated by this latter calculation, we may need to express this wealth in millions (or billions!) to keep the final answers reasonable. Explore the possibilities!!

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