David and Goliath

7360 /www/nrich/html/content/id/7360/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"> <br></br> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/7352">Warm-up</a></li> <li><a href="http://nrich.maths.org/7352">Try this next</a></li> <li><a href="http://nrich.maths.org/7352">Think higher</a></li> <li><a href="http://nrich.maths.org/7352">Read: mathematics</a></li> <li><a href="http://nrich.maths.org/7352">Read: science</a></li> <li><a href="http://nrich.maths.org/7352">Explore further</a></li> </ul> <div> </div> <br></br> <p>In the tables below are some of the top performing shot putters of all time, their weight in kilograms, and the distance they threw in metres.<br></br> <br></br> Look at the two data sets. Do any results stand out?<br></br> <br></br> <span style="font-weight: bold;">What questions occur to you?</span><br></br> <br></br> Choose appropriate statistical analyses to answer some of your questions.<br></br> Are there any other data you will need to collect? <br></br> You may wish to download <a href="/content/id/7360/ShotPutting.xls">this spreadsheet</a> containing the two data sets.<br></br> <br></br> It is suggested that heavier competitors are at an advantage in the shot put.<br></br> Do the data support that claim?<br></br> <br></br> What would be the effect on the competition of introducing weight categories (like those found in boxing or weightlifting), or giving lighter shots to lighter competitors?<br></br> <br></br> </p> <div style="text-align: left;"><span style="font-weight: bold;">Men's shot put:</span></div> <div style="text-align: left;"> </div> <table border="1"> <tbody> <tr> <td style="text-align: center;">Name</td> <td style="text-align: center;">Weight (kg)</td> <td style="text-align: center;">Distance (m)</td> </tr> <tr> <td style="text-align: center;">Randy Barnes</td> <td style="text-align: center;">137</td> <td style="text-align: center;">23.12</td> </tr> <tr> <td style="text-align: center;">Ulf Timmermann </td> <td style="text-align: center;">118 </td> <td style="text-align: center;">23.06 </td> </tr> <tr> <td style="text-align: center;">Alessandro Andrei </td> <td style="text-align: center;">118</td> <td style="text-align: center;">22.91</td> </tr> <tr> <td style="text-align: center;">Werner Günthör </td> <td style="text-align: center;">130 </td> <td style="text-align: center;">22.75 </td> </tr> <tr> <td style="text-align: center;">Kevin Toth </td> <td style="text-align: center;">144 </td> <td style="text-align: center;">22.67 </td> </tr> <tr> <td style="text-align: center;">Udo Beyer </td> <td style="text-align: center;">135</td> <td style="text-align: center;">22.64</td> </tr> <tr> <td style="text-align: center;">John Brenner </td> <td style="text-align: center;">127</td> <td style="text-align: center;">22.52</td> </tr> <tr> <td style="text-align: center;">Adam Nelson </td> <td style="text-align: center;">115</td> <td style="text-align: center;">22.51</td> </tr> <tr> <td style="text-align: center;">Reese Hoffa </td> <td style="text-align: center;">133</td> <td style="text-align: center;">22.43 </td> </tr> <tr> <td style="text-align: center;">Sergey Smirnov </td> <td style="text-align: center;">126</td> <td style="text-align: center;">22.24 </td> </tr> <tr> <td style="text-align: center;">John Godina </td> <td style="text-align: center;">129</td> <td style="text-align: center;">22.20 </td> </tr> <tr> <td style="text-align: center;">Sergey Gavryushin </td> <td style="text-align: center;">95</td> <td style="text-align: center;">22.10 </td> </tr> <tr> <td style="text-align: center;">Sergey Kasnauskas </td> <td style="text-align: center;">126 </td> <td style="text-align: center;">22.09 </td> </tr> <tr> <td style="text-align: center;">Aleksandr Baryshnikov </td> <td style="text-align: center;">130</td> <td style="text-align: center;">22.00</td> </tr> <tr> <td style="text-align: center;">Gregg Tafralis </td> <td style="text-align: center;">132</td> <td style="text-align: center;">21.98</td> </tr> <tr> <td style="text-align: center;">Mikhail Kostin </td> <td style="text-align: center;">120</td> <td style="text-align: center;">21.96</td> </tr> <tr> <td style="text-align: center;">Tomasz Majewski </td> <td style="text-align: center;">132</td> <td style="text-align: center;">21.95 </td> </tr> <tr> <td style="text-align: center;">Remigius Machura </td> <td style="text-align: center;">118</td> <td style="text-align: center;">21.93</td> </tr> <tr> <td style="text-align: center;">Cottrell J. Hunter </td> <td style="text-align: center;">135</td> <td style="text-align: center;">21.87</td> </tr> <tr> <td style="text-align: center;">Mike Stulce </td> <td style="text-align: center;">122</td> <td style="text-align: center;">21.82</td> </tr> </tbody> </table> <div> </div> <div> </div> <br></br> <p><span style="font-weight: bold;">Women's Shot Put:</span><br></br> </p> <br></br> <table border="1"> <tbody> <tr> <td style="text-align: center;">Name</td> <td style="text-align: center;">Weight (kg)</td> <td style="text-align: center;">Distance (m)</td> </tr> <tr> <td style="text-align: center;">Natalya Lisovskaya </td> <td style="text-align: center;">105 </td> <td style="text-align: center;">22.63 </td> </tr> <tr> <td style="text-align: center;">Ilona Briesenick </td> <td style="text-align: center;">95</td> <td style="text-align: center;">22.45 </td> </tr> <tr> <td style="text-align: center;">Helena Fibingerová </td> <td style="text-align: center;">95</td> <td style="text-align: center;">22.32 </td> </tr> <tr> <td style="text-align: center;">Claudia Losch </td> <td style="text-align: center;">84</td> <td style="text-align: center;">22.19</td> </tr> <tr> <td style="text-align: center;">Meisu Li </td> <td style="text-align: center;">92</td> <td style="text-align: center;">21.76</td> </tr> <tr> <td style="text-align: center;">Natalya Akhrimenko </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.73 </td> </tr> <tr> <td style="text-align: center;">Vita Pavlysh </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.69</td> </tr> <tr> <td style="text-align: center;">Xinmei Sui </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.66</td> </tr> <tr> <td style="text-align: center;">Verzhinia Veselinova </td> <td style="text-align: center;">95</td> <td style="text-align: center;">21.61</td> </tr> <tr> <td style="text-align: center;">Margitta Pufe </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.58 </td> </tr> <tr> <td style="text-align: center;">Ines Müller </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.57 </td> </tr> <tr> <td style="text-align: center;">Nunu Abashidze </td> <td style="text-align: center;">105</td> <td style="text-align: center;">21.53 </td> </tr> <tr> <td style="text-align: center;">Zhihong Huang </td> <td style="text-align: center;">100</td> <td style="text-align: center;">21.52 </td> </tr> <tr> <td style="text-align: center;">Larisa Peleshenko </td> <td style="text-align: center;">95</td> <td style="text-align: center;">21.46 </td> </tr> <tr> <td style="text-align: center;">Heike Hartwig </td> <td style="text-align: center;">95</td> <td style="text-align: center;">21.31</td> </tr> <tr> <td style="text-align: center;">Liane Schmuhl </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.27</td> </tr> <tr> <td style="text-align: center;">Astrid Kumbernuss </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.22</td> </tr> <tr> <td style="text-align: center;">Kathrin Neimke </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.21</td> </tr> <tr> <td style="text-align: center;">Helma Knorscheidt </td> <td style="text-align: center;">90</td> <td style="text-align: center;">21.19</td> </tr> <tr> <td style="text-align: center;">Heidi Krieger </td> <td style="text-align: center;">95</td> <td style="text-align: center;">21.10</td> </tr> </tbody> </table> <br></br> <br></br> <div class="framework"><span style="font-weight: bold;">NOTES AND BACKGROUND</span><br></br> <br></br> Data source: <a href="http://www.iaaf.org/statistics/toplists/inout=o/age=n/season=0/sex=M/all=y/legal=A/disc=SP/detail.html">IAAF</a><br></br> Mass of shot for male competitors: 7.260 kg (16 lb)<br></br> Mass of shot for female competitors: 4 kg (8.82 lb)</div> <br></br> </mdoxml> <mdoxml version="1.0"><br></br> <h3>Why do this problem?</h3> 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.<br></br> <h3>Possible approach</h3> <div>Display the data (or hand out <a href="/content/id/7360/David%20and%20Goliath.doc">this worksheet</a>) 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.</div> <div> </div> <div>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...</div> <div> </div> <div>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.</div> <div> </div> <div>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 <a href="/content/id/7360/ShotPutting.xls">this spreadsheet</a>, and more data from the IAAF on shot putting can be found <a href="http://www.iaaf.org/statistics/toplists/inout=o/age=n/season=0/sex=M/all=y/legal=A/disc=SP/detail.html"> here</a>.</div> <div> </div> <div>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.</div> <br></br> <h3>Key questions</h3> <div>Do any data points jump out at you?</div> <div>Does weight confer an advantage to shot putters?</div> <h3>Possible extension</h3> 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.<br></br> <h3>Possible support</h3> 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.<br></br></mdoxml> <mdoxml version="1.0">You could plot the data on a scatter graph to give you a feel for any relationships. <br></br></mdoxml> <mdoxml version="1.0">Weight lifting is the only strength event in the Olympics in which there are different weight categories. From this data of world records in weightlifting http://en.wikipedia.org/wiki/List_of_Olympic_records_in_weightlifting can you deduce a relationship between strength and size? Hint: For size, use weight. For strength use the maximum weight lifted. Plot different powers of one against the other to find a beautiful relationship between the two. Using your knowledge could you devise a set of weight categories and shot put weights such that men and women of different weight groups could compete together fairly?<br></br> <br></br> <br></br></mdoxml> 2 3 0 0 0 1 1 David and Goliath Does weight confer an advantage to shot putters? Applications STEM - General Applications sport Handling, Processing and Representing Data Interpreting data Handling, Processing and Representing Data Scatter graphs Handling, Processing and Representing Data Averages Handling, Processing and Representing Data Measures of spread