7367 /www/nrich/html/content/id/7367/ 1 2011-06-28T10:41:18 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/4834">Warm-up</a></li> <li><a href="http://nrich.maths.org/6574">Try this next</a></li> <li><a href="http://nrich.maths.org/6453">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><span style="font-weight: bold;">Which countries have the most naturally athletic populations?</span><br></br> <br></br> Below, we have provided the Beijing 2008 Olympics medal table.<br></br> What other information do you think should be taken into account to answer this question fairly?<br></br>  <br></br> Make a plan of the information you will collect and the calculations you will perform. Then carry out your plan to decide which countries are naturally most athletic.<br></br>  <br></br> Send us your top rated countries, together with your justification for the data and criteria you chose to include in your analysis.<br></br>  <br></br> In the Beijing 2008 Olympics the final medal table was as follows (<a href="/content/id/7367/Medals%202008.csv">spreadsheet CSV form</a>)<br></br>  </p> <br></br> <table style="" border=""> <colgroup> <col width="127"></col> <col width="46"></col> <col width="52"></col> <col width="62"></col> <col width="62"></col></colgroup> <tbody> <tr> <td align="left" height="18" width="127" style=""><font face="Arial">Country</font></td> <td align="left" style="text-align: right;" width="46"><font face="Arial">Gold</font></td> <td align="left" style="text-align: right;" width="52"><font face="Arial">Silver</font></td> <td align="left" style="text-align: right;" width="62"><font face="Arial">Bronze</font></td> <td align="left" style="text-align: right;" width="62"><font face="Arial">Total</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">China</font></td> <td align="right" sdnum="2052;" sdval="51" style="">51</td> <td align="right" sdnum="2052;" sdval="21" style="">21</td> <td align="right" sdnum="2052;" sdval="28" style="">28</td> <td align="right" sdnum="2052;" sdval="100" style=""><font face="Arial">100</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">USA</font></td> <td align="right" sdnum="2052;" sdval="36" style="">36</td> <td align="right" sdnum="2052;" sdval="38" style="">38</td> <td align="right" sdnum="2052;" sdval="36" style="">36</td> <td align="right" sdnum="2052;" sdval="110" style=""><font face="Arial">110</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Russian Fed.</font></td> <td align="right" sdnum="2052;" sdval="23" style="">23</td> <td align="right" sdnum="2052;" sdval="21" style="">21</td> <td align="right" sdnum="2052;" sdval="28" style="">28</td> <td align="right" sdnum="2052;" sdval="72" style=""><font face="Arial">72</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Great Britain</font></td> <td align="right" sdnum="2052;" sdval="19" style="">19</td> <td align="right" sdnum="2052;" sdval="13" style="">13</td> <td align="right" sdnum="2052;" sdval="15" style="">15</td> <td align="right" sdnum="2052;" sdval="47" style=""><font face="Arial">47</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Germany</font></td> <td align="right" sdnum="2052;" sdval="16" style="">16</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="15" style="">15</td> <td align="right" sdnum="2052;" sdval="41" style=""><font face="Arial">41</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Australia</font></td> <td align="right" sdnum="2052;" sdval="14" style="">14</td> <td align="right" sdnum="2052;" sdval="15" style="">15</td> <td align="right" sdnum="2052;" sdval="17" style="">17</td> <td align="right" sdnum="2052;" sdval="46" style=""><font face="Arial">46</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Korea</font></td> <td align="right" sdnum="2052;" sdval="13" style="">13</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="8" style="">8</td> <td align="right" sdnum="2052;" sdval="31" style=""><font face="Arial">31</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Japan</font></td> <td align="right" sdnum="2052;" sdval="9" style="">9</td> <td align="right" sdnum="2052;" sdval="6" style="">6</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="25" style=""><font face="Arial">25</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Italy</font></td> <td align="right" sdnum="2052;" sdval="8" style="">8</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="28" style=""><font face="Arial">28</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Netherlands</font></td> <td align="right" sdnum="2052;" sdval="7" style="">7</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="16" style=""><font face="Arial">16</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">France</font></td> <td align="right" sdnum="2052;" sdval="7" style="">7</td> <td align="right" sdnum="2052;" sdval="16" style="">16</td> <td align="right" sdnum="2052;" sdval="17" style="">17</td> <td align="right" sdnum="2052;" sdval="40" style=""><font face="Arial">40</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Ukraine</font></td> <td align="right" sdnum="2052;" sdval="7" style="">7</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="15" style="">15</td> <td align="right" sdnum="2052;" sdval="27" style=""><font face="Arial">27</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Jamaica</font></td> <td align="right" sdnum="2052;" sdval="6" style="">6</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="11" style=""><font face="Arial">11</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Spain</font></td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="18" style=""><font face="Arial">18</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Kenya</font></td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="14" style=""><font face="Arial">14</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Ethiopia</font></td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="7" style=""><font face="Arial">7</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Romania</font></td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="8" style=""><font face="Arial">8</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Belarus</font></td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="10" style="">10</td> <td align="right" sdnum="2052;" sdval="19" style=""><font face="Arial">19</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Norway</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="10" style=""><font face="Arial">10</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Canada</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="9" style="">9</td> <td align="right" sdnum="2052;" sdval="6" style="">6</td> <td align="right" sdnum="2052;" sdval="18" style=""><font face="Arial">18</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">New Zealand</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="9" style=""><font face="Arial">9</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Slovakia</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Brazil</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="8" style="">8</td> <td align="right" sdnum="2052;" sdval="15" style=""><font face="Arial">15</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Poland</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="6" style="">6</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="10" style=""><font face="Arial">10</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Czech Republic</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Hungary</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="5" style="">5</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="10" style=""><font face="Arial">10</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Georgia</font></td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Argentina</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Kazakhstan</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="7" style="">7</td> <td align="right" sdnum="2052;" sdval="13" style=""><font face="Arial">13</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Mexico</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style=""><font face="Arial">3</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Cuba</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="11" style="">11</td> <td align="right" sdnum="2052;" sdval="11" style="">11</td> <td align="right" sdnum="2052;" sdval="24" style=""><font face="Arial">24</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Mongolia</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Thailand</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">North Korea</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Switzerland</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Denmark</font></td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="7" style=""><font face="Arial">7</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Azerbaijan</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="7" style=""><font face="Arial">7</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Zimbabwe</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Belgium</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Dominican Rep.</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">India</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style=""><font face="Arial">3</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Latvia</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style=""><font face="Arial">3</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Panama</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Tunisia</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Uzbekistan</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Finland</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Indonesia</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="5" style=""><font face="Arial">5</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Slovenia</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="5" style=""><font face="Arial">5</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Turkey</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="8" style=""><font face="Arial">8</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Bahrain</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Bulgaria</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="5" style=""><font face="Arial">5</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Iran</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Portugal</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Cameroon</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Estonia</font></td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Iceland</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Ireland</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style=""><font face="Arial">3</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Kyrgyzstan</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Mauritius</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Rep. of Moldova</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Singapore</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Taiwan</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Trinidad/Tobago</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Croatia</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="5" style=""><font face="Arial">5</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Israel</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Sudan</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Tajikistan</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Armenia</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="6" style="">6</td> <td align="right" sdnum="2052;" sdval="6" style=""><font face="Arial">6</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Bahamas</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Chile</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Ecuador</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Greece</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Lithuania</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="5" style=""><font face="Arial">5</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Nigeria</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="3" style="">3</td> <td align="right" sdnum="2052;" sdval="4" style=""><font face="Arial">4</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Sweden</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="4" style="">4</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="5" style=""><font face="Arial">5</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Afghanistan</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Venezuela</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Egypt</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Malaysia</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Morocco</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Serbia</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style=""><font face="Arial">3</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">South Africa</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Togo</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Algeria</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Austria</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style="">2</td> <td align="right" sdnum="2052;" sdval="3" style=""><font face="Arial">3</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Vietnam</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style=""><font face="Arial">1</font></td> </tr> <tr> <td align="left" height="18" style=""><font face="Arial">Colombia</font></td> <td align="right" sdnum="2052;" sdval="0" style="">0</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="1" style="">1</td> <td align="right" sdnum="2052;" sdval="2" style=""><font face="Arial">2</font></td> </tr> </tbody> </table> <div> </div> <div> </div> <div> </div> <div style="font-weight: bold;">Extension Challenge:</div> <div> </div> <div>You could use data from previous Olympics (and the data from the London 2012 Games once they have taken place) to see the extent to which your criteria give a constant list of most athletic nations over time.</div> <div> </div> <div> </div> <div class="framework"><br></br> <strong>Notes and Background</strong><br></br> <br></br> The Plus article <a href="http://sport.maths.org/content/harder-better-faster-stronger">Harder, better, faster, stronger</a> explores some of the same ideas as this problem.<br></br>  </div></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <br></br> <p><span class="editorial">In this problem, we needed to find a way to use the Olympic medal tally in order to work out which country is the most athletic. </span><br></br> <span class="editorial"> </span><br></br> <span class="editorial">Joe and Matthew, from Chatham Grammar School, both considered the total number of medals which countries have won in previous Olympics. Matthew thought that because the 2008 Olympics contained</span> <span class="editorial">the greatest number of events</span><span class="editorial">, the top five medal winning countries from this Olympics would be the most athletic.</span></p> <p> </p> <p><span class="editorial">Matthew then ranked these five countries according to the number and type of medals won using a weighted points system:</span></p> <p><span class="editorial">he gave $15$ points for gold, $10$ points for silver and $5$ points for bronze, and then divided the sum of these scores by the number of Olympic games the country had participated in.</span></p> <p> </p> <table cellspacing="1" cellpadding="1" border="1" style="width: 688px; height: 261px;"> <tbody> <tr> <td style="text-align: center;">Country</td> <td style="text-align: center;"># Olympics attended</td> <td style="text-align: center;">Total # gold medals</td> <td style="text-align: center;">Total # silver medals</td> <td style="text-align: center;">Total # bronze medals</td> <td style="text-align: center;">Total weighted score</td> <td style="text-align: center;">Total weighted score / # Olympics attended</td> </tr> <tr> <td>USA</td> <td style="text-align: center;">27</td> <td style="text-align: center;">946</td> <td style="text-align: center;">765</td> <td style="text-align: center;">662</td> <td style="text-align: center;">25 137</td> <td style="text-align: center;">931</td> </tr> <tr> <td>Russia</td> <td style="text-align: center;">4</td> <td style="text-align: center;">108</td> <td style="text-align: center;">97</td> <td style="text-align: center;">110</td> <td style="text-align: center;">3 724</td> <td style="text-align: center;">931</td> </tr> <tr> <td>China</td> <td style="text-align: center;">7</td> <td style="text-align: center;">163</td> <td style="text-align: center;">117</td> <td style="text-align: center;">106</td> <td style="text-align: center;">4 144</td> <td style="text-align: center;">592</td> </tr> <tr> <td>Germany</td> <td style="text-align: center;">25</td> <td style="text-align: center;">374</td> <td style="text-align: center;">439</td> <td style="text-align: center;">469</td> <td style="text-align: center;">12 350</td> <td style="text-align: center;">494</td> </tr> <tr> <td>Great Britain</td> <td style="text-align: center;">28</td> <td style="text-align: center;">220</td> <td style="text-align: center;">277</td> <td style="text-align: center;">269</td> <td style="text-align: center;">7 420</td> <td style="text-align: center;">265</td> </tr> </tbody> </table> <p> </p> <div class="editorial"><span class="editorial">Because the USA and Russia had the same (and highest) result, Matthew then recalculated the USA weighted score for the last 4 Olympic games only, when both the USA and Russia competed:</span></div> <div class="editorial"> </div> <div>For the past $4$ Olympics, the USA had $153$ gold medals, $133$ silver medals and $120$ bronze medals.</div> <div> </div> <div>So the new total weighted score is</div> <div>$153\times15+133\times10+120\times5=4224$</div> <div>and the average over the four Olympics is</div> <div>$4224\div4=1056$</div> <div>Therefore the USA is the most athletic nation.</div> <div class="editorial"> </div> <div><span class="editorial">Elliott, from Wilson's School, considered the number of medals won but also wanted to take into account the population size of each country. He first listed the countries according to the number of gold medals achieved in the 2008 Olympics:</span></div> <div> </div> <div><span class="editorial"><mdo:image style="width: 271px; height: 538px;" src="7367%20_%201.JPG" alt=""></mdo:image></span></div> <div> </div> <div><span class="editorial">Elliott then calculated a weighted score from the medal tally:</span> $$ \text{Total Score} = \Big( 3 \times \text{# Gold medals} + 2 \times \text{# Silver medals} + 1 \times \text{# Bronze medals} \Big)\times 10^7 $$</div> <div><span class="editorial">He multiplied the weighted score by $10^7$ so that the Overall Results would contain reasonable sized numbers to divide by the population:</span> $$\text{Overall Result} = \text{Total Score} \div \text{Population} $$</div> <div> </div> <div><span class="editorial">The Overall Results have been rounded to the nearest whole number:</span></div> <div><mdo:image style="width: 401px; height: 522px;" src="7367.JPG" alt=""></mdo:image></div> <div> </div> <div><span class="editorial">From this, he ranked the countries according to their overall score, and concluded that Jamica is the most athletic nation.</span></div> <div><mdo:image style="width: 318px; height: 534px;" src="7367%20_%203.JPG" alt=""></mdo:image></div> <div> </div> <div><span class="editorial">Well done to Will and Ellie from Roundwood Park School who used the same method as Elliot.</span></div> <div class="editorial"> </div> <div><span class="editorial">Olie and Dan from Baston Primary School, and Owen and Jack from Chatham Grammar School, all started to think about using population size and also suggested that the wealth of countries should be taken into account when trying to identify the most athletic country - after all, a rich country may be very successful in the Olympic Games because a lot of money has been spent training and preparing their top sports men and women. Jack and Owen thought about using the Human Development Index to indicate how wealthy and developed a country is.</span></div> <div> </div> <div><span class="editorial">Can you suggest a mathematical formula to find the most athletic nation using information about the number of medals, population size and each country's wealth? Or perhaps you could consider other data, such as sporting event results, population age, prevalence of obesity, and investment in Olympic althetes to determine which country is the most athletic.</span></div> <br></br> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3>Why do this problem?</h3> This problem offers an engaging context for planning and carrying out a data-handling activity. Many problems that students meet are &quot;tidy&quot;; this activity prepares students for the messy nature of real-world data-handling. Students will need to make decisions about the data they need, and to search for that data.<br></br> <h3>Possible approach</h3> <div>Show the medal table from the 2008 Olympics.</div> <div>&quot;Here are the results from the 2008 Olympics. Can we conclude from this that China and the USA have the most naturally athletic populations?&quot;</div> <div>Allow some time for students to talk about this in pairs. Then bring the class together and collect ideas about other factors they think should be taken into account when deciding which nations are most naturally athletic.</div> <div> </div> <div>Next, split the class into groups of 3 or 4 and set them the task of developing a method for deciding which nations are most naturally athletic. This may be spread over a couple of lessons and homework time, as students will need to decide on the criteria they wish to use, carry out some research, and then present their findings.</div> <br></br> When groups present their findings, encourage the other groups to offer constructive feedback on the decisions they chose to make, the evidence they chose to include in their analysis, and the parts of the presentation they found most convincing. One way to do this is for each group to make a short presentation with time for comments and questions afterwards. Alternatively, groups could prepare a poster presentation and then time could be allowed for everyone to go round and look at each poster, writing feedback on post-it notes.<br></br> <h3>Key questions</h3> <div>Does the Olympic table rank countries according to their natural athleticism?</div> <div>What other factors apart from natural athleticism might affect a country's ranking at the Olympics?</div> <br></br> <h3>Possible extension</h3> Students could use data from previous Olympics to see the extent to which their criteria give a constant list of most athletic nations over time.<br></br> <h3>Possible support</h3> <div>Some simple and quantifiable criteria that students could use in their analysis could be population size and wealth of the nation. It may be worth finding out some of this data in advance in order to guide the students' searches.</div> <div> </div> <br></br>  <br></br>  <br></br>  <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">How might the population size of a nation affect its chances of winning a medal?<br></br> What about the wealth of a nation?<br></br>  <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p><span class="editorial">In this problem, we needed to find a way to use the Olympic medal tally in order to work out which country is the most athletic.  </span><br></br> <span class="editorial"> </span><br></br> <span class="editorial">Joe and Matthew, from Chatham Grammar School, both considered the total number of medals which countries have won in the previous three Olympics. Matthew thought that because there were the most number of events in the 2008 Olympics, the top five medal winning countries from this Olympics would be the most athletic.</span></p> <p> </p> <p><span class="editorial">Matthew then ranked these five countries according to the number and type of medals won using a weighted points system. He gave 15 points for gold, 10 points for silver and 5 points for bronze, and then divided the sum of these scores by the number of Olympic games the country had participated in.</span></p> <p> </p> <table border="1" cellpadding="1" cellspacing="1" style="width: 688px; height: 261px;"> <tbody> <tr> <td style="text-align: center;">Country</td> <td style="text-align: center;"># Olympics attended</td> <td style="text-align: center;">Total # gold medals</td> <td style="text-align: center;">Total # silver medals</td> <td style="text-align: center;">Total # bronze medals</td> <td style="text-align: center;">Total weighted score</td> <td style="text-align: center;">Total weighted score / # Olympics attended</td> </tr> <tr> <td>USA</td> <td style="text-align: center;">27</td> <td style="text-align: center;">946</td> <td style="text-align: center;">765</td> <td style="text-align: center;">662</td> <td style="text-align: center;">25 137</td> <td style="text-align: center;">931</td> </tr> <tr> <td>Russia</td> <td style="text-align: center;">4</td> <td style="text-align: center;">108</td> <td style="text-align: center;">97</td> <td style="text-align: center;">110</td> <td style="text-align: center;">3 724</td> <td style="text-align: center;">931</td> </tr> <tr> <td>China</td> <td style="text-align: center;">7</td> <td style="text-align: center;">163</td> <td style="text-align: center;">117</td> <td style="text-align: center;">106</td> <td style="text-align: center;">4 144</td> <td style="text-align: center;">592</td> </tr> <tr> <td>Germany</td> <td style="text-align: center;">25</td> <td style="text-align: center;">374</td> <td style="text-align: center;">439</td> <td style="text-align: center;">469</td> <td style="text-align: center;">12 350</td> <td style="text-align: center;">494</td> </tr> <tr> <td>Great Britain</td> <td style="text-align: center;">28</td> <td style="text-align: center;">220</td> <td style="text-align: center;">277</td> <td style="text-align: center;">269</td> <td style="text-align: center;">7 420</td> <td style="text-align: center;">265</td> </tr> </tbody> </table> <p> </p> <div class="editorial"><span class="editorial">Because the USA and Russia had the same (and highest) result, Matthew then recalculated the USA weighted score for the past 4 Olympic games only, when Russia also competed. For the past 4 Olympics, the USA had 153 gold medals, 133 silver medals and 120 bronze medals. So the new total weighted score is $153*15+133*10+120*5=4224$, and the average over the four Olympics is 4224/4=1056. He thus concluded that the USA is the most athletic nation.</span></div> <div class="editorial"> </div> <div><span class="editorial">Elliott, from Wilson&#39;s School, considered the number of medals won and the population size. He first listed the countries according to the number of gold medals achieved in the 2008 Olympics.</span></div> <div> </div> <div><span class="editorial"><mdo:image alt="" src="7367%20_%201.JPG" style="width: 271px; height: 538px;"></mdo:image></span></div> <div> </div> <div><span class="editorial">Elliott then calculated a weighted score from the medal tally:</span> $$ \text{Total Score} = \Big( 3 \times \text{# Gold medals} + 2 \times \text{# Silver medals} + 1 \times \text{# Bronze medals} \Big)\times 10^7 $$</div> <div><span class="editorial">He multiplied the weighted score by $10^7$ so that the Overall Results would be reasonable sized numbers:</span> $$\text{Overall Result} = \text{Total Score} \div \text{Population} $$</div> <div> </div> <div><mdo:image alt="" src="7367.JPG" style="width: 401px; height: 522px;"></mdo:image></div> <div> </div> <div><span class="editorial">From this, he ranked the countries according to their overall score, and concluded that Jamica is the most athletic nation.</span></div> <div><mdo:image alt="" src="7367%20_%203.JPG" style="width: 318px; height: 534px;"></mdo:image></div> <div> </div> <div><span class="editorial">Well done to Will and Ellie from Roundwood Park School who used the same method as Elliot.</span></div> <div class="editorial"> </div> <div><span class="editorial">Olie and Dan from Baston Primary School and Owen and Jack from Chatham Grammar School all started to think about using population size and the wealth of countries as a way to determine the most athletic country. Jack and Owen also thought about using the Human Development Index to indicate how wealthy and developed a country is.</span></div> <div> </div> <div><span class="editorial">Can you find a mathematical method to find the most athletic nation using information about the number of medals, population size and country wealth? Or perhaps you could consider other data, such as sporting event results, population age, prevalence of obesity, and investment in Olympic althetes to determine which country is the most athletic.</span></div> <p><br></br> <br></br>  </p> <br></br></mdoxml> 2 3 0 0 1 1 0 Who's the best? Which countries have the most naturally athletic populations? Handling, Processing and Representing Data Interpreting data Applications sport Handling, Processing and Representing Data Handling data