505 /www/nrich/html/content/97/05/six2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>There are different ways of working out the average of a set of numbers. This problem looks at using the mean. The mean is worked out by adding up the set of numbers and dividing the answer by how many numbers there are.</p> <p>For example, the mean of the numbers 2, 3, 4, and 5 is (2+3+4+5)/4 = 3.5</p> <p>Three students had collected some data for a project about bats. Each had collected a different set of readings for the wingspan of some bats. Unfortunately, each student had lost one measurement.</p> <p>Two of the students had already added up their data and worked out their individual means and the overall mean was also known. The known information is summarised below:</p> <p>Student A had collected 5 measurements, the others had each collected 6.</p> <table> <tbody> <tr align="center" valign="middle"> <td align="center" valign="middle" style="">Student</td> <td align="center" valign="middle" style="">Data set (wingspans in cm)</td> <td align="center" valign="middle" style="">Mean (cm)</td> </tr> </tbody> </table> <br></br> <table style="" border="1"> <tbody> <tr align="center" valign="middle"> <td align="center" valign="middle" width="50" style="">A</td> <td align="left" valign="middle" style="">12</td> <td align="center" valign="middle" style="">10</td> <td align="center" valign="middle" style="">16</td> <td align="center" valign="middle" style="">14</td> <td align="center" valign="middle" style="">-</td> <td align="center" valign="middle" style="">15</td> <td align="center" valign="middle" style=""> </td> <td align="center" valign="middle" width="50" style=""><b>13</b></td> </tr> <tr align="center" valign="middle"> <td align="center" valign="middle" width="50" style="">B</td> <td align="center" valign="middle" style="">13</td> <td align="center" valign="middle" style="">12</td> <td align="center" valign="middle" style="">-</td> <td align="center" valign="middle" style="">12</td> <td align="center" valign="middle" style="">14</td> <td align="center" valign="middle" style="">17</td> <td align="center" valign="middle" style="">16</td> <td align="center" valign="middle" width="50" style=""><b>14</b></td> </tr> <tr align="center" valign="middle"> <td align="center" valign="middle" width="50" style="">C</td> <td align="center" valign="middle" style="">11</td> <td align="center" valign="middle" style="">14</td> <td align="center" valign="middle" style="">15</td> <td align="center" valign="middle" style="">-</td> <td align="center" valign="middle" style="">11</td> <td align="center" valign="middle" style="">13</td> <td align="center" valign="middle" style="">12</td> <td align="center" valign="middle" width="50" style="">-</td> </tr> </tbody> </table> <p>The overall mean from the combined data = 13.35 cm Using the above information can you complete the table?</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>The total wingspan for data set <strong>A</strong> is 6 x 13 = 78 cm so the missing measurement is 78 - 67 = 11 cm.</p> <p>The total wingspan for data set <strong>B</strong> is 7 x 14 = 98 cm so the missing measurement is 98 - 84 = 14 cm.</p> <p>The overall mean is 13.35 cm so the total of all 20 measurements is 20 x 13.35 = 267 cm and the total wingspan for data set <strong>C</strong> is 267 - (78 + 98) = 91 cm.</p> <p>The missing measurement for data set <strong>C</strong> is 91 - 76 = 15 cm and the mean of data set <strong>C</strong> is 91/7 = 13 cm.</p> <br></br></mdoxml> 2 3 0 0 1 0 0 Three students had collected some data on the wingspan of some bats. Unfortunately, each student had lost one measurement. Can you find the missing information? Handling, Processing and Representing Data Mean Secondary Mapping Document Statistics – processing and representing