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<quiz>
  <question type="stack">
    <name>
      <text>36.2.3.3 Exercises Task 2</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p><p>

During the winter of \(1893/94\), Lord Rayleigh conducted an investigation into the density of nitrogen gas taken from various sources. He had previously found discrepancies between the density of nitrogen obtained by chemical decomposition and nitrogen obtained by removing oxygen from the air. Lord Rayleigh’s investigations led to the discovery of argon. The raw data obtained during his investigations are given below.</p><p><br></p>
<table>
<caption></caption>
<thead>
<tr>
<th scope="col">Date&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br></th>
<th scope="col">Source&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br></th>
<th scope="col">Weight&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br></th>
<th scope="col">Date&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br></th>
<th scope="col">Source&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br></th>
<th scope="col">Weight&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br></th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: left;">\(29/11/93\)<br></td>
<td style="text-align: left;">NO</td>
<td style="text-align: left;">\(2.30143\)<br></td>
<td style="text-align: left;">\(26/12/93\)</td>
<td style="text-align: left;">N\(_2\)O</td>
<td style="text-align: left;">\(2.29889\)</td>
</tr>
<tr>
<td style="text-align: left;">\(05/12/93\)</td>
<td style="text-align: left;">NO</td>
<td style="text-align: left;">\(2.29816\)</td>
<td style="text-align: left;">\(28/12/93\)</td>
<td style="text-align: left;">N\(_2\)O<br></td>
<td style="text-align: left;">\(2.29940\)</td>
</tr>
<tr>
<td style="text-align: left;">\(06/12/93\)</td>
<td style="text-align: left;">NO</td>
<td style="text-align: left;">\(2.30182\)</td>
<td style="text-align: left;">\(09/01/94\)</td>
<td style="text-align: left;">NH\(_4\)NO\(_2\)</td>
<td style="text-align: left;">\(2.29849\)</td>
</tr>
<tr>
<td style="text-align: left;">\(08/12/93\)</td>
<td style="text-align: left;">NO</td>
<td style="text-align: left;">\(2.29890\)</td>
<td style="text-align: left;">\(13/01/94\)</td>
<td style="text-align: left;">NH\(_4\)NO\(_2\)</td>
<td style="text-align: left;">\(2.29889\)</td>
</tr>
<tr>
<td style="text-align: left;">\(12/12/93\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.31017\)</td>
<td style="text-align: left;">\(29/01/94\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.31024\)</td>
</tr><tr>
<td style="text-align: left;">\(14/12/93\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.30986\)</td>
<td style="text-align: left;">\(30/01/94\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.31030\)</td>
</tr>
<tr>
<td style="text-align: left;">\(19/12/93\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.31010\)</td>
<td style="text-align: left;">\(01/02/94\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.31028\)</td>
</tr>
<tr>
<td style="text-align: left;">\(22/12/93\)</td>
<td style="text-align: left;">Air</td>
<td style="text-align: left;">\(2.31001\)</td>
<td style="text-align: center;"></td>
<td style="text-align: center;"></td>
<td><br></td></tr></tbody></table><br>

<ol class="HELM_parts">
 <li><p>Organise the data into a frequency table using the classes \(2.29-2.30\), \(2.30-2.31\), \(2.31-2.32\). Fill in the blank in the following statement.</p> 
<p>The highest class is obtained entirely from&nbsp;[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p></li>

<li>Classify the data according to the two sources 'Air' and 'Other'. Order each data set and hence find the median, the hinges and the mid-spreads for each data set. Keep 5 decimal places.</li>
<table class="HELM_table">
<caption></caption>
<thead>
<tr>
<th scope="col"></th>
<th scope="col">Air</th>
<th scope="col">Other</th>
</tr>
</thead>
<tbody>
<tr>
<td><b>Median</b></td>
<td>[[input:ans2]][[validation:ans2]][[feedback:prt2]]</td>
<td>[[input:ans6]][[validation:ans6]][[feedback:prt6]]</td>
</tr>
<tr>
<td><b>Upper Hinge</b></td>
<td>[[input:ans3]][[validation:ans3]][[feedback:prt3]]</td>
<td>[[input:ans7]][[validation:ans7]][[feedback:prt7]]</td>
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<tr>
<td><b>Lower Hinge</b></td>
<td>[[input:ans4]][[validation:ans4]][[feedback:prt4]]</td>
<td>[[input:ans8]][[validation:ans8]][[feedback:prt8]]</td>
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<tr>
<td><b>Midspread</b></td>
<td>[[input:ans5]][[validation:ans5]][[feedback:prt5]]</td>
<td>[[input:ans9]][[validation:ans9]][[feedback:prt9]]</td>
</tr>
</tbody>
</table></ol>]]></text>
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      <text><![CDATA[<p><b>Comment</b>: What do the box-and-whisker plots tell you about the nitrogen obtained from the two sources? Box-and-whisker plot tells us that some other element is present in Air which is responsible for the additional weight. This additional element subsequently proved to be the inert gas argon.</p>]]></text>
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      <text>ta1: [[1,true,Air],[0,false,Non-air]]
ta2: 2.31017
ta3: 2.31026
ta4: 2.31006
ta5: 0.00020
ta6: 2.29890
ta7: 2.30042
ta8: 2.29869
ta9: 0.00173</text>
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      </testinput>
      <testinput>
        <name>ans2</name>
        <value>dispdp(ta2,5)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>dispdp(ta3,5)</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>dispdp(ta4,5)</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>dispdp(ta5,5)</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>dispdp(ta6,5)</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>dispdp(ta7,5)</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>dispdp(ta8,5)</value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value>dispdp(ta9,5)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt4-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt5-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt6</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt6-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt7</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt7-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt8</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt8-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt9</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt9-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>0</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>dispdp(ev(ta2+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>dispdp(ev(ta3+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>dispdp(ev(ta4+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>dispdp(ev(ta5+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>dispdp(ev(ta6+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>dispdp(ev(ta7+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>dispdp(ev(ta8+2,simp),4)</value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value>dispdp(ev(ta9+2,simp),4)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt5-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt6</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt6-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt7</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt7-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt8</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt8-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt9</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt9-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
