<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>36.2.1.2 (not used for Edinburgh) Mid-spread, high-spread and low-spread for a  distribution: exercise</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>

<p>Find the five-number summary and the mid-spread, high-spread and low-spread for the distribution given below:</p>
<table style="width:90%">
<tbody><tr><td>{@M[1]@}</td><td>{@M[11]@}</td><td>{@M[18]@}</td><td>{@M[22]@}</td><td>{@M[21]@}</td><td>{@M[25]@}</td><td>{@M[8]@}</td><td>{@M[24]@}</td><td>{@M[4]@}</td><td>{@M[15]@}</td><td>{@M[27]@}</td><td>{@M[7]@}</td><td>{@M[29]@}</td><td>{@M[23]@}</td><td>{@M[10]@}</td></tr>
<tr><td>{@M[12]@}</td><td>{@M[28]@}</td><td>{@M[2]@}</td><td>{@M[16]@}</td><td>{@M[3]@}</td><td>{@M[17]@}</td><td>{@M[19]@}</td><td>{@M[26]@}</td><td>{@M[20]@}</td><td>{@M[5]@}</td><td>{@M[6]@}</td><td>{@M[14]@}</td><td>{@M[30]@}</td><td>{@M[13]@}</td><td>{@M[9]@}</td></tr>
</tbody></table>
<br>
<center>
<table class="HELM_table">
<tbody>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>Lowest Value</b></td><td>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</td></tr>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>Lower Hinge</b></td><td>[[input:ans2]] [[validation:ans2]][[feedback:prt2]]</td></tr>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>Low-Spread</b></td><td>[[input:ans3]] [[validation:ans3]][[feedback:prt3]]</td></tr>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>Median</b></td><td>[[input:ans4]] [[validation:ans4]][[feedback:prt4]]</td></tr>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>Mid-Spread</b></td><td>[[input:ans5]] [[validation:ans5]][[feedback:prt5]]</td></tr>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>Upper Hinge</b></td><td>[[input:ans6]] [[validation:ans6]][[feedback:prt6]]</td></tr>
<tr style="border-bottom: 1px solid #000;"><td style="text-align: center;"><b>High-Spread</b></td><td>[[input:ans7]] [[validation:ans7]][[feedback:prt7]]</td></tr>
<tr><td style="text-align: center;"><b>Highest Value</b></td><td>[[input:ans8]] [[validation:ans8]][[feedback:prt8]]</td></tr>
</tbody>
</table>
</center>
<br>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ul>
<li>The lowest value is \({@M[1]@}\)<br></li>
<li>The Lower Hinge is the 25th percentile, so it is given by \(({@M[7]@}+{@M[8]@})/2\)<br></li>
<li>The Low-Spread is the difference between the lowest value and the median: \(({@M[15]@}+{@M[16]@})/2-{@M[1]@}\)<br></li>
<li>The Median is the middle number of the distribution:\(({@M[15]@}+{@M[16]@})/2\), in this case, since we have thirty elements the median is the average of the 15th and 16th elements of the distribution.<br></li>
<li>The Mid-Spread spread is given by the mean absolute deviation, which is the average distance to the mean:\(({@M[24]@}+{@M[25]@}/2-({@M[7]@}+{@M[8]@})/2\)<br></li>
<li>The Upper Hinge is the 75th percentile: \(({@M[24]@}+{@M[25]@})/2\)<br></li>
<li>The High-Spread is the difference between the highest value and the median\({@M[30]@}-({@M[15]@}+{@M[16]@})/2\)<br></li>
<li>The highest value is \({@M[30]@}\)<br></li>
</ul>]]></text>
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      <text>2020070100</text>
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      <text>M:[rand([0,1]),2,rand([2,3]),rand([2,3]),rand([4,5]),rand([5,6]),rand([5,6]),6, rand([7,8]),8,rand([8,9]),rand([9,10]),rand([10,11]),11,rand([11,12]),12,rand([13,14]),rand([13,14]),rand([14,15]),rand([16,17]),17,rand([16,17,18]),18,rand([18,19]),19,rand([20,21,22]),rand([20,21,22]),22,rand([23,24,25,26]),rand([27,28,29,30])];
ta1:M[1];
ta2:(M[7]+M[8])/2;
ta3:((M[15]+M[16])/2)-M[1];
ta4:(M[15]+M[16])/2;
ta5:(M[24]+M[25])/2-(M[7]+M[8])/2;
ta6:(M[24]+M[25])/2;
ta7:M[30]-(M[15]+M[16])/2;
ta8:M[30];</text>
    </questionvariables>
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      <text>\(lowest value={@ta1@},   lower hinge={@ta2@},  low spread={@ta3@}, median={@ta4@},  mid-spread={@ta5@},  upper hinge={@ta6@},  high-spread={@ta7@},  highest value={@ta8@}\)</text>
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        <value>ev(ta2+6,simp)</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ev(ta3+6,simp)</value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value>ev(ta4+6,simp)</value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value>ev(ta5+6,simp)</value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value>ev(ta6+6,simp)</value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value>ev(ta7+6,simp)</value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value>ev(ta8+6,simp)</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>
    </qtest>
  </question>
</quiz>
