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      <text>36.2.1.5 The box-and-whisker diagram</text>
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      <text><![CDATA[<h4>The box-and-whisker diagram</h4><br>

<p>In order to visually summarise a data set, we can use a box and whisker plot as well as a stem-and-leaf diagram. A box-and-whisker diagram of the original (unrounded) Inter-Party Competition data is shown below and the procedure necessary for drawing a plot is discussed.</p>
<p>You should note that there are several similar methods recommended by different authors for drawing box-and-whisker plots and so the methods recommended in statistical texts may vary a little from those given below.</p><p><img src="@@PLUGINFILE@@/36.2.1.5%20The%20box-and-whisker%20diagram.svg" alt="A box-and-whisker diagram of the original (unrounded) Inter-Party Competition data " class="img-responsive atto_image_button_text-bottom" width="440" height="56"></p><p><br></p>

<p>The diagram is constructed as follows:</p>
<ol>
<li><b>The Box</b></li>
<ul>
<li>The left-hand vertical is placed at the lower hinge (\(39\));</li>
<li>The right-hand vertical is placed at the upper hinge (\(48.65\));</li>
<li>The vertical in the box is placed at the median (\(45.05\)).</li><br>
</ul>

<li><b>The Whiskers</b></li>
<p>Notice that the mid-spread of the data (the difference between the hinges) is \(9.65\).</p>
<ul>
<li>Find the greatest value which is within one mid-spread (\(9.65\)) of the upper hinge (\(48.65\)). Here \(48.65+9.65=58.3\) so the greatest value is \(50.4\).</li>
<li>Find the least value which is within one mid-spread (\(9.65\)) of the lower hinge (\(39\)). Here \(39−9.65=29.35\) so the least value is \(33.4\).</li><br>
</ul>
<p>Connect the greatest and least values to the box by means of dashed lines.</p>

<li><b>The Outlying Values</b></li>
</ol><br>

<p>Mark as large dots any values which are more than \(1.5\) mid-spreads from the hinges. In this case, \(1.5\) mid-spreads give a value of about \(14.33\) and so we mark dots which represent values which are higher than \(48.65 + 14.33 = 62.88\) and values which are lower than \(39 - 14.33 = 24.67\). In this example, there are no values greater than \(62.88\), but there are \(7\) values which are less than \(24.67\). Notice that half of the data values lie in the box and that the tails show up well in the diagram. The diagram shows the left-skew (skewness refers to the tail) present in the data.</p>]]></text>
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