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<title>Histograms</title>
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<h1 align="center">Histograms</h1>
<div class="def">
<p><b>Histogram</b>: a graphical display of data using bars of different heights.</p>
</div><p>&nbsp;</p>
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/histogram.gif" alt="Histogram" width="232" height="208" /></p>
<p>&nbsp;</p>
<p>It&nbsp;is&nbsp;similar to a <a href="bar-graphs.html">Bar Chart</a>, but a histogram groups numbers into <b>ranges </b>.</p>
<p>The height of each bar shows how many fall into each range.</p>
<p>And you decide what ranges to use!</p>
<div style="clear:both"></div>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/orange-orchard.jpg" width="89" height="200" alt="orange orchard" /></p>
<h3>Example: Height of Orange Trees</h3>
<p>You measure the height of every tree in the orchard in centimeters (cm)</p>
<p>The heights vary from 100 cm to 340 cm</p>
<p>You decide to put the results into groups of 50 cm: </p>
<ul>
<li>The <b>100 to just below 150 cm</b> range, </li>
<li>The <b>150 to just below 200 cm</b> range, </li>
<li>etc...</li>
</ul>
<p>So a tree that is 260 cm tall is added to the &quot;250-300&quot; range. </p><p>And here is the result:</p>
<p class="center"><img src="images/histogram-heights.svg" alt="histogram heights" /></p>
<p>You can see (for example) that there are <b>30</b> trees from <b>150 cm to just below 200 cm tall</b> </p>
<p>(PS: you can create graphs like that using <a href="data-graph.html">Make your own Histogram</a>)</p>
</div>
<p>Notice that the horizontal axis is continuous like a <a href="../number-line.html">number line</a>: <img src="images/histogram-x-axis.svg" alt="histogram x axis" /></p>
<p>&nbsp;</p>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/arrow-pup.jpg" width="122" height="200" alt="puppy" /></p>
<h3>Example: How much is that puppy growing?</h3>
<p>Each month you measure how much weight your pup has gained and get these results:</p>
<p class="center"> <b>0.5, 0.5, 0.3, &minus;0.2, 1.6, 0, 0.1, 0.1, 0.6, 0.4</b></p>
<p>They vary from &minus;0.2 (the pup lost weight that month) to 1.6</p>
<p>Put in order from lowest to highest weight gain:</p>
<p class="center"><b>&minus;0.2, 0, 0.1, 0.1, 0.3, 0.4, 0.5, 0.5, 0.6, 1.6</b></p>
<p>You decide to put the results into groups of 0.5: </p>
<ul>
<li>The <b>&minus;0.5 to just below 0</b> range, </li>
<li>The <b>0 to just below 0.5</b> range, </li>
<li>etc...</li>
</ul>
<p>And here is the result:</p>
<p class="center"><img src="images/histogram-weight-change.svg" alt="histogram weight change" /></p>
<p>(There are no values from 1 to just below 1.5,
but we still show the space.)</p>
</div>
<div class="words">
<p>The range of each bar is also called the <b>Class Interval</b></p>
<p>In the example above each class interval&nbsp;is <b>0.5</b></p>
</div>
<p>&nbsp;</p>
<p>Histograms are a great way to show results of <a href="data-discrete-continuous.html">continuous data</a>, such as: </p>
<ul>
<li>weight</li>
<li>height</li>
<li>how much time</li>
<li>etc. </li>
</ul>
<p>But when the data is in <b>categories</b> (such as Country or Favorite Movie), we should use a <a href="bar-graphs.html">Bar Chart</a>.</p>
<p class="center"><img src="images/bar-chart-vs-histogram.svg" alt="bar chart vs histogram" /></p>
<p>&nbsp;</p>
<h2>Frequency Histogram</h2>
<p>A Frequency Histogram is a special graph that uses vertical columns to show frequencies (how many times each score occurs): </p>
<table border="0" align="center">
<tr align="center">
<td><img src="images/frequency-histogram.svg" alt="Frequency Histogram" /></td>
</tr>
<tr align="center">
<td>Here I have added up how often 1 occurs (2 times), <br>
how often 2 occurs (5 times), etc, <br>
and shown them as a histogram.</td>
</tr>
</table>
<p>&nbsp;</p>
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<div class="related">
<a href="data-graph.html">Make your own Histogram</a>
<a href="bar-graphs.html">Bar Graphs</a>
<a href="line-graphs.html">Line Graphs</a>
<a href="pie-charts.html">Pie Charts</a>
<a href="pictographs.html">Pictographs</a>
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