<p style="text-align:justify"><span style="font-size:14px">For most of the work you do in this book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A rule of thumb is to use a histogram when the data set consists of 100 values or more.</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">A&nbsp;<strong>histogram</strong>&nbsp;consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents (for instance, distance from your home to school). The vertical axis is labeled either&nbsp;<strong>frequency</strong>&nbsp;or&nbsp;<strong>relative frequency</strong>&nbsp;(or percent frequency or probability). The graph will have the same shape with either label. The histogram (like the stemplot) can give you the shape of the data, the center, and the spread of the data.</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">The relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample. (Remember, frequency is defined as the number of times an answer occurs.) If:</span></p>

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<ul>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><em>f</em>&nbsp;= frequency</span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><em>n</em>&nbsp;= total number of data values (or the sum of the individual frequencies), and</span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><em>RF</em>&nbsp;= relative frequency,</span></p>
	</li>
</ul>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">then:</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span class="math-tex">\(RF=\frac{f}{n}\)</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">For example, if three students in Mr. Ahab&#39;s English class of 40 students received from 90%&nbsp;<span style="color:black">to 100%, then,&nbsp;<em>f</em>&nbsp;= 3,&nbsp;<em>n</em>&nbsp;= 40, and&nbsp;&nbsp;</span><span class="math-tex">\(RF=\frac{f}{n}=\frac{3}{10}=0.075\)</span>&nbsp;<span style="background-color:white"><span style="color:black">. 7.5% of the students received 90&ndash;100%. 90&ndash;100% are quantitative measures.</span></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="background-color:white"><strong><span style="color:black">To construct a histogram</span></strong><span style="color:black">, first decide how many&nbsp;<strong>bars</strong>&nbsp;or&nbsp;<strong>intervals</strong>, also called classes, represent the data. Many histograms consist of five to 15 bars or classes for clarity. The number of bars needs to be chosen. Choose a starting point for the first interval to be less than the smallest data value. A&nbsp;<strong>convenient starting point</strong>&nbsp;is a lower value carried out to one more decimal place than the value with the most decimal places. </span></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="background-color:white"><span style="color:black">For example, if the value with the most decimal places is 6.1 and this is the smallest value, a convenient starting point is 6.05 (6.1 &ndash; 0.05 = 6.05). We say that 6.05 has more precision. If the value with the most decimal places is 2.23 and the lowest value is 1.5, a convenient starting point is 1.495 (1.5 &ndash; 0.005 = 1.495). If the value with the most decimal places is 3.234 and the lowest value is 1.0, a convenient starting point is 0.9995 (1.0 &ndash; 0.0005 = 0.9995). If all the data happen to be integers and the smallest value is two, then a convenient starting point is 1.5 (2 &ndash; 0.5 = 1.5). Also, when the starting point and other boundaries are carried to one additional decimal place, no data value will fall on a boundary. The next two examples go into detail about how to construct a histogram using continuous data and how to create a histogram using discrete data.</span></span></span></p>