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  <question type="description">
    <name>
      <text>36.1.3.2 Frequency tables/ Discrete data</text>
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      <text><![CDATA[<h4>Discrete data</h4>
<p>A frequency table for discrete data is very similar to one for categorical data except that we put the values of the variable in increasing order.</p>
<p>For example, the numbers of vehicles passing a point on a road in each of 100 intervals of length one minute are recorded. These data are summarised in the frequency table below.</p>
<table class="HELM_table" style="text-align: center; width: 90%;">
<thead>
<tr style="border-bottom: 1px solid #000;">
<th>Numbers of <br> Vehicles <br> \(x\) </th>
<th>Frequency</th>
<th>Cumulative <br> Frequency </th>
<th>Relative <br> Frequency </th>
<th>Cumulative <br> Relative <br> Frequency</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td> <td>0</td> <td>0</td> <td>0.00</td> <td>0.00</td>
</tr>
<tr>
<td>1</td> <td>0</td> <td>0</td> <td>0.00</td> <td>0.00</td>
</tr>
<tr>
<td>2</td> <td>0</td> <td>0</td> <td>0.00</td> <td>0.00</td> 
</tr>
<tr>
<td>3</td> <td>4</td> <td>4</td> <td>0.04</td> <td>0.04</td> 
</tr>
<tr>
<td>4</td> <td>3</td> <td>7</td> <td>0.03</td> <td>0.07</td>
</tr>
<tr>
<td>5</td> <td>5</td> <td>12</td> <td>0.05</td> <td>0.12</td>
</tr>
<tr>
<td>6</td> <td>8</td> <td>20</td> <td>0.08</td> <td>0.20</td>
</tr>
<tr>
<td>7</td> <td>10</td> <td>30</td> <td>0.10</td> <td>0.30</td>
</tr>
<tr>
<td>8</td> <td>19</td> <td>49</td> <td>0.19</td> <td>0.49</td>
</tr>
<tr>
<td>9</td> <td>12</td> <td>61</td> <td>0.12</td> <td>0.61</td> 
</tr>
<tr>
<td>10</td> <td>13</td> <td>74</td> <td>0.13</td> <td>0.74</td> 
</tr>
<tr>
<td>11</td> <td>7</td> <td>81</td> <td>0.07</td> <td>0.81</td>
</tr>
<tr>
<td>12</td> <td>4</td> <td>85</td> <td>0.04</td> <td>0.85</td> 
</tr>
<tr>
<td>13</td> <td>11</td> <td>96</td> <td>0.11</td> <td>0.96</td> 
</tr>
<tr>
<td>14</td> <td>0</td> <td>96</td> <td>0.00</td> <td>0.96</td>
</tr>
<tr>
<td>15</td> <td>1</td> <td>97</td> <td>0.01</td> <td>0.97</td> 
</tr>
<tr>
<td>16</td> <td>2</td> <td>99</td> <td>0.02</td> <td>0.99</td> 
</tr>
<tr>
<td>17</td> <td>0</td> <td>99</td> <td>0.00</td> <td>0.99</td>
</tr>
<tr>
<td>18</td> <td>1</td> <td>100</td> <td>0.01</td> <td>1.00</td>
</tr>
<tr style="border-bottom: 1px solid #000;">
<td>\(x &gt; 18\)</td> <td>0</td> <td>100</td> <td>0.00</td> <td>1.00</td>
</tr>
<tr>
<td>Total</td> <td>100</td> <td></td> <td>1.00</td> <td></td> 
</tr>
</tbody>
</table>
<br>
<p>We have also included the <b>cumulative frequency</b> and the <b>cumulative relative frequency</b>.</p>
<p><b>Cumulative frequency</b>: The <b>cumulative frequency</b> for a value \( x_{i}\) of a discrete variable \(X\) is the total frequency for values of \(X\) where \(X \leq x_{i}\).</p>
<p><b>Cumulative relative frequency</b>: The <b>cumulative relative frequency</b> is the cumulative frequency divided by the total frequency.</p>
<p>Notice that we have also included a category "\(x&gt;18\)'' since there is not a definite upper limit to the number of vehicles which we might observe.</p>]]></text>
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