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Context social science.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>This table gives demographic data for households in the North East of England (UK) in {year}.&nbsp;</p>\n<table border=\"0.1\" style=\"height: 90px; width: 515px; border: solid;\" height=\"108\">\n<tbody>\n<tr style=\"border-style: solid; border-color: #000000;\">\n<td style=\"width: 150.92391967773438px; height: 34px;\"><strong>People per household</strong></td>\n<td style=\"width: 39.293479919433594px; height: 34px;\">1</td>\n<td style=\"width: 36.27717590332031px; height: 34px;\">2</td>\n<td style=\"width: 44.32065200805664px; height: 34px;\">3</td>\n<td style=\"width: 44.32065200805664px; height: 34px;\">4</td>\n<td style=\"width: 44.32065200805664px; height: 34px;\">5</td>\n<td style=\"width: 45.33967590332031px; height: 34px;\">6</td>\n</tr>\n<tr style=\"border-style: solid; border-color: #000000;\">\n<td style=\"width: 150.92391967773438px; height: 50px;\"><strong>Number of households (1000s)</strong></td>\n<td style=\"width: 39.293479919433594px; height: 50px;\">{f1}</td>\n<td style=\"width: 36.27717590332031px; height: 50px;\">{f2}</td>\n<td style=\"width: 44.32065200805664px; height: 50px;\">{f3}</td>\n<td style=\"width: 44.32065200805664px; height: 50px;\">{f4}</td>\n<td style=\"width: 44.32065200805664px; height: 50px;\">{f5}</td>\n<td style=\"width: 45.33967590332031px; height: 50px;\">{f6}</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><em>Data (adapted) from the ONS website.</em></p>", "advice": "<p><strong>(a)</strong></p>\n<p>To find the mean use the formula $\\frac{\\Sigma fx}{\\Sigma f}$</p>\n<p>In other words</p>\n<ul>\n<li>multiply each&nbsp;value by its corresponding frequency:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<br/>Work out $1\\times\\var{f1}, 2\\times \\var{f2}, 3\\times\\var{f3}$ etc&nbsp;</li>\n<li>add up all of these:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <br/>$(1\\times\\var{f1})+(2\\times \\var{f2})+(3\\times\\var{f3}+ (4\\times\\var{f4}) + (5\\times\\var{f5}) + (6\\times\\var{f6})$</li>\n<li>divide by the total number of households:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <br/>Total households = $\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}+\\var{f5}+\\var{f6} =&nbsp;\\var{f1+f2+f3+f4+f5+f6}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</li>\n</ul>\n<p></p>\n<p>In other words <br/>$\\frac{(1\\times\\var{f1})+(2\\times \\var{f2})+(3\\times\\var{f3})+ (4\\times\\var{f4}) + (5\\times\\var{f5}) + (6\\times\\var{f6})}{\\var{f1+f2+f3+f4+f5+f6}}$</p>\n<p>$=\\frac{\\var{sfx}}{\\var{tot}}=\\var{precround(sfx/(tot),2)}$</p>\n<p></p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>The median is the \"middle\" value.&nbsp;</p>\n<p>In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.</p>\n<p>First add up the frequencies to find $n$, for a large total frequency,&nbsp;the median is the value at the $\\frac{n}{2}^{th}$ position (be careful working with small datasets).<br/><br/>We need to add up the frequencies until we reach this value and then the class we land in is the median.</p>\n<p>In our example, the total frequency is $\\var{tot}$, the median is the value at the&nbsp;$\\frac{n}{2}=\\frac{\\var{tot}}{2}^{th}$ position, i.e. value number $\\var{(tot)/2}$</p>\n<p>From our table, we can calculate the following cumulative frequencies:</p>\n<table border=\"0.1\" style=\"height: 90px; width: 515px; border: solid;\" height=\"108\">\n<tbody>\n<tr style=\"border-style: solid; border-color: #000000;\">\n<td style=\"width: 150.92391967773438px; height: 34px;\"><strong>People per household</strong></td>\n<td style=\"width: 39.293479919433594px; height: 34px;\">1</td>\n<td style=\"width: 36.27717590332031px; height: 34px;\">2</td>\n<td style=\"width: 44.32065200805664px; height: 34px;\">3</td>\n<td style=\"width: 44.32065200805664px; height: 34px;\">4</td>\n<td style=\"width: 44.32065200805664px; height: 34px;\">5</td>\n<td style=\"width: 45.33967590332031px; height: 34px;\">6</td>\n</tr>\n<tr style=\"border-style: solid; border-color: #000000;\">\n<td style=\"width: 150.92391967773438px; height: 50px;\"><strong>Cumulative frequency</strong></td>\n<td style=\"width: 39.293479919433594px; height: 50px;\">{cf[0]}</td>\n<td style=\"width: 36.27717590332031px; height: 50px;\">{cf[1]}</td>\n<td style=\"width: 44.32065200805664px; height: 50px;\">{cf[2]}</td>\n<td style=\"width: 44.32065200805664px; height: 50px;\">{cf[3]}</td>\n<td style=\"width: 44.32065200805664px; height: 50px;\">{cf[4]}</td>\n<td style=\"width: 45.33967590332031px; height: 50px;\">{cf[5]}</td>\n</tr>\n</tbody>\n</table>\n<p>And by looking at our cumulative frequencies we can see that&nbsp;value number $\\var{(tot)/2}$ occurs at some point in column $\\var{median}$, therefore the median number of people per household is $\\var{median}$.</p>\n<p><strong>(c)</strong></p>\n<p>The mode is the number which occurs most often. 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