// Numbas version: finer_feedback_settings
{"name": "Find sample mean, standard deviation, median and interquartile range, , ", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"r1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sort(r0)", "description": "", "name": "r1"}, "things": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'tomatoes '", "description": "", "name": "things"}, "median": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.5*(r1[11]+r1[12])", "description": "", "name": "median"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "24", "description": "", "name": "n"}, "uquartile": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.25*r1[17]+0.75*r1[18]", "description": "", "name": "uquartile"}, "u": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(20..60)", "description": "", "name": "u"}, "whatever": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'weights'", "description": "", "name": "whatever"}, "interq": {"templateType": "anything", "group": "Ungrouped variables", "definition": "uquartile-lquartile", "description": "", "name": "interq"}, "l": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..19)", "description": "", "name": "l"}, "var": {"templateType": "anything", "group": "Ungrouped variables", "definition": "variance(r0,true)", "description": "", "name": "var"}, "description": {"templateType": "anything", "group": "Ungrouped variables", "definition": "' from a new kind of tomato plant.'", "description": "", "name": "description"}, "lquartile": {"templateType": "anything", "group": "Ungrouped variables", 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"functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{precround(mean(r0),1)}", "minValue": "{precround(mean(r0),1)}", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{siground(stdev(r0,true),3)}", "minValue": "{siground(stdev(r0,true),3)}", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{median}", "minValue": "{median}", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "{interq}", "minValue": "{interq}", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<table border=\"1\" align=\"center\">\n<tbody>\n<tr><th>Sample Mean (1 dp)</th><th>Sample Standard Deviation (3 sig figs)</th><th>Median (exact value)</th><th>Interquartile Range (exact value)</th></tr>\n<tr align=\"center\"><th>[[0]]</th><th>[[1]]</th><th>[[2]]</th><th>[[3]]</th></tr>\n</tbody>\n</table>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>The following data are the {whatever}, in {units}, of $\\var{n}$ {things} {description}</p>\n    <table border=\"1\">\n    <tbody>\n    <tr>\n    <td>$\\var{r0[0]}$</td>\n    <td>$\\var{r0[1]}$</td>\n    <td>$\\var{r0[2]}$</td>\n    <td>$\\var{r0[3]}$</td>\n    <td>$\\var{r0[4]}$</td>\n    <td>$\\var{r0[5]}$</td>\n    <td>$\\var{r0[6]}$</td>\n    <td>$\\var{r0[7]}$</td>\n    </tr>\n    <tr>\n    <td>$\\var{r0[8]}$</td>\n    <td>$\\var{r0[9]}$</td>\n    <td>$\\var{r0[10]}$</td>\n    <td>$\\var{r0[11]}$</td>\n    <td>$\\var{r0[12]}$</td>\n    <td>$\\var{r0[13]}$</td>\n    <td>$\\var{r0[14]}$</td>\n    <td>$\\var{r0[15]}$</td>\n    </tr>\n    <tr>\n    <td>$\\var{r0[16]}$</td>\n    <td>$\\var{r0[17]}$</td>\n    <td>$\\var{r0[18]}$</td>\n    <td>$\\var{r0[19]}$</td>\n    <td>$\\var{r0[20]}$</td>\n    <td>$\\var{r0[21]}$</td>\n    <td>$\\var{r0[22]}$</td>\n    <td>$\\var{r0[23]}$</td>\n    </tr>\n    </tbody>\n    </table>", "tags": ["checked2015", "cr1", "data analysis", "elementary statistics", "interquartile range", "IQR", "lower quartile", "LQ", "MAS1604", "MAS8380", "MAS8401", "mean", "mean ", "median", "quartile", "sample mean", "sample standard deviation", "sc", "statistics", "tested1", "upper quartile", "UQ"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>11/07/2012:</strong></p>\n        <p><strong><br /></strong>Added tags.</p>\n        <p>Calculation not yet checked.</p>\n        <p><strong>23/07/2012:</strong></p>\n        <p>Added description.</p>\n        <p>Checked calculation, OK.</p>\n        <p>Two minor typos changed.</p>\n        <p><strong>3/08/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>Question appears to be working correctly.</p>\n        <p><strong>19/12/2012:</strong></p>\n        <p>Changed to new stats extension functions for variance and stdev. Still using the uniform distribution. Checked calculations again.</p>\n        <p>Added tested1 tag.</p>\n        <p><strong>21/12/2012:</strong></p>\n        <p>Checked rounding, OK. Added cr1 tag.&nbsp;</p>\n        <p>Scenarios possible. Added sc tag.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p><strong>Sample mean:</strong> The sample mean is $\\frac{\\var{sum(r0)}}{\\var{len(r0)}} = \\var{precround(mean(r0),1)}$ to 1 decimal place.</p>\n<p><strong>Sample standard deviation:</strong> The sample standard deviation is $\\var{stdev(r0,true)}=\\var{siground(stdev(r0,true),3)}$ to 3 significant figures.</p>\n<p>If you order the data in increasing order you get the following table:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$\\var{r1[0]}$</td>\n<td>$\\var{r1[1]}$</td>\n<td>$\\var{r1[2]}$</td>\n<td>$\\var{r1[3]}$</td>\n<td>$\\var{r1[4]}$</td>\n<td>$\\var{r1[5]}$</td>\n<td>$\\var{r1[6]}$</td>\n<td>$\\var{r1[7]}$</td>\n</tr>\n<tr>\n<td>$\\var{r1[8]}$</td>\n<td>$\\var{r1[9]}$</td>\n<td>$\\var{r1[10]}$</td>\n<td>$\\var{r1[11]}$</td>\n<td>$\\var{r1[12]}$</td>\n<td>$\\var{r1[13]}$</td>\n<td>$\\var{r1[14]}$</td>\n<td>$\\var{r1[15]}$</td>\n</tr>\n<tr>\n<td>$\\var{r1[16]}$</td>\n<td>$\\var{r1[17]}$</td>\n<td>$\\var{r1[18]}$</td>\n<td>$\\var{r1[19]}$</td>\n<td>$\\var{r1[20]}$</td>\n<td>$\\var{r1[21]}$</td>\n<td>$\\var{r1[22]}$</td>\n<td>$\\var{r1[23]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Denote the ordered data by $x_j$, thus $x_{10}=\\var{r1[9]}$ for example.</p>\n<p><strong>Median:</strong> The median lies between the 12th and 13th entries in the ordered table and is given by:</p>\n<p>\\[0.5\\times x_{12}+0.5\\times x_{13} = 0.5\\times\\var{r1[11]}+0.5\\times \\var{r1[12]}=\\var{median}\\]</p>\n<p><strong>Interquartile range:&nbsp;</strong>As there is an even number of values, the Lower Quartile will lie between two values. Its position is calculated by finding</p>\n<p>\\[\\frac{n+1}{4}=\\frac{\\var{n+1}}{4}=6\\frac{1}{4}\\]</p>\n<p>Hence the Lower Quartile lies between the 6th and 7th entries in the ordered table.</p>\n<p>It is \\[0.75\\times x_6+0.25\\times x_7 = 0.75\\times\\var{r1[5]}+0.25\\times \\var{r1[6]}=\\var{lquartile}\\]</p>\n<p>Once again as there is an even number of values, the Upper Quartile will lie between two values and its position is calculated by finding</p>\n<p>\\[\\frac{3(n+1)}{4}=\\frac{\\var{3*(n+1)}}{4}=18\\frac{3}{4}\\]</p>\n<p>Hence the Upper Quartile lies between the 18th and 19th entries in the ordered table.</p>\n<p>We find it is \\[0.25\\times x_{18}+0.75\\times x_{19} = 0.25\\times\\var{r1[17]}+0.75\\times \\var{r1[18]}=\\var{uquartile}\\]</p>\n<p>The interquartile range is defined to be</p>\n<p>\\[ \\text{Upper Quartile} &ndash; \\text{Lower Quartile} \\]</p>\n<p>and so in this case we have:</p>\n<p>\\[ \\text{Interquartile range} = \\var{uquartile}-\\var{lquartile}=\\var{interq} \\]</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}