// Numbas version: exam_results_page_options
{"name": "Maths Support: Descriptive statistics", "type": "exam", "duration": 0, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "allQuestions": true, "shuffleQuestions": false, "questions": [], "percentPass": 0, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "preventleave": false, "browse": true, "showfrontpage": false, "showresultspage": "never"}, "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Find mean and standard deviation of differences between samples", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["cr1", "data analysis", "differences", "elementary statistics", "mean", "mean of differences", "standard deviation", "standard deviation of differences", "statistics", "stats", "tested1", "variance"], "metadata": {"description": "\n    \t\t        \t\t<p>An experiment is performed twice, each with $5$ outcomes</p>\n    \t\t        \t\t                    <p>$x_i,\\;y_i,\\;i=1,\\dots 5$&nbsp;. Find mean and s.d. of their differences $y_i-x_i,\\;i=1,\\dots 5$.</p>\n    \t\t        \n    \t\t", "licence": "None specified"}, "statement": "<p>{Something} for $\\var{thismany}$ {objects} {performing} were:</p>\n<table border=\"1\">\n<tbody>\n<tr><th>{object}</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr>\n<tr><th align=\"left\">First {attempt}</th>\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</tr>\n<tr><th align=\"left\">Second {attempt}</th>\n<td>$\\var{r2[0]}$</td>\n<td>$\\var{r2[1]}$</td>\n<td>$\\var{r2[2]}$</td>\n<td>$\\var{r2[3]}$</td>\n<td>$\\var{r2[4]}$</td>\n</tr>\n</tbody>\n</table>\n<p>Answer the following questions to 3 d.p.:</p>", "advice": "\n  <p>The table of differences is given by:</p>\n  <table border=\"1\">\n  <tbody>\n  <tr><th>{object}</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr>\n  <tr><th align=\"left\">First {attempt}</th>\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  </tr>\n  <tr><th align=\"left\">Second {attempt}</th>\n  <td>$\\var{r2[0]}$</td>\n  <td>$\\var{r2[1]}$</td>\n  <td>$\\var{r2[2]}$</td>\n  <td>$\\var{r2[3]}$</td>\n  <td>$\\var{r2[4]}$</td>\n  </tr>\n  <tr><th align=\"left\">Differences</th>\n  <td>$\\var{d[0]}$</td>\n  <td>$\\var{d[1]}$</td>\n  <td>$\\var{d[2]}$</td>\n  <td>$\\var{d[3]}$</td>\n  <td>$\\var{d[4]}$</td>\n  </tr>\n  </tbody>\n  </table>\n  <p>The mean of the differences is $\\var{meandiff}$.</p>\n  <p>The variance $V$ of the differences is <br/>\\[\\begin{eqnarray*} V&amp;=&amp;\\frac{1}{4}\\left(\\simplify[]{({d[0]}^2+{d[1]}^2+{d[2]}^2+{d[3]}^2+{d[4]}^2)}-5\\times \\var{meandiff}^2\\right)\\\\ &amp;=&amp;\\var{variance(d,true)} \\end{eqnarray*} \\]<br/>Hence we have the standard deviation = $\\sqrt{V}=\\var{stdiff}$ to 3 decimal places.</p>\n  \n  ", "rulesets": {"std": ["all", 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"templateType": "anything"}, "mu1": {"name": "mu1", "group": "Ungrouped variables", "definition": "random(16..20#0.5)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "list(vector(r2)-vector(r1))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["meandiff", "performing", "attempt", "r1", "objects", "mu2", "object", "sig1", "thismany", "stdiff", "sig2", "something", "r2", "mu1", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n        \n        \n        <p>Find the mean and standard deviations of the difference between first and second {attempt}s.</p>\n        \n        \n        \n        <p>Calculate differences for second {attempt} &#8211; first {attempt}.</p>\n        \n        \n        \n        <p>Please note that it is second {attempt} &#8211; first {attempt}</p>\n        \n        \n        \n        <p>Mean of difference = [[0]]  (input as an exact decimal)</p>\n        \n        \n        \n        <p>Standard deviation of difference = [[1]] (input to 3 decimal places)</p>\n        \n        \n      \n      ", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": 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