// Numbas version: exam_results_page_options
{"name": "Shortened Sample standard deviation", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Shortened Sample standard deviation", "tags": [], "metadata": {"description": "<p>Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The following table gives the examination marks in {exam1} for a group of $n=\\var{n}$ students.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">{exam1}</th>\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<td>$\\var{r0[8]}$</td>\n<td>$\\var{r0[9]}$</td>\n<th align=\"left\">Mean = $\\var{mean1}$</th>\n</tr>\n</tbody>\n</table>\n<p>Find the standard deviation for the {exam1} examination marks.</p>", "advice": "<p>The solution to the first part is here &ndash; the other parts can be done in the same way.</p>\n<p>For {exam1} we have the mean is:</p>\n<p>\\[\\simplify[]{({r0[0]} + {r0[1]} + {r0[2]} + {r0[3]} + {r0[4]} + {r0[5]} + {r0[6]} + {r0[7]} + {r0[8]} + {r0[9]}) / {n} = {mean1}}\\]</p>\n<p>The variance is given by the formula:</p>\n<p>\\[\\textrm{Variance} = \\frac{1}{n}\\left(\\sum_{i=1}^{n}(x_i -\\mu)^2\\right)\\]</p>\n<p>where the $x_i$ are the exam scores for {exam1}, $n=\\var{n}$ the number of students and $\\mu=\\var{mean1}$ the sample mean.</p>\n<p>The Standard Deviation is then the square root of the Variance i.e.</p>\n<p>&nbsp;Standard Deviation = $\\sqrt{\\var{var1}} = \\var{stdev1}$ to one decimal place.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"s": {"name": "s", "group": "Ungrouped variables", "definition": "2", "description": "", "templateType": "anything", "can_override": false}, "ssq1": {"name": "ssq1", "group": "Ungrouped variables", "definition": "sum(map(x^2,x,r0))", "description": "", "templateType": "anything", "can_override": false}, "overallmean": {"name": 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