// Numbas version: finer_feedback_settings
{"name": "MLE of the standard deviation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "MLE of the standard deviation", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Once our measurement apparatus has been built, we can use it to remove wrongly produced baskets from the production line. However, as you have seen in the lecture, we need to consider the precision of our measurement apparatus. To meet the requirements of the CEO of Cartonax,&nbsp;we need to&nbsp;specify&nbsp;measurement values $L_{min}$, $W_{min}$ below which baskets get rejected and&nbsp;$L_{max}$, $W_{max}$ above which baskets get rejected.&nbsp;</p>\n<p>Before these values can be set, the precision of the measurement apparatus has to be determined. In this exercise, you will practice with&nbsp;specifying&nbsp;this precision in terms of the standard deviation $\\sigma$. You will estimate the standard deviation from a sample of measurement values, just as you will have to do during the third&nbsp;lab.</p>\n<p>Remember, you can estimate the standard deviation&nbsp;$\\sigma$ from a sample using:</p>\n<p>$\\sigma_{est}=\\sqrt{\\frac{\\sum(x_i-\\mu_{est})^2}{n}}$</p>\n<p>In which $x_i$ are the individual measurement values, $\\mu_{est}$ is the mean measurement value and $n$ is the sample size.&nbsp;</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x6": {"name": "x6", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x7": {"name": "x7", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x8": {"name": "x8", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x9": {"name": "x9", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "x10": {"name": "x10", "group": "Ungrouped variables", "definition": "random(46.5 .. 47.5#0.001)", "description": "", "templateType": "randrange"}, "mu": {"name": "mu", "group": "Ungrouped variables", "definition": "(x1+x2+x3+x4+x5+x6+x7+x8+x9+x10)/10", "description": "", "templateType": "anything"}, "sigmaest": {"name": "sigmaest", "group": "Ungrouped variables", "definition": "sqrt(((x1-mu)^2+(x2-mu)^2+(x3-mu)^2+(x4-mu)^2+(x5-mu)^2+(x6-mu)^2+(x7-mu)^2+(x8-mu)^2+(x9-mu)^2+(x10-mu)^2)/10)", "description": "", "templateType": "anything"}, "l1": {"name": "l1", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l2": {"name": "l2", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l3": {"name": "l3", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l4": {"name": "l4", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l5": {"name": "l5", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l6": {"name": "l6", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l7": {"name": "l7", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l8": {"name": "l8", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l9": {"name": "l9", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "l10": {"name": "l10", "group": "Ungrouped variables", "definition": "random(75.8 .. 76.2#0.001)", "description": "", "templateType": "randrange"}, "mul": {"name": "mul", "group": "Ungrouped variables", "definition": "(l1+l2+l3+l4+l5+l6+l7+l8+l9+l10)/10", "description": "", "templateType": "anything"}, "sigmaestl": {"name": "sigmaestl", "group": "Ungrouped variables", "definition": "sqrt(((l1-mul)^2+(l2-mul)^2+(l3-mul)^2+(l4-mul)^2+(l5-mul)^2+(l6-mul)^2+(l7-mul)^2+(l8-mul)^2+(l9-mul)^2+(l10-mul)^2)/10)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "x9", "x10", "mu", "sigmaest", "l1", "l2", "l3", "l4", "l5", "l6", "l7", "l8", "l9", "l10", "mul", "sigmaestl"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Suppose you measure the width $W$ of some basked of which you know the exact value $W$ = 47,00mm ten times. Due to the inaccuracy of your measurement apparatus, you obtain the following values:</p>\n<table height=\"242\" style=\"width: 245px;\">\n<tbody>\n<tr>\n<td style=\"width: 50px;\">measurement</td>\n<td style=\"width: 127px;\">value (mm)</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">1</td>\n<td style=\"width: 127px;\">{x1}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">2</td>\n<td style=\"width: 127px;\">{x2}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">3</td>\n<td style=\"width: 127px;\">{x3}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">4</td>\n<td style=\"width: 127px;\">{x4}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">5</td>\n<td style=\"width: 127px;\">{x5}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">6</td>\n<td style=\"width: 127px;\">{x6}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">7</td>\n<td style=\"width: 127px;\">{x7}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">8</td>\n<td style=\"width: 127px;\">{x8}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">9</td>\n<td style=\"width: 127px;\">{x9}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">10</td>\n<td style=\"width: 127px;\">{x10}</td>\n</tr>\n</tbody>\n</table>\n<p>What is the sample mean?&nbsp;</p>\n<p>Give your answer in mm.</p>", "minValue": "{mu}", "maxValue": "{mu}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": "0", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "20", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate the standard deviation of your measurement apparatus if it is used to measure the width $W$ by calculating $\\sigma_{West}$.</p>\n<p>Give your answer in mm.</p>", "minValue": "{sigmaest}", "maxValue": "{sigmaest}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "eu"], "correctAnswerStyle": "eu"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Suppose you measure the&nbsp;length&nbsp;$L$ of some basked of which you know the exact value $L$ = 76,00mm ten times. Due to the inaccuracy of your measurement apparatus, you obtain the following values:</p>\n<table height=\"242\" style=\"width: 245px;\">\n<tbody>\n<tr>\n<td style=\"width: 50px;\">measurement</td>\n<td style=\"width: 127px;\">value (mm)</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">1</td>\n<td style=\"width: 127px;\">{l1}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">2</td>\n<td style=\"width: 127px;\">{l2}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">3</td>\n<td style=\"width: 127px;\">{l3}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">4</td>\n<td style=\"width: 127px;\">{l4}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">5</td>\n<td style=\"width: 127px;\">{l5}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">6</td>\n<td style=\"width: 127px;\">{l6}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">7</td>\n<td style=\"width: 127px;\">{l7}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">8</td>\n<td style=\"width: 127px;\">{l8}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">9</td>\n<td style=\"width: 127px;\">{l9}</td>\n</tr>\n<tr>\n<td style=\"width: 50px;\">10</td>\n<td style=\"width: 127px;\">{l10}</td>\n</tr>\n</tbody>\n</table>\n<p>What is the sample mean?&nbsp;</p>\n<p>Give your answer in mm.</p>", "minValue": "{mul}", "maxValue": "{mul}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": "0", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "20", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate the standard deviation of your measurement apparatus when it is used to measure the length $L$ by calculating $\\sigma_{Lest}$.</p>\n<p>Give your answer in mm.</p>", "minValue": "{sigmaestl}", "maxValue": "{sigmaestl}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "eu"], "correctAnswerStyle": "eu"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Mart Greuell", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3806/"}]}]}], "contributors": [{"name": "Mart Greuell", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3806/"}]}