// Numbas version: finer_feedback_settings
{"name": "Coursework 1", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], []], "questions": [{"name": "Classify described random variables as qualitative or quantitative (edited)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Nikon Kurnosov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28343/"}], "tags": ["checked2015"], "metadata": {"description": "<p>Choosing whether given random variables are qualitative or quantitative.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>State whether the following variables are Qualitative or Quantitative.&nbsp;</p>\n  <p>Note that you will be deducted one mark for every wrong choice. However the minimum mark is 0.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"qual1": {"name": "qual1", "group": "Ungrouped variables", "definition": "[\"Types of PC used by small businesses in the north-east\",\"Marital status of questionnaire respondents\",\"Month of the year in which small shops record their highest sales\",\"Type of tenure for those in the licensed trade business\",\"Subjects studied at A level by students in this class\"]", "description": "", "templateType": "anything", "can_override": false}, "ind1": {"name": "ind1", "group": "Ungrouped variables", "definition": "2*vector(ind)-vector(1,1,1)", "description": "", "templateType": "anything", "can_override": false}, "ch1": {"name": "ch1", "group": "Ungrouped variables", "definition": "switch(ind[0]=0,random(qual),random(quant))", "description": "", "templateType": "anything", "can_override": false}, "ch2": {"name": "ch2", "group": "Ungrouped variables", "definition": "switch(ind[1]=0,random(qual except ch1),random(quant except ch1))", "description": "", "templateType": "anything", "can_override": false}, "qual": {"name": "qual", "group": "Ungrouped variables", "definition": "qual1+qual2", "description": "", "templateType": "anything", "can_override": false}, "quant2": {"name": "quant2", "group": "Ungrouped variables", "definition": "[\"The number of people requiring a special in-flight meal\",\"The average volume of bottles of wine imported from South America\",\"Salaries of University of Leicester graduates six months after graduation\",\"The distance travelled by taxis for a particular cab firm every day\",\"Total annual sales for a large American departmental store\",\"The total cost of a student's text books for this semester\"]", "description": "", "templateType": "anything", "can_override": false}, "ch3": {"name": "ch3", "group": "Ungrouped variables", "definition": "switch(ind[2]=0,random(qual except [ch1,ch2]),random(quant except [ch1,ch2]))", "description": "", "templateType": "anything", "can_override": false}, "qual2": {"name": "qual2", "group": "Ungrouped variables", "definition": "[\"Ice cream flavour preferred by children\",\"Brand of sportswear preferred by athletes\",\"Favourite type of film by UK cinema-goers\",\"Mobile phone price-plan\",\"Shape of swimming pools in local authority-run leisure centres\"]", "description": "", "templateType": "anything", "can_override": false}, "quant1": {"name": "quant1", "group": "Ungrouped variables", "definition": "[\"The number of orders received by a catering company\",\"The height of students taking Statistics courses at Leicester this year\", \"Your quarterly gas bill\", \"The time spent on hold at a credit call centre\",\"The average shipping time for orders placed with a TV shopping channel\",\"The annual electricity bill for a large UK Supermarket\"]", "description": "", "templateType": "anything", "can_override": false}, "quant": {"name": "quant", "group": "Ungrouped variables", "definition": "quant1+quant2", "description": "", "templateType": "anything", "can_override": false}, "cind": {"name": "cind", "group": "Ungrouped variables", "definition": "-1*ind1", "description": "", "templateType": "anything", "can_override": false}, "ind": {"name": "ind", "group": "Ungrouped variables", "definition": "random([[0,0,0],[1,0,0],[0,1,0],[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]])", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "transpose(matrix(list(cind),list(ind1)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["quant1", "quant2", "qual2", "cind", "qual1", "m", "ch1", "ch2", "ch3", "quant", "ind", "ind1", "qual"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["{ch1}", "{ch2}", "{ch3}"], "matrix": "m", "layout": {"type": "all", "expression": ""}, "answers": ["Qualitative", "Quantitative"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Distributions and moments - Q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>For the function:</p>\n<p>\\[f(x)=\\frac{x}{c}, \\quad&nbsp; x=1,2,3,4\\]</p>\n<p></p>\n<p><em>In parts a,c,d you can enter values as a number rounded to 3 decimal points or as a&nbsp; fraction.</em></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ans_a": {"name": "ans_a", "group": "Ungrouped variables", "definition": "10", "description": "", "templateType": "number", "can_override": false}, "ans_c": {"name": "ans_c", "group": "Ungrouped variables", "definition": "3", "description": "", "templateType": "anything", "can_override": false}, "ans_d": {"name": "ans_d", "group": "Ungrouped variables", "definition": "10", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ans_a", "ans_c", "ans_d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the value of the constant&nbsp; $c$ so that $f(x)$ satisfies the conditions of being a probability mass function for a random variable $X$</p>", "answer": "{ans_a}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"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": "<p>For the following questions using the value $c$ defined in the pervious part.</p>\n<p>Write down the probability distribution function (or cumulative distribution function):</p>\n<table style=\"height: 20px; width: 450px;\">\n<tbody>\n<tr style=\"height: 10px;\">\n<td rowspan=\"2\" style=\"height: 14px; width: 100px; text-align: right;\">$F(x)= \\begin{cases} \\\\ \\\\ \\\\ \\end{cases} $</td>\n<td style=\"height: 10px; width: 300px; text-align: left;\">[[0]],</td>\n<td style=\"height: 10px; width: 100px; text-align: left;\">$x=1,2,3,4$</td>\n</tr>\n<tr style=\"height: 10px;\">\n<td style=\"height: 10px; width: 300px; text-align: left;\">[[1]],</td>\n<td style=\"height: 10px; width: 100px; text-align: left;\">otherwise</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "ans_a", "part": "p0", "must_go_first": true}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "x*(1+x)/(2*{ans_a})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "ans_a", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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": "<p>Find the population mean</p>\n<p>$\\mu=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "ans_a", "part": "p0", "must_go_first": true}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans_c}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the population variance</p>\n<p>$Var(X)=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "ans_a", "part": "p0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans_d}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": 3, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Distributions and moments - Q8", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>For the function:</p>\n<p>\\[f(x)=\\frac{x^3}{4}, \\quad 0&lt; x &lt;c\\]</p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ans_a": {"name": "ans_a", "group": "Ungrouped variables", "definition": "2", "description": "", "templateType": "number", "can_override": false}, "ans_c": {"name": "ans_c", "group": "Ungrouped variables", "definition": "32/20", "description": "", "templateType": "anything", "can_override": false}, "ans_d": {"name": "ans_d", "group": "Ungrouped variables", "definition": "64/(25*24)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ans_a", "ans_c", "ans_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": "<p>Determine&nbsp; the constant&nbsp; $c$ in terms of $n$ so that $f(x)$ satisfies the conditions of being a probability density function for a continuous random variable $X$</p>\n<p>$c=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans_a}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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": "<p>Write down the probability distribution function (or cumulative distribution function) for $x$:</p>\n<table style=\"height: 20px; width: 750px;\">\n<tbody>\n<tr style=\"height: 10px;\">\n<td rowspan=\"2\" style=\"height: 14px; width: 101.25px; text-align: right;\">$F(x)= \\begin{cases} \\\\ \\\\ \\\\ \\end{cases} $</td>\n<td style=\"height: 10px; width: 200px; text-align: left;\">[[0]],</td>\n<td style=\"height: 10px; width: 200px; text-align: left;\">$0&lt; x&lt; $[[1]]</td>\n</tr>\n<tr style=\"height: 10px;\">\n<td style=\"height: 10px; width: 200px; text-align: left;\">0,</td>\n<td style=\"height: 10px; width: 200px; text-align: left;\">otherwise</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "x^4/16", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans_a}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the mean of $X$</p>", "answer": "{ans_c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the variance of $X$</p>", "answer": "{ans_d}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Probability, expectation and variance of exponential distribution ( copy)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Nikon Kurnosov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28343/"}], "tags": ["checked2015"], "metadata": {"description": "<p>Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "\n    <p>The time, &nbsp;in {period} between {this} follows an exponential distribution with rate $\\var{ra}$ i.e.&nbsp;</p>\n  <p>\\[X \\sim \\operatorname{exp}(\\var{ra})\\]</p>\n    ", "advice": "\n    <p>If $X \\sim \\operatorname{exp}(\\lambda)$ then&nbsp;$\\displaystyle \\operatorname{E}[X] =\\frac{1}{\\lambda}$&nbsp;and &nbsp;$\\displaystyle \\operatorname{Var}(X)=\\frac{1}{\\lambda^2}$.</p>\n  <p>Also $P(X \\lt a)=1-e^{-\\lambda a}$.</p>\n  <p>a)</p>\n  <p>If $X \\sim \\operatorname{exp}(\\var{ra})$ then:</p>\n  <p>$\\displaystyle \\operatorname{E}[X] =\\frac{1}{\\lambda}=\\frac{1}{\\var{ra}}=\\var{ans1}$ to 3 decimal places.</p>\n  <p>$\\displaystyle \\operatorname{Var}(X) =\\frac{1}{\\lambda^2}=\\frac{1}{\\var{ra}^2}=\\var{ans2}$ to 3 decimal places.</p>\n  <p>b)</p>\n  <p>$P(X \\lt \\var{thistime}) = 1 -(e ^ {-\\var{ ra} \\times \\var{thistime}}) = 1 -(e ^ { -\\var{ra * thistime}}) = \\var{ans3}$ to 3 decimal places.</p>\n    ", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"this": {"name": "this", "group": "Ungrouped variables", "definition": "\"customer arrivals at the check-in desk at Airport \"", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "precround(1/ra^2,3)", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "precround(tans3,3)", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "precround(1/ra,3)", "description": "", "templateType": "anything", "can_override": false}, "thistime": {"name": "thistime", "group": "Ungrouped variables", "definition": "random(0.8..1.8#0.1)", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.001", "description": "", "templateType": "anything", "can_override": false}, "ra": {"name": "ra", "group": "Ungrouped variables", "definition": "random(0.2..1.2#0.1)", "description": "", "templateType": "anything", "can_override": false}, "that": {"name": "that", "group": "Ungrouped variables", "definition": "\"two customers arriving \"", "description": "", "templateType": "anything", "can_override": false}, "tans3": {"name": "tans3", "group": "Ungrouped variables", "definition": "1-exp(-ra*thistime)", "description": "", "templateType": "anything", "can_override": false}, "period": {"name": "period", "group": "Ungrouped variables", "definition": "\"minutes\"", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["that", "this", "ans1", "ans2", "ans3", "period", "ra", "tol", "tans3", "thistime"], "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        <p>Find $\\operatorname{E}[X]$ between {this}:</p>\n      <p>$\\operatorname{E}[X]=\\;$?[[0]]{period} (enter as a decimal correct to 3 decimal places).</p>\n      <p>Find $\\operatorname{Var}(X)$:</p>\n      <p>$\\operatorname{Var}(X)=\\;$?[[1]](enter as a decimal correct to 3 decimal places).</p>\n        ", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans1-tol", "maxValue": "ans1+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans2-tol", "maxValue": "ans2+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "<p>Find the probability that the time between {that} is less than $\\var{thistime}$ {period}:</p>\n        <p>&nbsp;$P(X \\lt \\var{thistime})=\\;$?[[0]](enter as a decimal correct to 3 decimal places)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans3-tol", "maxValue": "ans3+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Formula for the MGF (copy)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Drovandi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9840/"}, {"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}, {"name": "Nikon Kurnosov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28343/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>What is the formula for the MGF of a continuous RV $X$?</p>", "advice": "<p>$m_X(s) =\\mbox{E}[e^{sX}] =\\int_x e^{sx}f(x)dx$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "// Reveal answers, score and advice\nthis.display.revealAnswer();\nthis.display.showScore();\nNumbas.controls.getAdvice();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$m_X(s) =\\mbox{E}[e^{sX}] =\\int_x e^{sx}f(x)dx$", "$m_X(s) =\\mbox{E}[es^{X}] =\\int_x es^{x}f(x)dx$", "$m_X(s) =\\mbox{E}[s^{Xe}] =\\int_x s^{xe}f(x)dx$"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "MGF of the standard normal distribution (copy)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Drovandi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9840/"}, {"name": "adam bretherton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18177/"}, {"name": "Nikon Kurnosov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28343/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The MGF of the standard Normal distribution ($\\mu = 0, \\sigma^2 = 1$) is given by $\\frac{s^2}{2}$?</p>", "advice": "<p>This is actually the CGF of the standard normal.</p>\n<p>The MGF is $\\exp(\\frac{s^2}{2})$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "// Reveal answers, score and advice\nthis.display.revealAnswer();\nthis.display.showScore();\nNumbas.controls.getAdvice();", "order": "before"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["False", "True"], "matrix": ["1", 0], "distractors": ["", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "InterimTest - Question 1 as 2021", "extensions": ["stats"], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A pharmaceutical company wants to know whether an experimental drug has a stabilising effect&nbsp;on blood pressure.</p>\n<p>Twenty randomly selected subjects were given the drug and after sufficient time for the drug to have an impact, their systolic blood pressures were recorded.</p>\n<table>\n<tbody>\n<tr>\n<td>106</td>\n<td>118</td>\n<td>118</td>\n<td>123</td>\n<td>128</td>\n</tr>\n<tr>\n<td>128</td>\n<td>129</td>\n<td>130</td>\n<td>132</td>\n<td>133</td>\n</tr>\n<tr>\n<td>136</td>\n<td>136</td>\n<td>137</td>\n<td>140</td>\n<td>140</td>\n</tr>\n<tr>\n<td>143</td>\n<td>147</td>\n<td>152</td>\n<td>161</td>\n<td>184</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<h4><strong><em>In the questions where you need to enter numeric values, please round your answers to 3 decimal places</em></strong></h4>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"nobs": {"name": "nobs", "group": "Data", "definition": "20", "description": "<p>random(15..20)</p>", "templateType": "anything", "can_override": false}, "sample": {"name": "sample", "group": "Data", "definition": "sort([106, 118, 118, 123, 128, 128, 129, 130, 132, 133, 136, 136, 137, 140, 140, 143, 147, 152, 161, 184])", "description": "<p>sort(repeat(round(normalsample(MeanPop, StdPop)),Nobs))</p>", "templateType": "anything", "can_override": false}, "meanpop": {"name": "meanpop", "group": "Data", "definition": "random(50..500)", "description": "", "templateType": "anything", "can_override": false}, "stdpop": {"name": "stdpop", "group": "Data", "definition": "if(MeanPop<200,random(5..20),random(50..100))", "description": "", "templateType": "anything", "can_override": false}, "minSample": {"name": "minSample", "group": "Data", "definition": "min(sample)", "description": "", "templateType": "anything", "can_override": false}, "maxSample": {"name": "maxSample", "group": "Data", "definition": "max(sample)", "description": "", "templateType": "anything", "can_override": false}, "Nbins": {"name": "Nbins", "group": "Frequency distribution", "definition": "9", "description": "<p>if(U-L&lt;50, (U-L)/5, if((U-L)/10&lt;10, (U-L)/10, if(mod((U-L)/10,6)=0, 6, if(mod((U-L)/10,7)=0, 7, if(mod((U-L)/10,8)=0, 8,10)))))</p>", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Frequency distribution", "definition": "floor(minSample/10)*10", "description": "", "templateType": "anything", "can_override": false}, "u": {"name": "u", "group": "Frequency distribution", "definition": "ceil(MaxSample/10)*10", "description": "", "templateType": "anything", "can_override": false}, "breaks": {"name": "breaks", "group": "Frequency distribution", "definition": "[105, 115,  125, 135, 145, 155, 165, 175]", "description": "<p>if(U-L&lt;50, iterate(x+(U-L)/5/Nbins*5,x,L+(U-L)/5/Nbins*5,Nbins-1),iterate(x+(U-L)/10/Nbins*10,x,L+(U-L)/10/Nbins*10,Nbins-1))</p>", "templateType": "anything", "can_override": false}, "FreqIntervals": {"name": "FreqIntervals", "group": "Frequency distribution", "definition": "latex(Intervals2String(Breaks))", "description": "", "templateType": "anything", "can_override": false}, "Freqs": {"name": "Freqs", "group": "Frequency distribution", "definition": "FreqTable(sample,breaks)", "description": "", "templateType": "anything", "can_override": false}, "RelFreqs": {"name": "RelFreqs", "group": "Frequency distribution", "definition": "list(vector(Freqs)/Nobs)", "description": "", "templateType": "anything", "can_override": false}, "midpoints": {"name": "midpoints", "group": "Grouped Statistics", "definition": "midpoints4groups(l,breaks)", "description": "", "templateType": "anything", "can_override": false}, "midpoints_last": {"name": "midpoints_last", "group": "Grouped Statistics", "definition": "midpoints[length(midpoints)-1]", "description": "", "templateType": "anything", "can_override": false}, "samplemean": {"name": "samplemean", "group": "Ungrouped variables", "definition": "mean(sample)", "description": "", "templateType": "anything", "can_override": false}, "groupedMean": {"name": "groupedMean", "group": "Grouped Statistics", "definition": "grMean(midpoints,RelFreqs)", "description": "", "templateType": "anything", "can_override": false}, "samplestd": {"name": "samplestd", "group": "Ungrouped variables", "definition": "stdev(sample,true)", "description": "", "templateType": "anything", "can_override": false}, "groupedVar": {"name": "groupedVar", "group": "Grouped Statistics", "definition": "grVar(midpoints,relfreqs,nobs)", "description": "", "templateType": "anything", "can_override": false}, "groupedStd": {"name": "groupedStd", "group": "Grouped Statistics", "definition": "sqrt(groupedVar)", "description": "", "templateType": "anything", "can_override": false}, "sampleSum": {"name": "sampleSum", "group": "Ungrouped variables", "definition": "sum(vector(sample))", "description": "", "templateType": "anything", "can_override": false}, "sample2Sum": {"name": "sample2Sum", "group": "Ungrouped variables", "definition": "sum(vector(map(x^2,x, sample)))", "description": "", "templateType": "anything", "can_override": false}, "sampleMedian": {"name": "sampleMedian", "group": "Ungrouped variables", "definition": "median(sample)", "description": "", "templateType": "anything", "can_override": false}, "sampleIQR": {"name": "sampleIQR", "group": "Ungrouped variables", "definition": "samplequartiles[2]-samplequartiles[0]", "description": "", "templateType": "anything", "can_override": false}, "sampleQuartiles": {"name": "sampleQuartiles", "group": "Ungrouped variables", "definition": "sample3Quartiles(sample)", "description": "<p>quartiles(sample)</p>", "templateType": "anything", "can_override": false}, "midrange": {"name": "midrange", "group": "Ungrouped variables", "definition": "(max(sample)+min(sample))/2", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "CI variables", "definition": "random([90,95,99])", "description": "", "templateType": "anything", "can_override": false}, "marginoferror": {"name": "marginoferror", "group": "CI variables", "definition": "zAlpha2*samplestd/sqrt(nobs)", "description": "", "templateType": "anything", "can_override": false}, "zAlpha2": {"name": "zAlpha2", "group": "CI variables", "definition": "siground(normalinv(1-(1-alpha/100)/2,0,1),4)", "description": "", "templateType": "anything", "can_override": false}, "LeftLimit": {"name": "LeftLimit", "group": "CI variables", "definition": "samplemean-marginoferror", "description": "", "templateType": "anything", "can_override": false}, "RightLimit": {"name": "RightLimit", "group": "CI variables", "definition": "samplemean+marginoferror", "description": "", "templateType": "anything", "can_override": false}, "sampleVar": {"name": "sampleVar", "group": "Ungrouped variables", "definition": "samplestd^2", "description": "", "templateType": "anything", "can_override": false}, "alphatrim": {"name": "alphatrim", "group": "Ungrouped variables", "definition": "5", "description": "", "templateType": "anything", "can_override": false}, "trimmedmean": {"name": "trimmedmean", "group": "Ungrouped variables", "definition": "mean(sample[1..19])", "description": "", "templateType": "anything", "can_override": false}, "trimmedstd": {"name": "trimmedstd", "group": "Ungrouped variables", "definition": "stdev(sample[1..19],true)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["samplemean", "samplestd", "sampleSum", "sample2Sum", "sampleMedian", "sampleIQR", "sampleQuartiles", "midrange", "sampleVar", "alphatrim", "trimmedmean", "trimmedstd"], "variable_groups": [{"name": "Data", "variables": ["nobs", "sample", "meanpop", "stdpop", "minSample", "maxSample"]}, {"name": "Frequency distribution", "variables": ["Nbins", "breaks", "FreqIntervals", "l", "u", "Freqs", "RelFreqs"]}, {"name": "Grouped Statistics", "variables": ["midpoints_last", "midpoints", "groupedMean", "groupedVar", "groupedStd"]}, {"name": "CI variables", "variables": ["alpha", "marginoferror", "zAlpha2", "LeftLimit", "RightLimit"]}], "functions": {"intervals2String": {"parameters": [["Breaks", "list of number"]], "type": "string", "language": "javascript", "definition": "        var out = '';\n        out+= '(0,'+Breaks[0].toString()+'],';\n        for(i =0; i<Breaks.length-2; i++ ) {\n            out+='('+Breaks[i].toString()+','+Breaks[i+1].toString()+'],'\n        }\n        out+='('+Breaks[Breaks.length-2].toString()+',\\\\infty)'\n        return out;"}, "FreqTable": {"parameters": [["sample", "list of number"], ["Breaks", "list of number"]], "type": "list", "language": "javascript", "definition": "var out=[];\nvar j=0;\nvar count=0;\nfor (i=0; i<Breaks.length-1; i++){\n   while (j<sample.length && sample[j]<=Breaks[i]){\n    count++;\n    j++;\n   }\n   out.push(count);\n   count=0;\n}\nout.push(sample.length-(j))\nreturn out;"}, "midpoints4groups": {"parameters": [["left", "number"], ["breaks", "list of number"]], "type": "list", "language": "javascript", "definition": "var out=[];\nout.push((left+breaks[0])/2)\nfor (var i=0; i<breaks.length-1; i++){\n      out.push((breaks[i]+breaks[i+1])/2);\n}\nreturn out;"}, "grMean": {"parameters": [["MidPoints", "list of number"], ["RelFreqs", "list of number"]], "type": "number", "language": "javascript", "definition": "var out=0;\n\nfor (var i=0; i<MidPoints.length; i++){\n      out+=MidPoints[i]*RelFreqs[i];\n}\nreturn out;"}, "grVar": {"parameters": [["MidPoints", "list of number"], ["RelFreqs", "list of number"], ["n", "number"]], "type": "number", "language": "javascript", "definition": "var out=0;\nvar sM=0;\nfor (var i=0; i<MidPoints.length; i++){\n      sM+=MidPoints[i]*RelFreqs[i];\n};\n\n\nfor (var i=0; i<MidPoints.length; i++){\n      out+=(MidPoints[i]-sM)^2*RelFreqs[i];\n};\n\nout*=(n/(n-1));\nreturn out;"}, "sample3Quartiles": {"parameters": [["sample", "list of number"]], "type": "list", "language": "javascript", "definition": "var out=[];\nvar Q1=0;\nvar Q2=0;\nvar Q3=0;\nvar nq1l=0;\nvar nq1r=0;\nvar nq2l=0;\nvar nq2r=0;\nvar nq3l=0;\nvar nq3r=0;\n\nvar n=sample.length;\nnq1l=Math.floor(1+((n-1)/4)); nq1r=Math.ceil(1+((n-1)/4));\nnq2l=Math.floor(1+2*((n-1)/4)); nq2r=Math.ceil(1+2*((n-1)/4));\nnq3l=Math.floor(1+3*((n-1)/4)); nq3r=Math.ceil(1+3*((n-1)/4));\nsample=sample.sort();\n\n\n//out.push(n);\n//out.push(sample[0]);\n//out.push(sample[nq1l-1]); out.push(sample[nq1r-1]);\n//out.push(sample[nq2l-1]); out.push(sample[nq2r-1]);\n//out.push(sample[nq3l-1]); out.push(sample[nq3r-1]);\nout.push((sample[nq1l-1]+sample[nq1r-1])/2);\nout.push((sample[nq2l-1]+sample[nq2r-1])/2);\nout.push((sample[nq3l-1]+sample[nq3r-1])/2);\n\nreturn(out);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Part 1. Descriptive stats", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calcuate the following descriptive statistics of the sample:</p>\n<p></p>\n<p>Sample mean:</p>\n<p>$\\bar{x}=$[[0]]</p>\n<p>Sample variance:</p>\n<p>Var$(x)=$[[6]]</p>\n<p>Sample standard deviation:</p>\n<p>$s_X=$[[1]]</p>\n<p>First Quartile:</p>\n<p>$Q_1=$[[2]]</p>\n<p>Sample median:</p>\n<p>$\\textbf{Median}=$[[3]]</p>\n<p>Third Quartile:</p>\n<p>$Q_3=$[[4]]</p>\n<p>Interquartile range:</p>\n<p>$\\textbf{IQR}=$[[5]]</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "SampleMean", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sampleMean", "maxValue": "sampleMean", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "SampleStDev", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "samplestd", "maxValue": "samplestd", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Q1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sampleQuartiles[0]", "maxValue": "sampleQuartiles[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Median", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sampleQuartiles[1]", "maxValue": "sampleQuartiles[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Q3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sampleQuartiles[2]", "maxValue": "sampleQuartiles[2]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "IQR", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sampleIQR", "maxValue": "sampleIQR", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "SampleVar", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sampleVar-0.005", "maxValue": "sampleVar+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Part 2. Frequency distribution", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Construct a relative frequency distribution for the data, taking as your grouping intervals the following $\\var{Nbins}$ intervals:</p>\n<p>\\[\\var{FreqIntervals}\\]</p>\n<p>Write a list of the corresponding frequencies as numbers separated by commas (for example, 1,2,3,2,1)</p>\n<p></p>\n<p>[[0]]</p>\n<p>Write a list of the relative frequencies as fractions separated by commas (for example, 1/9, 2/9, 1/3, 2/9, 1/9)</p>\n<p></p>\n<p>[[1]]</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"type": "list-of-numbers", "useCustomName": true, "customName": "Frequencies", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "{Freqs}", "allowFractions": false, "correctAnswerFractions": false, "isSet": false, "show_input_hint": true, "separator": ","}}, {"type": "list-of-numbers", "useCustomName": true, "customName": "Relative Frequencies", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "{RelFreqs}", "allowFractions": true, "correctAnswerFractions": true, "isSet": false, "show_input_hint": true, "separator": ","}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Part 3. Trimmed sample", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the following statistics for the $\\alpha$-trimmed&nbsp; sample, if $\\alpha=\\var{alphaTrim}$%:</p>\n<p></p>\n<p>$\\alpha$-trimmed mean:</p>\n<p>[[0]]</p>\n<p>trimmed sample deviation:</p>\n<p>[[1]]</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "TrimmedMean", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "trimmedMean-0.005", "maxValue": "trimmedMean+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "TrimmedStDev", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "trimmedstd-0.005", "maxValue": "trimmedstd+0.005", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Mean, SD, median and IQR (copy)", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Nikon Kurnosov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28343/"}], "tags": [], "metadata": {"description": "<p>Find mean, SD, median and IQR for a sample.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Find the mean, SD, median and IQR for the following sample of $\\var{n}$ data values:</p>\n<table>\n<tbody>\n<tr>\n<td>{r0[0]}</td>\n<td>{r0[1]}</td>\n<td>{r0[2]}</td>\n<td>{r0[3]}</td>\n<td>{r0[4]}</td>\n<td>{r0[5]}</td>\n<td>{r0[6]}</td>\n<td>{r0[7]}</td>\n<td>{r0[8]}</td>\n<td>{r0[9]}</td>\n<td>{r0[10]}</td>\n<td>{r0[11]}</td>\n</tr>\n<tr>\n<td>{r0[12]}</td>\n<td>{r0[13]}</td>\n<td>{r0[14]}</td>\n<td>{r0[15]}</td>\n<td>{r0[16]}</td>\n<td>{r0[17]}</td>\n<td>{r0[18]}</td>\n<td>{r0[19]}</td>\n<td>{r0[20]}</td>\n<td>{r0[21]}</td>\n<td>{r0[22]}</td>\n<td>{r0[23]}</td>\n</tr>\n</tbody>\n</table>\n<p>Find the sample mean to 1 decimal place and the sample standard deviation&nbsp;to 3 significant figures.</p>", "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} = 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"description": "", "templateType": "anything", "can_override": false}, "r0": {"name": "r0", "group": "Ungrouped variables", "definition": "repeat(random(l..u),24)", "description": "", "templateType": "anything", "can_override": false}, "whatever": {"name": "whatever", "group": "Ungrouped variables", "definition": "'weights'", "description": "", "templateType": "anything", "can_override": false}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "random(20..60)", "description": "", "templateType": "anything", "can_override": false}, "stdev": {"name": "stdev", "group": "Ungrouped variables", "definition": "precround(stdev(r0,true),2)", "description": "", "templateType": "anything", "can_override": false}, "var": {"name": "var", "group": "Ungrouped variables", "definition": "variance(r0,true)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["uquartile", "r0", "description", 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"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{precround(mean(r0),1)}", "maxValue": "{precround(mean(r0),1)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, 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"showfrontpage": true, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "autoSubmit": true, "allowAttemptDownload": false, "downloadEncryptionKey": "", "showresultspage": "review"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": false, "showactualmarkwhen": "oncompletion", "showtotalmarkwhen": "always", "showanswerstatewhen": "inreview", "showpartfeedbackmessageswhen": "inreview", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": false, "intro": "", "end_message": "", "results_options": {"printquestions": false, "printadvice": false}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": false, "reviewshowfeedback": true, "showactualmark": false, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Nikon Kurnosov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/28343/"}], "extensions": ["stats"], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": []}