// Numbas version: finer_feedback_settings
{"name": "Central Tendency", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "90", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], []], "questions": [{"name": "Mean", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "tags": ["median", "mode", "Rebel", "REBEL", "rebel", "rebelmaths", "sample mean", "standard deviation", "statistics", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>To find the mean: Add up all the values. Then divide by the number of values.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p>$\\text{mean}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "strictPrecision": false, "minValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Calculate the <strong>mean</strong>&nbsp;of the following set of numbers correct&nbsp;to one decimal place:</p>\n<p>$\\var{a1}, \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}$ .</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(9..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(5..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(7..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(0..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a7": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a7", "description": ""}, "a6": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}}, "metadata": {"description": "<div class=\"description\">\n<p>calculating mean</p>\n<p>rebelmaths</p>\n</div>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Mode, Median, Mean", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {"isnotalist": {"definition": "return !Array.isArray(a);", "type": "boolean", "language": "javascript", "parameters": [["a", "list"]]}}, "ungrouped_variables": ["dat", "a", "mo", "me", "md"], "tags": ["descriptive statistics", "mean", "median", "mode", "Rebel", "REBEL", "rebel", "rebelmaths", "statistics", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>The mean, median and mode are all averages. Each gives us some information about a typical member of a set of data.</p>\n<p>To calculate the&nbsp;<strong>mean</strong>, you need to find the total of all the test scores and divide it by the number of scores -- in this case 10.</p>\n<p>The&nbsp;<strong>median</strong>&nbsp;is the middle score,&nbsp;<em>when the scores are arranged in order.</em>&nbsp;In this case the number of scores is even, so we need to find the mean of the 5th and 6th scores.</p>\n<p>The&nbsp;<strong>mode&nbsp;</strong>is the most frequent score.&nbsp;</p>\n<p>See&nbsp;<b><span style=\"font-size: 11.0pt; line-height: 115%; font-family: 'Calibri','sans-serif'; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-GB; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"><a href=\"http://www.skillsyouneed.com/num/averages.html\">http://www.skillsyouneed.com/num/averages.html&nbsp;</a>&nbsp;</span></b></p>\n<p>for more information on these three types of average.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>{a[0]}, &nbsp;{a[1]}, &nbsp;{a[2]}, {a[3]}, {a[4]}, {a[5]}, {a[6]}, {a[7]}, {a[8]}, {a[9]}</p>\n<p>Mean: [[0]]</p>\n<p>Median: [[1]]</p>\n<p>Mode: [[2]]</p>\n<p>Give your answers to 1 decimal place where appropriate.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The&nbsp;<strong>median</strong>&nbsp;is the middle score,&nbsp;<em>when the scores are arranged in order.</em>&nbsp;In this case the number of scores is even, so we need to find the mean of the 5th and 6th scores.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "me", "minValue": "me", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "md", "minValue": "md", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "mo", "minValue": "mo", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Find the mean, median and mode of the following 10 test scores.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"dat": {"definition": "satisfy(\n  [a],\n  [\n    //a is given as a list by generating 10 numbers between 4 and 18\n    repeat(random(4..18),10)],\n  [ //the conditions are given to force one mode and a reasonably large variance\n    //to give some variation.\n    length(mode(a))=1,\n    variance(a)>8\n    ],\n  250\n  )", "templateType": "anything", "group": "Ungrouped variables", "name": "dat", "description": ""}, "a": {"definition": "dat[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "mo": {"definition": "mode(a)[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "mo", "description": ""}, "me": {"definition": "mean(a)", "templateType": "anything", "group": "Ungrouped variables", "name": "me", "description": ""}, "md": {"definition": "median(a)", "templateType": "anything", "group": "Ungrouped variables", "name": "md", "description": ""}}, "metadata": {"description": "<p>Find the mean, median and mode of a list of 10 test scores.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Mean, Median, Mode for Auto", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "tags": ["halesowen college", "median", "mode", "rebel", "Rebel", "REBEL", "rebelmaths", "sample mean", "standard deviation", "statistics", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Mean: Add up all the numbers and divide by the number of numbers.</p>\n<p>Median: middle value</p>\n<p>Mode: most common value</p>\n<p></p>", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": "1", "prompt": "<p>$\\text{mean}=\\;\\;$[[0]] (correct to two decimal places)</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To find the mean:</p>\n<p>1. Add up all the numbers.</p>\n<p>2. Divide by the number of numbers.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.01, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{precround(1/7*(a1+a2+a3+a4+a5+a6+a7),2)}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\text{median}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To find the median:</p>\n<p>List the numbers in order of increasing size.&nbsp;</p>\n<p>The median is then the middle number.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a4}", "minValue": "{a4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 2, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\text{mode}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The mode is the number that occurs most often.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a2}", "minValue": "{a2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 2, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The fuel emissions (in g/km of CO2) of a sample of 7&nbsp;diesel cars of similar type have been recorded as follows:</p>\n<p>$\\var{a2}, \\var{a7}, \\var{a1}, \\var{a5}, \\var{a3}, \\var{a6}$ and $\\var{a4}$.</p>\n<p>Calculate the mean, median and mode of these emissions.<br/><br/></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(110..115)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "a2", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(116..121)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(126..130 except a6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(122..125)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a7": {"definition": "random(131..140)", "templateType": "anything", "group": "Ungrouped variables", "name": "a7", "description": ""}, "a6": {"definition": "random(126..130)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}}, "metadata": {"description": "<div class=\"description\">\n<p>Topics covered are calculating the mean, median, mode and standard deviation.</p>\n<p>rebelmaths</p>\n</div>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Julie's copy of Jack's copy of SOEE5154 - Mean, median, mode and standard deviation", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "parts": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>$\\text{mean}=\\;\\;$[[0]]</p>\n<p>Enter decimal answers to 1 decimal places.</p>", "gaps": [{"precision": "1", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "precisionPartialCredit": "0", "correctAnswerFraction": false, "showCorrectAnswer": true, "minValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "variableReplacements": [], "marks": "1", "allowFractions": false, "showFeedbackIcon": true, "maxValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "correctAnswerStyle": "plain"}], "scripts": {}}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>$\\text{median}=\\;\\;$[[0]]</p>", "gaps": [{"correctAnswerStyle": "plain", "type": "numberentry", "correctAnswerFraction": false, "showCorrectAnswer": true, "minValue": "{a4}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 2, "allowFractions": false, "showFeedbackIcon": true, "maxValue": "{a4}", "notationStyles": ["plain", "en", "si-en"], "scripts": {}}], "scripts": {}}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>$\\text{mode}=\\;\\;$[[0]]</p>", "gaps": [{"correctAnswerStyle": "plain", "type": "numberentry", "correctAnswerFraction": false, "showCorrectAnswer": true, "minValue": "{a4}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 2, "allowFractions": false, "showFeedbackIcon": true, "maxValue": "{a4}", "notationStyles": ["plain", "en", "si-en"], "scripts": {}}], "scripts": {}}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>$\\text{range}=\\;\\;$[[0]]</p>", "gaps": [{"showpreview": true, "answersimplification": "std", "type": "jme", "checkingaccuracy": 0.01, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "vsetrangepoints": 5, "answer": "{a2-a3}", "checkvariablenames": false, "expectedvariablenames": [], "variableReplacements": [], "marks": 2, "checkingtype": "absdiff", "showFeedbackIcon": true, "scripts": {}}], "scripts": {}}], "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "functions": {}, "variables": {"a4": {"description": "", "group": "Ungrouped variables", "name": "a4", "definition": "random(1..3)", "templateType": "anything"}, "a7": {"description": "", "group": "Ungrouped variables", "name": "a7", "definition": "a4", "templateType": "anything"}, "a2": {"description": "", "group": "Ungrouped variables", "name": "a2", "definition": "random(7..8)", "templateType": "anything"}, "a5": {"description": "", "group": "Ungrouped variables", "name": "a5", "definition": "random(-4..-3)", "templateType": "anything"}, "a3": {"description": "", "group": "Ungrouped variables", "name": "a3", "definition": "random(-6..-5)", "templateType": "anything"}, "a1": {"description": "", "group": "Ungrouped variables", "name": "a1", "definition": "random(-2..-1)", "templateType": "anything"}, "a6": {"description": "", "group": "Ungrouped variables", "name": "a6", "definition": "random(4..6)", "templateType": "anything"}}, "advice": "<p>Mean: $\\mu = \\frac{1}{N}\\sum\\limits_{i=1}^N x_i$</p>\n<p>Median: middle value</p>\n<p>Mode: most common value</p>\n<p>Range: Highest value - lowest value</p>", "statement": "<p>For the last 7 days in October, the express train arrived late at it's destination by the times (in minutes) listed below. A negative number means that the trian was early by that number of minutes. Calculate the <strong>mean</strong>, <strong>median</strong>, <strong>mode</strong> and <strong>range&nbsp;</strong>of the data.</p>\n<p>$\\var{a1}, \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}$ .</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "metadata": {"description": "<div class=\"description\">\n<p>Exam covering questions on the Errorsr part of the SOEE5154M Maths course.</p>\n<p>Topics covered are calculating the mean, median, mode and standard deviation.</p>\n<p>rebelmaths</p>\n</div>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": ["median", "mode", "rebelmaths", "sample mean", "standard deviation", "statistics"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question"}, {"name": "Averages (frequency table)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "b"], "tags": ["average", "frequency table", "REBEL", "rebel", "Rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>See \"show steps\" within this question for more help.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "1", "vsetrangepoints": 5, "prompt": "<p>What is the mean value (correct to 2 decimal places)?</p>", "expectedvariablenames": [], "checkingaccuracy": "2", "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To find the mean use the formula $\\frac{\\Sigma fx}{\\Sigma f}$</p>\n<p>In other words $\\frac{(0\\times\\var{f1})+(1\\times \\var{f2})+(2\\times\\var{f3})+(3\\times\\var{f4}) +(4\\times\\var{f5})+(5\\times\\var{f6})}{\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}+\\var{f5}+\\var{f6}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "{mn}", "marks": "4", "checkvariablenames": false, "checkingtype": "dp", "type": "jme"}, {"stepsPenalty": "1", "prompt": "<p>What is the median value?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "{median}", "minValue": "{median}", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The median is the \"middle\" value.&nbsp;</p>\n<p>In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.</p>\n<p>First add up the frequencies to find $n$.</p>\n<p>Case 1. When the sum of the frequencies is odd, then the median is the value at the $\\frac{n+1}{2}^{th}$ position.<br/>Case 2. When the sum of the frequencies is even, then the median is the average of values at the positions $\\frac{n}{2}^{th}$ and $\\frac{n+1}{2}^{th}$.</p>\n<p><br/>We need to add up the frequencies until we reach this value and then the class we land in is the median.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "<p>What is the mode? (If it is undefined, enter \"0\".)</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "1", "minValue": "1", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The mode is the number which occurs most often. In other words the class&nbsp;with the &nbsp;highest frequency.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Calculate the mean, the median and the mode for the following frequency table:</p>\n<table border=\"0.1\" style=\"border: solid;\">\n<tbody>\n<tr>\n<td>Class</td>\n<td>0</td>\n<td>1</td>\n<td>2</td>\n<td>3</td>\n<td>4</td>\n<td>5</td>\n</tr>\n<tr>\n<td>Frequency</td>\n<td>{f1}</td>\n<td>{f2}</td>\n<td>{f3}</td>\n<td>{f4}</td>\n<td>{f5}</td>\n<td>{f6}</td>\n</tr>\n</tbody>\n</table>", "variable_groups": [{"variables": ["f1", "f2", "f3", "f4", "f5", "f6"], "name": "Frequencies"}, {"variables": ["cf2", "cf3", "cf4", "cf5", "tot"], "name": "Cumulative"}, {"variables": ["a1", "a2", "a3", "a4", "a5", "mp5", "median"], "name": "Median calculations"}, {"variables": ["sfx", "mn"], "name": "Mean calculations"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f1": {"definition": "random(5..20)", "templateType": "anything", "group": "Frequencies", "name": "f1", "description": ""}, "f2": {"definition": "f1+a", "templateType": "anything", "group": "Frequencies", "name": "f2", "description": ""}, "f3": {"definition": "f1-1", "templateType": "anything", "group": "Frequencies", "name": "f3", "description": ""}, "f4": {"definition": "f1-a", "templateType": "anything", "group": "Frequencies", "name": "f4", "description": ""}, "f5": {"definition": "f1-b", "templateType": "anything", "group": "Frequencies", "name": "f5", "description": ""}, "f6": {"definition": "a", "templateType": "anything", "group": "Frequencies", "name": "f6", "description": ""}, "mp5": {"definition": "tot/2", "templateType": "anything", "group": "Median calculations", "name": "mp5", "description": ""}, "tot": {"definition": "cf5+f6", "templateType": "anything", "group": "Cumulative", "name": "tot", "description": ""}, "sfx": {"definition": "0*f1+1*f2+2*f3+3*f4+4*f5+5*f6", "templateType": "anything", "group": "Mean calculations", "name": "sfx", "description": ""}, "a1": {"definition": "switch(f1<mp5,1,f1=mp5,0.5,f1>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a1", "description": ""}, "a3": {"definition": "switch(cf3<mp5,1,cf3=mp5,0.5,cf3>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a3", "description": ""}, "a2": {"definition": "switch(cf2<mp5,1,cf2=mp5,0.5,cf2>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a2", "description": ""}, "a5": {"definition": "switch(cf5<mp5,1,cf5=mp5,0.5,cf5>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a5", "description": ""}, "a4": {"definition": "switch(cf4<mp5,1,cf4=mp5,0.5,cf4>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a4", "description": ""}, "cf4": {"definition": "cf3+f4", "templateType": "anything", "group": "Cumulative", "name": "cf4", "description": ""}, "cf5": {"definition": "cf4+f5", "templateType": "anything", "group": "Cumulative", "name": "cf5", "description": ""}, "cf2": {"definition": "f1+f2", "templateType": "anything", "group": "Cumulative", "name": "cf2", "description": ""}, "cf3": {"definition": "cf2+f3", "templateType": "anything", "group": "Cumulative", "name": "cf3", "description": ""}, "a": {"definition": "random(1..f1-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(a..f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "mn": {"definition": "sfx/tot", "templateType": "anything", "group": "Mean calculations", "name": "mn", "description": ""}, "median": {"definition": "a1+a2+a3+a4+a5", "templateType": "anything", "group": "Median calculations", "name": "median", "description": ""}}, "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Julie's copy of Mean from a frequency table", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "f", "q", "p", "s", "r", "t", "Answer", "Total", "data"], "tags": ["rebelmaths"], "advice": "<p>You need to calculate Ali's total score and then divide this by the total number of games he played.</p>\n<p>$ (\\var{a}&nbsp; \\times \\var{p}) + (\\var{b} \\times \\var{q}) + (\\var{c}&nbsp; \\times \\var{r}) + (\\var{d} \\times \\var{s}) + (\\var{f} \\times \\var {t}) = \\var{Total} $</p>\n<p>$ \\var{Total} \\div 20 =\\var{Answer} $</p>", "rulesets": {}, "parts": [{"prompt": "<p>{table ( data, [\"Score\", \"Frequency\"]) }</p>\n<p></p>\n<p>Mean Score: [[0]]</p>\n<p>Do not round your answer.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{Total}/20", "minValue": "{Total}/20", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Ali plays a computer game 20 times. In each game he gets a score between -10 and 10.</p>\n<p>His results are shown in the table below.</p>\n<p>Calculate his mean score over the 20 games.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "20 -a-b-c-d", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "q": {"definition": "random(-4..-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(-10..-5)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(5..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "t": {"definition": "random(8..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "Answer": {"definition": "Total/20", "templateType": "anything", "group": "Ungrouped variables", "name": "Answer", "description": ""}, "Total": {"definition": "a*p + b*q+c*r +d*s +f*t\n", "templateType": "anything", "group": "Ungrouped variables", "name": "Total", "description": ""}, "data": {"definition": "[ [p,a],[q,b],[r,c],[s,d],[t,f]]", "templateType": "anything", "group": "Ungrouped variables", "name": "data", "description": ""}}, "metadata": {"description": "<p>Scores (including negatives)&nbsp; in 20 games and frequency given -- calculate mean.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Julie's copy of Mean from a frequency table - classes", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "f", "q", "p", "s", "r", "t", "stdev", "Answer", "x", "Total", "data"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>$\\Sigma fx= (\\var{a}&nbsp; \\times \\var{q}) + (\\var{b} \\times \\var{p}) +( \\var{c}&nbsp; \\times \\var{s}) + (\\var{d} \\times \\var{r}) + (\\var{f} \\times \\var {t}) = \\var{Total} $</p>\n<p>mean $=\\frac{\\Sigma fx}{\\Sigma f}= \\var{Total} \\div 20 =\\var{Answer} $</p>", "rulesets": {}, "parts": [{"prompt": "<p></p>\n<table border=\"1\" height=\"91\" width=\"573\">\n<tbody>\n<tr><th align=\"left\">Class ( in euro)</th><th>frequency</th></tr>\n<tr><th align=\"left\">{q-5} but less than {q+5}</th><th>{a}</th></tr>\n<tr><th align=\"left\">{p-5} but less than {p+5}</th><th>{b}</th></tr>\n<tr><th align=\"left\">{s-5} but less than {s+5}</th><th>{c}</th></tr>\n<tr><th align=\"left\">{r-5} but less than {r+5}</th><th>{d}</th></tr>\n<tr><th align=\"left\">{t-5} but less than {t+5}</th><th>{f}</th></tr>\n</tbody>\n</table>\n<p></p>\n<p>Mean: [[0]]euro (correct to 2 decimal places)</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{Total}/20", "strictPrecision": false, "minValue": "{Total}/20", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "4", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>In CITech Ltd there was a special fundraising drive among staff for ebola affected regions of Africa. A sister of one of the staff is an aid worker in Africa. The frequency table below describes the amount in euro donated by individual staff. Calculate the mean for the data.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(0..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "20 -a-b-c-d", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "q": {"definition": "x+10", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "x+20", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "x+30", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "x+40", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "t": {"definition": "x+50", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "stdev": {"definition": "sqrt((a*q^2 + b*p^2+c*s^2 +d*r^2 +f*t^2)/20- (Total/20)^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "stdev", "description": ""}, "Answer": {"definition": "Total/20", "templateType": "anything", "group": "Ungrouped variables", "name": "Answer", "description": ""}, "x": {"definition": "random(10..90#10)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "Total": {"definition": "a*q + b*p+c*s +d*r +f*t\n", "templateType": "anything", "group": "Ungrouped variables", "name": "Total", "description": ""}, "data": {"definition": "[ [p,a],[q,b],[r,c],[s,d],[t,f]]", "templateType": "anything", "group": "Ungrouped variables", "name": "data", "description": ""}}, "metadata": {"description": "<p>Scores&nbsp; in 20 games and frequency given -- calculate mean.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Mean, median, mode and range", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "tags": ["median", "mode", "rebel", "Rebel", "REBEL", "rebelmaths", "sample mean", "standard deviation", "statistics"], "advice": "<p>Mean: $\\mu = \\frac{1}{N}\\sum\\limits_{i=1}^N x_i$</p>\n<p>Median: middle value</p>\n<p>Mode: most common value</p>\n<p>Range: highest value - lowest value.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": "1", "prompt": "\n      <p>$\\text{mean}=\\;\\;$[[0]]</p>\n        <p>Enter decimal answers to 3 decimal places.</p>\n      ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.01, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "marks": 3, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "<p>To find the mean:</p>\n<p>1. Add up all the numbers.</p>\n<p>2. Divide by the number of numbers.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\text{median}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 1, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{a4}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "<p>To find the median:</p>\n<p>List the numbers in order of increasing size.&nbsp;</p>\n<p>The median is then the middle number.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>$\\text{mode}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 1, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{a4}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "<p>The mode is the number that occurs most often.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>$\\text{range}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.01, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{a2-a3}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Seven students were asked how they rated the online maths assessment tool numbas on a scale of 0-10, with 0 representing terrible and 10 representing excellent. The results are below. Calculate the <strong>mean</strong>, <strong>median</strong>, <strong>mode</strong> and <strong>range </strong>for the set of data.</p>\n<p>$\\var{a1}, \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}$ .</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a1": {"definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(0..1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(9..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(4..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(6..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a7": {"definition": "a4", "templateType": "anything", "group": "Ungrouped variables", "name": "a7", "description": ""}, "a6": {"definition": "random(7..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}}, "metadata": {"description": "<div class=\"description\">\n<p>Exam covering questions on the Errorsr part of the SOEE5154M Maths course.</p>\n<p>Topics covered are calculating the mean, median, mode and standard deviation.</p>\n<p>rebelmaths</p>\n</div>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Mean missing data", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "variables": {"f": {"name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..9)"}, "tot": {"name": "tot", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "a+b+c+d"}, "g": {"name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "5*mean"}, "d": {"name": "d", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..9)"}, "b": {"name": "b", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(1..9#1)"}, "c": {"name": "c", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(1..9#1)"}, "mean": {"name": "mean", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(a+b+c+d+f)/5"}, "a": {"name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..9)"}}, "advice": "<p>$\\frac{\\var{a}+\\var{b}+\\var{c}+\\var{d}+x}{5}=\\var{mean}$,</p>\n<p>$\\var{a}+\\var{b}+\\var{c}+\\var{d}+x=5\\times\\var{mean}$,</p>\n<p></p>\n<p>$\\var{tot}+x=\\var{g}$,</p>\n<p>$x=\\var{g}-\\var{tot}$</p>\n<p>$x=\\var{f}$</p>\n<p></p>", "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f", "mean", "g", "tot"], "tags": ["mean", "Rebel", "REBEL", "rebel", "rebelmaths"], "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"type": "gapfill", "showFeedbackIcon": true, "steps": [{"type": "information", "showFeedbackIcon": true, "marks": 0, "prompt": "<p>To find the mean of a set of numbers add them together and divide by the number of numbers.</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}}], "marks": 0, "stepsPenalty": "1", "prompt": "<p>The mean of $\\var{a}, \\var{b}, \\var{c}, \\var{d}$ and $x$ is $\\var{mean}$, find the value of $x$.</p>\n<p>$x=$[[0]]</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"allowFractions": false, "minValue": "{f}", "correctAnswerStyle": "plain", "marks": 1, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "scripts": {}, "maxValue": "{f}", "type": "numberentry", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}], "showCorrectAnswer": true, "scripts": {}}], "statement": "<p>Find the value of x given information about the mean</p>", "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "type": "question"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "preventifunattempted", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "allowAttemptDownload": true, "downloadEncryptionKey": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>This homework will be looking at measures of central tendancy (mean, mode, median) and range. This shouldn't be tricky but let me know if you are having a problem with a certain question. Please ensure that you write all notes on lined paper, with your name on and give them to me at our next lesson.</p>", "end_message": "<p>Thank you for doing this. 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