// Numbas version: finer_feedback_settings
{"name": "Descriptive Statistics", "metadata": {"description": "<p>Basic descriptive statistics - measures of centre and spread, from a list of data and frequency tables.</p>", "licence": "None specified"}, "duration": 3600, "percentPass": "90", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": "8", "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": "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": "Standard deviation of a list of numbers with hints", "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/"}], "variables": {"var": {"name": "var", "description": "", "definition": "sigma^2", "group": "Ungrouped variables", "templateType": "anything"}, "x": {"name": "x", "description": "", "definition": "random(4,5,8)", "group": "Ungrouped variables", "templateType": "anything"}, "sigma": {"name": "sigma", "description": "", "definition": "stdev(data)", "group": "Ungrouped variables", "templateType": "anything"}, "data": {"name": "data", "description": "", "definition": "repeat(random(1..30),x)", "group": "Ungrouped variables", "templateType": "anything"}, "mean": {"name": "mean", "description": "", "definition": "mean(data)", "group": "Ungrouped variables", "templateType": "anything"}}, "showQuestionGroupNames": false, "advice": "<p>Standard deviation = $\\sqrt{\\frac{\\Sigma (x-\\text{mean})^2}{n}}$</p>\n<p>What is the mean? Add up the numbers and divide by the number of numbers getting an answer of {mean}.</p>\n<p>Now, subtract the mean individually from each of the numbers given and square the result.&nbsp;</p>\n<p>Now add up these results. This is the '$\\Sigma (x-\\text{mean})^2$' part in the formula.<br/>Divide by {x}&nbsp;the number of values. This gives an answer of {var}.</p>\n<p>Finally, find the square root to get an answer of {sigma}.</p>", "tags": ["rebel", "Rebel", "REBEL", "rebelmaths"], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>Just showing how to use the stdev function from the stats extension&nbsp;to calculate the standard deviation of a list of numbers.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Find the Standard Deviation</p>", "type": "question", "rulesets": {}, "functions": {}, "variable_groups": [], "ungrouped_variables": ["data", "sigma", "x", "mean", "var"], "preamble": {"js": "", "css": ""}, "parts": [{"steps": [{"type": "information", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "prompt": "<p>Standard deviation = $\\sqrt{\\frac{\\Sigma (x-\\text{mean})^2}{n}}$</p>\n<p>To find the standard deviation, first find the mean of the list of numbers.&nbsp;</p>\n<p>What is the mean?</p>\n<p>Now, subtract the mean individually from each of the numbers given and square the result.&nbsp;</p>\n<p>Now add up these results. This is the '$\\Sigma (x-\\text{mean})^2$' part in the formula.<br/>Divide by $n$ where $n$ is the number of values.</p>\n<p>Finally, find the square root.</p>"}], "showCorrectAnswer": true, "precision": "1", "showPrecisionHint": false, "minValue": "{sigma}", "precisionType": "dp", "prompt": "<p>Find the standard deviation of the following list&nbsp;of numbers {data}.</p>\n<p>Give your answer correct to one decimal place.</p>", "precisionMessage": "<p>You have not given your answer to the correct number of decimal places.</p>", "stepsPenalty": "1", "type": "numberentry", "precisionPartialCredit": 0, "marks": "5", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "strictPrecision": false, "maxValue": "{sigma}", "allowFractions": false, "variableReplacements": []}], "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}]}, {"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"}, {"name": "Cumulative frequency distribution", "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": ["a", "c", "b", "d", "g", "f", "tot", "thing"], "tags": ["cr1", "data analysis", "fitted value", "Rebel", "REBEL", "rebel", "rebelmaths", "regression", "residual value", "sc", "statistics"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Calculate the cumulative frequecy distribution and the relative cumulative frequency distribution.</p>\n<table border=\"1\" height=\"91\" width=\"573\">\n<tbody>\n<tr><th align=\"left\">x</th><th>Cumulative Frequency Distribution</th><th>\n<p>Relative Cumulative Frequency Distribution</p>\n<p>Enter answer in decimal form (not percentage)</p>\n<p>(correct to 2 decimal places)</p>\n</th></tr>\n<tr><th align=\"left\">Less than 50</th>\n<td style=\"text-align: center;\">[[0]]</td>\n<td>[[1]]</td>\n</tr>\n<tr><th align=\"left\">Less than 60</th>\n<td style=\"text-align: center;\">[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr><th align=\"left\">Less than 70</th>\n<td style=\"text-align: center;\">[[4]]</td>\n<td>[[5]]</td>\n</tr>\n<tr><th align=\"left\">Less than 80</th>\n<td style=\"text-align: center;\">[[6]]</td>\n<td>[[7]]</td>\n</tr>\n<tr><th align=\"left\">Less than 90</th>\n<td style=\"text-align: center;\">[[8]]</td>\n<td>[[9]]</td>\n</tr>\n<tr><th align=\"left\">Less than 100</th>\n<td style=\"text-align: center;\">[[10]]</td>\n<td>[[11]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a}", "strictPrecision": true, "minValue": "{a}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{a}/tot", "strictPrecision": false, "minValue": "{a}/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{b}", "minValue": "{a}+{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b})/{tot}", "strictPrecision": false, "minValue": "({a}+{b})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{b}+{c}", "minValue": "{a}+{b}+{c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c})/{tot}", "strictPrecision": false, "minValue": "({a}+{b}+{c})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{b}+{c}+{d}", "minValue": "{a}+{b}+{c}+{d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d})/{tot}", "strictPrecision": false, "minValue": "({a}+{b}+{c}+{d})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d}+{f})", "minValue": "({a}+{b}+{c}+{d}+{f})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d}+{f})/{tot}", "strictPrecision": false, "minValue": "({a}+{b}+{c}+{d}+{f})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{b}+{c}+{d}+{f}+{g}", "minValue": "{a}+{b}+{c}+{d}+{f}+{g}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d}+{f}+{g})/{tot}", "strictPrecision": false, "minValue": "({a}+{b}+{c}+{d}+{f}+{g})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The table below shows the frequency distribution for {thing}.</p>\n<table height=\"91\" width=\"573\" border=\"1\">\n<tbody>\n<tr><th style=\"text-align: center;\" align=\"left\">x</th><th>f</th></tr>\n<tr><th align=\"left\">40 but less than 50</th>\n<td>{a}</td>\n</tr>\n<tr><th align=\"left\">50 but less than 60</th>\n<td>{b}</td>\n</tr>\n<tr><th align=\"left\">60 but less than 70</th>\n<td>{c}</td>\n</tr>\n<tr><th align=\"left\">70 but less than 80</th>\n<td>{d}</td>\n</tr>\n<tr><th align=\"left\">80 but less than 90</th>\n<td>{f}</td>\n</tr>\n<tr><th align=\"left\">90 but less than 100</th>\n<td>{g}</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(1..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "f", "description": ""}, "tot": {"definition": "a+b+c+d+f+g", "templateType": "anything", "group": "Ungrouped variables", "name": "tot", "description": ""}, "thing": {"definition": "random('marks achieved by first year students in an assessment', ' the number of visits to a gym in a year by first year marketing students')", "templateType": "anything", "group": "Ungrouped variables", "name": "thing", "description": ""}}, "metadata": {"description": "<p>Cumulative Frequency Distribution</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": "Cumulative frequency ", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Q11_cumlative_frequnecy_1.jpg", "/srv/numbas/media/question-resources/Q11_cumlative_frequnecy_1.jpg"], ["question-resources/Q11_cumlative_frequnecy.jpg", "/srv/numbas/media/question-resources/Q11_cumlative_frequnecy.jpg"], ["question-resources/Q11_cumlative_frequnecy_2.jpg", "/srv/numbas/media/question-resources/Q11_cumlative_frequnecy_2.jpg"]], "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": [], "tags": ["cumulative", "rebel", "REBEL", "Rebel", "rebelmaths"], "advice": "<p>Check you're using the correct axis.</p>", "rulesets": {}, "parts": [{"prompt": "<p>How many people waited less than 20 minutes?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "10", "minValue": "10", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Give an estimate for the number of people who waited between 20 and 40 minutes.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "24", "minValue": "22", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>The cumulative frequency diagram gives information about the time, in minutes, 50 people were kept waiting at hospital.</p>\n<p><img src=\"resources/question-resources/Q11_cumlative_frequnecy_2.jpg\"/></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {}, "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": "Qualitative v Quantative", "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": ["quant1", "quant2", "qual2", "cind", "qual1", "m", "ch1", "ch2", "ch3", "quant", "ind", "ind1", "qual"], "tags": ["qualitative variables", "quantitative variables", "random variables", "rebel", "Rebel", "REBEL", "rebelmaths", "statistics"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "shuffleChoices": true, "matrix": "m", "shuffleAnswers": true, "minAnswers": 0, "variableReplacements": [], "answers": ["<p>Qualitative (Categorical)</p>", "<p>Quantitative (Numerical)</p>"], "warningType": "none", "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "showCorrectAnswer": true, "scripts": {}, "marks": 0, "choices": ["{ch1}", "{ch2}", "{ch3}"], "type": "m_n_x", "displayType": "radiogroup", "minMarks": 0, "layout": {"expression": "", "type": "all"}}], "statement": "<p>State whether the following variables are Qualitative (Categorical) or Quantitative(numerical).&nbsp;</p>\n<p>Note that you will be deducted one mark for every wrong choice. However the minimum mark is 0.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"quant1": {"definition": "[\"The number of orders received by a catering company\",\"The height of students taking Statistics courses at Newcastle 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\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "quant1", "description": ""}, "quant2": {"definition": "[\"The number of people requiring a special in-flight meal\",\"The average volume of bottles of wine imported from South America\",\"Salaries of Newcastle University 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\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "quant2", "description": ""}, "qual2": {"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\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "qual2", "description": ""}, "cind": {"definition": "-1*ind1", "templateType": "anything", "group": "Ungrouped variables", "name": "cind", "description": ""}, "qual1": {"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\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "qual1", "description": ""}, "m": {"definition": "transpose(matrix(list(cind),list(ind1)))", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "ch1": {"definition": "switch(ind[0]=0,random(qual),random(quant))", "templateType": "anything", "group": "Ungrouped variables", "name": "ch1", "description": ""}, "ch2": {"definition": "switch(ind[1]=0,random(qual except ch1),random(quant except ch1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ch2", "description": ""}, "ch3": {"definition": "switch(ind[2]=0,random(qual except [ch1,ch2]),random(quant except [ch1,ch2]))", "templateType": "anything", "group": "Ungrouped variables", "name": "ch3", "description": ""}, "quant": {"definition": "quant1+quant2", "templateType": "anything", "group": "Ungrouped variables", "name": "quant", "description": ""}, "ind": {"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]])", "templateType": "anything", "group": "Ungrouped variables", "name": "ind", "description": ""}, "ind1": {"definition": "2*vector(ind)-vector(1,1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ind1", "description": ""}, "qual": {"definition": "qual1+qual2", "templateType": "anything", "group": "Ungrouped variables", "name": "qual", "description": ""}}, "metadata": {"description": "<p>Choosing whether given random variables are qualitiative or quantitative.</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": "Summation notation ", "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/"}], "tags": ["REBEL", "rebel", "Rebel", "rebelmaths", "summation"], "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The following table lists five pairs of $x$ and $f$ values.</p>\n<table height=\"91\" border=\"1\" width=\"573\">\n<tbody>\n<tr><th align=\"left\">$\\mathbf{x}$</th><th>{x1}</th><th>{x2}</th><th>{x3}</th><th>{x4}</th><th>{x5}</th></tr>\n<tr><th align=\"left\">$\\mathbf{f} $</th>\n<td>{f1}</td>\n<td>{f2}</td>\n<td>{f3}</td>\n<td>{f4}</td>\n<td>{f5}</td>\n</tr>\n</tbody>\n</table>", "advice": "", "rulesets": {}, "variables": {"f1": {"name": "f1", "group": "Ungrouped variables", "definition": "random(2 .. 20#1)", "description": "", "templateType": "randrange"}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "random(5 .. 20#1)", "description": "", "templateType": "randrange"}, "f3": {"name": "f3", "group": "Ungrouped variables", "definition": "random(5 .. 20#1)", "description": "", "templateType": "randrange"}, "f4": {"name": "f4", "group": "Ungrouped variables", "definition": "random(7 .. 10#1)", "description": "", "templateType": "randrange"}, "f5": {"name": "f5", "group": "Ungrouped variables", "definition": "random(10 .. 20#1)", "description": "", "templateType": "randrange"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(3 .. 4#1)", "description": "", "templateType": "randrange"}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "random(5 .. 6#1)", "description": "", "templateType": "randrange"}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(1 .. 2#1)", "description": "", "templateType": "randrange"}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(7 .. 8#1)", "description": "", "templateType": "randrange"}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(9 .. 10#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f1", "f2", "f3", "f4", "f5", "x2", "x3", "x1", "x4", "x5"], "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>$\\sum x = $ &nbsp;[[0]]</p>\n<p>$\\sum f = $ [[1]]</p>\n<p>$\\sum fx = $ [[2]]</p>\n<p>$\\sum fx^2 =$ [[3]]</p>", "stepsPenalty": 0, "steps": [{"type": "information", "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>$\\Sigma$ just means 'sum of' or total.</p>\n<p>For example:</p>\n<p>$\\Sigma x$ means add up the $x$ values</p>\n<p></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x1}+{x2}+{x3}+{x4}+{x5}", "maxValue": "{x1}+{x2}+{x3}+{x4}+{x5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}+{f2}+{f3}+{f4}+{f5}", "maxValue": "{f1}+{f2}+{f3}+{f4}+{f5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}*{x1}+{f2}*{x2}+{f3}*{x3}+{f4}*{x4}+{f5}*{x5}", "maxValue": "{f1}*{x1}+{f2}*{x2}+{f3}*{x3}+{f4}*{x4}+{f5}*{x5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}*{x1}^2+{f2}*{x2}^2+{f3}*{x3}^2+{f4}*{x4}^2+{f5}*{x5}^2", "maxValue": "{f1}*{x1}^2+{f2}*{x2}^2+{f3}*{x3}^2+{f4}*{x4}^2+{f5}*{x5}^2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Summation notation 2 ", "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": ["x2", "x3", "x1", "x6", "x4", "x5"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths", "summation"], "preamble": {"css": "", "js": ""}, "advice": "<p>The symbol $\\Sigma$ means 'sum of' or 'total'.</p>\n<p></p>\n<p>$\\sum y&nbsp; $ means add up the&nbsp;$y$ values.&nbsp;&nbsp;</p>\n<p>$(\\sum y)^2 &nbsp;$&nbsp; means add up the $y$ values and then square your answer. <br/><br/></p>\n<p>$\\sum y^2 &nbsp;$ means square each of the $y$ values then add them up.</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>Find</p>\n<p>$\\sum y = $ &nbsp;[[0]]</p>\n<p>$(\\sum y)^2 = $ [[1]]</p>\n<p>$\\sum y^2 = $ [[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{x1}+{x2}+{x3}+{x4}+{x5}+{x6}", "minValue": "{x1}+{x2}+{x3}+{x4}+{x5}+{x6}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "({x1}+{x2}+{x3}+{x4}+{x5}+{x6})^2", "minValue": "({x1}+{x2}+{x3}+{x4}+{x5}+{x6})^2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{x1}^2+{x2}^2+{x3}^2+{x4}^2+{x5}^2+{x6}^2", "minValue": "{x1}^2+{x2}^2+{x3}^2+{x4}^2+{x5}^2+{x6}^2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Six adults spent {x1}, {x2}, {x3}, {x4}, {x5} and {x6} euros on lottery tickets last month. Let $y$ denote last month's lottery ticket expenses for an adult.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"x2": {"definition": "random(10..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x2", "description": ""}, "x3": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x3", "description": ""}, "x1": {"definition": "random(1..30#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x1", "description": ""}, "x6": {"definition": "random(5..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x6", "description": ""}, "x4": {"definition": "random(5..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x4", "description": ""}, "x5": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x5", "description": ""}}, "metadata": {"description": "<p>Summation Notation</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": []}]}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "warn", "message": "<p>Times up</p>"}, "timedwarning": {"action": "warn", "message": "<p><span style=\"display: inline !important; float: none; background-color: transparent; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;\">5 minutes remain to complete this exam. Remember you can pause it to take a break.</span></p>"}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>You have 8 questions to complete in 60 minutes. You can pause the exam at any time and resume later. This online quiz is worth 3%.</p>\n<p>The pass mark is 90%. You can ask for hints and regenerate questions as you go. Once you reach 90% do not enter the exam again as this will reset your score to 0 and you will have to retake the quiz.&nbsp;</p>\n<p>Good luck - remember this acts as study for the final exam!</p>", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Aoife O'Brien", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1693/"}], "extensions": ["stats"], "custom_part_types": [], "resources": [["question-resources/Q11_cumlative_frequnecy_1.jpg", "/srv/numbas/media/question-resources/Q11_cumlative_frequnecy_1.jpg"], ["question-resources/Q11_cumlative_frequnecy.jpg", "/srv/numbas/media/question-resources/Q11_cumlative_frequnecy.jpg"], ["question-resources/Q11_cumlative_frequnecy_2.jpg", "/srv/numbas/media/question-resources/Q11_cumlative_frequnecy_2.jpg"]]}