// Numbas version: finer_feedback_settings
{"name": "STAT6013 Descriptive Statistics", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "Catherine's copy of SOEE5154 - Mean, median, mode ", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "tags": [], "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "functions": {}, "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>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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.</p>\n<p>rebelmaths</p>\n</div>"}, "variable_groups": [], "variables": {"a4": {"definition": "random(1..3)", "templateType": "anything", "name": "a4", "group": "Ungrouped variables", "description": ""}, "a2": {"definition": "random(7..8)", "templateType": "anything", "name": "a2", "group": "Ungrouped variables", "description": ""}, "a6": {"definition": "random(4..6)", "templateType": "anything", "name": "a6", "group": "Ungrouped variables", "description": ""}, "a7": {"definition": "a4", "templateType": "anything", "name": "a7", "group": "Ungrouped variables", "description": ""}, "a5": {"definition": "random(-4..-3)", "templateType": "anything", "name": "a5", "group": "Ungrouped variables", "description": ""}, "a3": {"definition": "random(-6..-5)", "templateType": "anything", "name": "a3", "group": "Ungrouped variables", "description": ""}, "a1": {"definition": "random(-2..-1)", "templateType": "anything", "name": "a1", "group": "Ungrouped variables", "description": ""}}, "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>", "parts": [{"gaps": [{"precisionPartialCredit": "0", "allowFractions": false, "maxValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionType": "dp", "minValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "showPrecisionHint": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "precision": "1", "type": "numberentry", "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "precisionMessage": "You have not given your answer to the correct precision.", "marks": "1"}], "type": "gapfill", "scripts": {}, "prompt": "<p>$\\text{mean}=\\;\\;$[[0]]</p>\n<p>Enter decimal answers to 1 decimal places.</p>", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0}, {"gaps": [{"allowFractions": false, "maxValue": "{a4}", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "minValue": "{a4}", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "mustBeReducedPC": 0, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "marks": 2}], "type": "gapfill", "scripts": {}, "prompt": "<p>$\\text{median}=\\;\\;$[[0]]</p>", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0}, {"gaps": [{"allowFractions": false, "maxValue": "{a4}", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "minValue": "{a4}", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "scripts": {}, "mustBeReducedPC": 0, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReduced": false, "marks": 2}], "type": "gapfill", "scripts": {}, "prompt": "<p>$\\text{mode}=\\;\\;$[[0]]</p>", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0}, {"gaps": [{"expectedvariablenames": [], "answersimplification": "std", "variableReplacements": [], "showCorrectAnswer": true, "checkvariablenames": false, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "answer": "{a2-a3}", "checkingtype": "absdiff", "showpreview": true, "scripts": {}, "showFeedbackIcon": true, "type": "jme", "checkingaccuracy": 0.01, "vsetrange": [0, 1], "marks": 2}], "type": "gapfill", "scripts": {}, "prompt": "<p>$\\text{range}=\\;\\;$[[0]]</p>", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0}], "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Mean from a frequency table (all positive values)", "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": [], "preamble": {"css": "", "js": ""}, "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 0 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": ""}, "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(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(0..1)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(6..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(4..5)", "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": {"notes": "", "description": "<p>Scores in 20 games and frequency given -- calculate mean.</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": "Julie's copy of Mean Value 3", "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": {}, "tags": [], "type": "question", "advice": "<p>To find the mean:</p>\n<p>Add up all the values. Then divide by the number of values.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\var{x1},\\var{x2},\\var{x3},\\var{x4},\\var{x5}$</p>", "marks": "2", "maxValue": "meanx", "minValue": "meanx", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\var{y1},\\var{y2},\\var{y3},\\var{y4}$</p>", "marks": "2", "maxValue": "meany", "minValue": "meany", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Find the mean each of the following arrays of numbers:&nbsp;</p>", "variable_groups": [{"variables": ["y1", "y2", "y3", "y4", "meany"], "name": "Part a"}, {"variables": ["x1", "x2", "x3", "x4", "x5", "meanx"], "name": "Part b"}], "progress": "in-progress", "preamble": {"css": "", "js": ""}, "variables": {"y2": {"definition": "random(1..199 except y1)", "templateType": "anything", "group": "Part a", "name": "y2", "description": ""}, "meanx": {"definition": "(x1+x2+x3+x4+x5)/5", "templateType": "anything", "group": "Part b", "name": "meanx", "description": ""}, "meany": {"definition": "(y1+y2+y3+y4)/4", "templateType": "anything", "group": "Part a", "name": "meany", "description": ""}, "y1": {"definition": "random(1..199)", "templateType": "anything", "group": "Part a", "name": "y1", "description": ""}, "x2": {"definition": "random(4..99 except x1)", "templateType": "anything", "group": "Part b", "name": "x2", "description": ""}, "x3": {"definition": "random(4..99 except x1 except x2)", "templateType": "anything", "group": "Part b", "name": "x3", "description": ""}, "y3": {"definition": "random(1..199 except y1 except y2)", "templateType": "anything", "group": "Part a", "name": "y3", "description": ""}, "x1": {"definition": "random(4..99)", "templateType": "anything", "group": "Part b", "name": "x1", "description": ""}, "y4": {"definition": "random(1..199 except y1 except y2 except y3)", "templateType": "anything", "group": "Part a", "name": "y4", "description": ""}, "x4": {"definition": "random(4..99 except x1 except x2 except x3)", "templateType": "anything", "group": "Part b", "name": "x4", "description": ""}, "x5": {"definition": "random(4..99 except x1 except x2 except x3 except x4)", "templateType": "anything", "group": "Part b", "name": "x5", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "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, Median, Mode and Standard Deviation 2", "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", "sample mean", "standard deviation", "statistics"], "preamble": {"css": "", "js": ""}, "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>Standard deviation: $\\sigma = \\sqrt{ \\frac{\\sum_{i=1}^N (x_i-\\mu)^2}{N}}$</p>", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p>$\\text{mean}=\\;\\;$[[0]] (correct to two decimal places)</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "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"}, {"prompt": "<p>$\\text{median}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "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"}, {"prompt": "<p>$\\text{mode}=\\;\\;$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "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"}, {"prompt": "<p>$\\text{standard deviation}=\\;\\;$[[0]] (correct to two decimal places)</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.01, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{precround(sqrt(1/7*(a1^2+a2^2+a3^2+a4^2+a5^2+a6^2+a7^2)-(1/7(a1+a2+a3+a4+a5+a6+a7))^2),2)}", "marks": "6", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Seven inter-county gaa players who are also students in CIT were each asked how many times they have been to the library in CIT this semester. Their answers were as follows:</p>\n<p>$\\var{a2}, \\var{a7}, \\var{a1}, \\var{a5}, \\var{a3}, \\var{a6}, \\var{a4}$ .</p>\n<p>Calculate the mean, median, mode and standard deviation.<br/><br/></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "a2", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(7..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(20..30 except a6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(13..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a7": {"definition": "random(31..35)", "templateType": "anything", "group": "Ungrouped variables", "name": "a7", "description": ""}, "a6": {"definition": "random(20..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}}, "metadata": {"notes": "<p><strong>&nbsp;</strong></p>", "description": "<div class=\"description\">\n<p>Topics covered are calculating the mean, median, mode and standard deviation.</p>\n</div>", "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": "Julie's copy of Cumulative frequency distribution - no relative.", "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", "regression", "residual value", "sc", "statistics"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Calculate the cumulative frequecy distribution.</p>\n<table border=\"1\" height=\"91\" width=\"573\">\n<tbody>\n<tr><th align=\"left\">x</th><th>Cumulative Frequency Distribution</th></tr>\n<tr><th align=\"left\">Less than 50</th>\n<td style=\"text-align: center;\">[[0]]</td>\n</tr>\n<tr><th align=\"left\">Less than 60</th>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n<tr><th align=\"left\">Less than 70</th>\n<td style=\"text-align: center;\">[[2]]</td>\n</tr>\n<tr><th align=\"left\">Less than 80</th>\n<td style=\"text-align: center;\">[[3]]</td>\n</tr>\n<tr><th align=\"left\">Less than 90</th>\n<td style=\"text-align: center;\">[[4]]</td>\n</tr>\n<tr><th align=\"left\">Less than 100</th>\n<td style=\"text-align: center;\">[[5]]</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": [], "precision": 0, "maxValue": "{a}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": "0.5", "minValue": "{a}", "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}, {"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}, {"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}, {"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}, {"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}], "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": {"notes": "", "description": "<p>Cumulative Frequency Distribution</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Mean from a frequency table - classes of different width", "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": [], "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-15} but less than {q+15}</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-25} but less than {t+25}</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": [], "precision": "2", "maxValue": "{Total}/20", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": "6", "minValue": "{Total}/20", "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", "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+70", "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(20..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": {"notes": "", "description": "<p>Scores&nbsp; in 20 games and frequency given -- calculate mean.</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": "Histogram (equal class width)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}], "tags": [], "metadata": {"description": "<p>Create random histogram using geogebra</p>", "licence": "None specified"}, "statement": "<p>The histogram below&nbsp;gives information about $\\var{description[index]}$</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/U3emHUxY',[['B',B],['H',H]])}</p>\n<h3></h3>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"min_b": {"name": "min_b", "group": "Ungrouped variables", "definition": "0", "description": "<p>minimum class boundary</p>", "templateType": "anything", "can_override": false}, "value": {"name": "value", "group": "Ungrouped variables", "definition": "B[index2]", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "list(min_b..max_b#class_width)", "description": "", "templateType": "anything", "can_override": false}, "max_b": {"name": "max_b", "group": "Ungrouped variables", "definition": "min_b+n_classes*class_width", "description": "<p>maximum class boundary</p>", "templateType": "anything", "can_override": false}, "text1": {"name": "text1", "group": "Ungrouped variables", "definition": "[\"customers spent less than\", \"passengers waited less than\"]", "description": "", "templateType": "anything", "can_override": false}, "Total": {"name": "Total", "group": "Ungrouped variables", "definition": "sum(Hvector)", "description": "", "templateType": "anything", "can_override": false}, "relfreq": {"name": "relfreq", "group": "Ungrouped variables", "definition": "Hvector/Total", "description": "", "templateType": "anything", "can_override": false}, "TableHeading": {"name": "TableHeading", "group": "Ungrouped variables", "definition": "['Time in minutes', 'Value of transaction (\u20ac)']", "description": "", "templateType": "anything", "can_override": false}, "ChosenTableHeading": {"name": "ChosenTableHeading", "group": "Ungrouped variables", "definition": "TableHeading[index]", "description": "", "templateType": "anything", "can_override": false}, "Bvector": {"name": "Bvector", "group": "Ungrouped variables", "definition": "vector(B)", "description": "", "templateType": "anything", "can_override": false}, "class_width": {"name": "class_width", "group": "Ungrouped variables", "definition": "random(1,2,3,4)", "description": "", "templateType": "anything", "can_override": false}, "H": {"name": "H", "group": "Ungrouped variables", "definition": "repeat(random(1..10#2),n_classes)", "description": "", "templateType": "anything", "can_override": false}, "index2": {"name": "index2", "group": "Ungrouped variables", "definition": "random(2,3,4,5)", "description": "", "templateType": "anything", "can_override": false}, "Hvector": {"name": "Hvector", "group": "Ungrouped variables", "definition": "vector(H)", "description": "", "templateType": "anything", "can_override": false}, "description": {"name": "description", "group": "Ungrouped variables", "definition": "['the value (in \u20ac) of transactions at a local newsagents in one day.', 'the time (in minutes) that passengers spent waiting at a bus stop for the number 5 bus.'] ", "description": "", "templateType": "anything", "can_override": false}, "text2": {"name": "text2", "group": "Ungrouped variables", "definition": "[\"euros\",\"minutes for the number 5 bus\"]", "description": "", "templateType": "anything", "can_override": false}, "chosendescription": {"name": "chosendescription", "group": "Ungrouped variables", "definition": "description[index]", "description": "", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the class width of this histogram?</p>", "minValue": "class_width", "maxValue": "class_width", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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>Derive the frequency distribution that was used to draw this histogram and fill in the relative frequency, correct to 2 decimal places.</p>\n<table border=\"1\">\n<tbody>\n<tr><th>$\\var{ChosenTableHeading}$</th><th>Frequency</th><th>Relative Frequency</th></tr>\n<tr><th align=\"left\">[[1]] but less than&nbsp;[[2]]</th>\n<td>[[8]]</td>\n<td>[[13]]</td>\n</tr>\n<tr><th align=\"left\">[[2]]&nbsp;but less than&nbsp;[[3]]</th>\n<td>[[9]]</td>\n<td>[[14]]</td>\n</tr>\n<tr><th align=\"left\">[[3]] but less than&nbsp;[[4]]</th>\n<td>[[10]]</td>\n<td>[[15]]</td>\n</tr>\n<tr><th align=\"left\">[[4]]&nbsp;but less than&nbsp;[[5]]</th>\n<td>[[11]]</td>\n<td>[[16]]</td>\n</tr>\n<tr><th align=\"left\">\n<p>[[5]] but less than&nbsp;[[6]]</p>\n</th>\n<td>[[12]]</td>\n<td>[[17]]</td>\n</tr>\n<tr><th align=\"left\">\n<p>[[6]]&nbsp;but less than&nbsp;[[7]]</p>\n</th>\n<td>[[0]]</td>\n<td>[[18]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "numberentry", 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"showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "relfreq[5]", "maxValue": "relfreq[5]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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, "prompt": "<p>What percentage of&nbsp;$\\var{text1[index]}$ $\\var{value}$ &nbsp;$\\var{text2[index]}$? Please give your answer to the nearest whole number.</p>", "minValue": "percentage", "maxValue": "percentage", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "0", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Julie's copy of Mean from a frequency table - classes 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": 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5.4pt;\n\tmso-para-margin-top:0cm;\n\tmso-para-margin-right:0cm;\n\tmso-para-margin-bottom:10.0pt;\n\tmso-para-margin-left:0cm;\n\tline-height:115%;\n\tmso-pagination:widow-orphan;\n\tfont-size:11.0pt;\n\tfont-family:\"Calibri\",\"sans-serif\";\n\tmso-ascii-font-family:Calibri;\n\tmso-ascii-theme-font:minor-latin;\n\tmso-hansi-font-family:Calibri;\n\tmso-hansi-theme-font:minor-latin;\n\tmso-fareast-language:EN-US;}\n</style>\n<![endif]--><span style=\"font-size: 15pt; font-family: 'Arial','sans-serif';\"></span>The personnel manager of CITech Ltd has analysed the ages of the company's employees. The results are shown in the table below. Calculate the mean for the data.</p>", "variable_groups": [], "progress": "in-progress", "type": "question", "variables": {"a": {"definition": "random(8..16)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "50-(a+b+d+f)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..14)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(5..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "random(0..5)", "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)/50- (Total/50)^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "stdev", "description": ""}, "Answer": {"definition": "Total/50", "templateType": "anything", "group": "Ungrouped variables", "name": "Answer", "description": ""}, "x": {"definition": "random(15..35#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": {"notes": "", "description": "<p>Scores&nbsp; in 20 games and frequency given -- calculate mean.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "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", 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