// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Relative Percentage Frequency", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "variables": {"norm1": {"description": "", "templateType": "anything", "name": "norm1", "definition": "map(round(x),x,list((y/sum(freqdays))*vector(freqdays)))", "group": "Ungrouped variables"}, "freqdays1": {"description": "", "templateType": "anything", "name": "freqdays1", "definition": "sort(repeat(random(2..50),n1))", "group": "Ungrouped variables"}, "what": {"description": "", "templateType": "anything", "name": "what", "definition": "'daily sales'", "group": "Ungrouped variables"}, "m": {"description": "", "templateType": "anything", "name": "m", "definition": "max(freqdays1)", "group": "Ungrouped variables"}, "freqdays": {"description": "", "templateType": "anything", "name": "freqdays", "definition": "freqdays1+freqdays2", "group": "Ungrouped variables"}, "n1": {"description": "", "templateType": "anything", "name": "n1", "definition": "4", "group": "Ungrouped variables"}, "r": {"description": "", "templateType": "anything", "name": "r", "definition": "random(0..5)", "group": "Ungrouped variables"}, "daysopen": {"description": "", "templateType": "anything", "name": "daysopen", "definition": "sum(norm1)", "group": "Ungrouped variables"}, "rel": {"description": "", "templateType": "anything", "name": "rel", "definition": "map(precround(100*norm1[x]/daysopen,1),x,0..2*n1-2)", "group": "Ungrouped variables"}, "freqdays2": {"description": "", "templateType": "anything", "name": "freqdays2", "definition": "revsort(repeat(random(2..m-1),n1-1))", "group": "Ungrouped variables"}, "a": {"description": "", "templateType": "anything", "name": "a", "definition": "map(s*x,x,0..7)", "group": "Ungrouped variables"}, "things": {"description": "", "templateType": "anything", "name": "things", "definition": "'Sales'", "group": "Ungrouped variables"}, "num": {"description": "", "templateType": "anything", "name": "num", "definition": "'Number of days'", "group": "Ungrouped variables"}, "y": {"description": "", "templateType": "anything", "name": "y", "definition": "random(300..320)", "group": "Ungrouped variables"}, "forwhat": {"description": "", "templateType": "anything", "name": "forwhat", "definition": "'for a large retailer in '+random(2010,2011,2012)", "group": "Ungrouped variables"}, "units": {"description": "", "templateType": "anything", "name": "units", "definition": "'in thousands of pounds'", "group": "Ungrouped variables"}, "s": {"description": "", "templateType": "anything", "name": "s", "definition": "random(5..15#5)", "group": "Ungrouped variables"}}, "statement": "\n  <p>The following table shows {what}, $X$, {units} {forwhat}.</p>\n  <p>Calculate the relative percentage frequencies (to one decimal place for all).</p>\n  ", "parts": [{"gaps": [{"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[0]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[0]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[1]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[1]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[2]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[2]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[3]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[3]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[4]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[4]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[5]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[5]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "maxValue": "rel[6]", "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "correctAnswerFraction": false, "minValue": "rel[6]", "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "numberentry", "marks": 1, "showFeedbackIcon": true}], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "showCorrectAnswer": true, "variableReplacements": [], "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "prompt": "<p></p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">{things}</th>\n<td>{num}</td>\n<td>Relative Percentages</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[0]}\\le X \\lt \\var{a[1]}$</th>\n<td>$\\var{norm1[0]}$</td>\n<td>[[0]]</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[1]}\\le X \\lt \\var{a[2]}$</th>\n<td>$\\var{norm1[1]}$</td>\n<td>[[1]]</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[2]}\\le X \\lt \\var{a[3]}$</th>\n<td>$\\var{norm1[2]}$</td>\n<td>[[2]]</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[3]}\\le X \\lt \\var{a[4]}$</th>\n<td>$\\var{norm1[3]}$</td>\n<td>[[3]]</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[4]}\\le X \\lt \\var{a[5]}$</th>\n<td>$\\var{norm1[4]}$</td>\n<td>[[4]]</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[5]}\\le X \\lt \\var{a[6]}$</th>\n<td>$\\var{norm1[5]}$</td>\n<td>[[5]]</td>\n</tr>\n<tr>\n<th align=\"left\">$\\var{a[6]}\\le X \\lt \\var{a[7]}$</th>\n<td>$\\var{norm1[6]}$</td>\n<td>[[6]]</td>\n</tr>\n</tbody>\n</table>", "unitTests": [], "type": "gapfill", "marks": 0, "showFeedbackIcon": true}], "variable_groups": [], "rulesets": {}, "metadata": {"description": "<p>Given a table of the number of days in which sales were between &pound;x1000 and &pound;(x+1)1000 find the relative percentage frequencies of these volume of sales.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {"revsort": {"type": "list", "language": "jme", "definition": "list(-1*vector(sort(list(-1*vector(a)))))", "parameters": [["a", "list"]]}}, "ungrouped_variables": ["a", "what", "freqdays", "daysopen", "things", "m", "forwhat", "units", "s", "num", "rel", "n1", "y", "freqdays1", "freqdays2", "r", "norm1"], "advice": "<p>By summing the 'number of days' column we note that there were&nbsp;$\\var{daysopen}$&nbsp;days &nbsp;in the year when sales took place.&nbsp;</p>\n<p>So to work out the relative percentage for a given sales interval, we must calculate $\\frac{\\text{number of days}}{\\var{daysopen}}\\times 100$</p>\n<p></p>\n<p></p>\n<p>E.g. for the interval&nbsp;$\\var{a[0]}\\le X \\lt \\var{a[1]}$:</p>\n<p>There were $\\var{norm1[0]}$ days out of the&nbsp;&nbsp;$\\var{daysopen}$ when&nbsp;there were between $\\var{a[0]}$&nbsp;and&nbsp;$\\var{a[1]}$ thousand pounds worth of&nbsp;sales (including &nbsp;$\\var{a[0]}$ thousand&nbsp;but not&nbsp;$\\var{a[1]}$ thousand) .</p>\n<p>Hence the relative frequency percentage for such sales is given by \\[100 \\times \\frac{\\var{norm1[0]}}{\\var{daysopen}}\\%=\\var{rel[0]}\\%\\]&nbsp;to one decimal place.</p>\n<p>&nbsp;</p>", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": ["stats"], "name": "Simon's copy of Relative Percentage Frequency", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}