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{"name": "Calculate relative percentage frequencies from table of data", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"daysopen": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sum(norm1)", "description": "", "name": "daysopen"}, "freqdays2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "revsort(repeat(random(2..m-1),n1-1))", "description": "", "name": "freqdays2"}, "things": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'Sales'", "description": "", "name": "things"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "max(freqdays1)", "description": "", "name": "m"}, "n1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "4", "description": "", "name": "n1"}, "forwhat": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'for a large retailer in '+random(2010,2011,2012)", "description": "", "name": "forwhat"}, "units": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'in thousands of pounds'", "description": "", "name": "units"}, "r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "name": "r"}, "what": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'daily sales'", "description": "", "name": "what"}, "freqdays": {"templateType": "anything", "group": "Ungrouped variables", "definition": "freqdays1+freqdays2", "description": "", "name": "freqdays"}, "s": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..15#5)", "description": "", "name": "s"}, "num": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'Number of days'", "description": "", "name": "num"}, "norm1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(round(x),x,list((y/sum(freqdays))*vector(freqdays)))", "description": "", "name": "norm1"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(s*x,x,0..7)", "description": "", "name": "a"}, "rel": {"templateType": "anything", "group": "Ungrouped variables", "definition": "map(precround(100*norm1[x]/daysopen,1),x,0..2*n1-2)", "description": "", "name": "rel"}, "y": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(300..320)", "description": "", "name": "y"}, "freqdays1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sort(repeat(random(2..50),n1))", "description": "", "name": "freqdays1"}}, "ungrouped_variables": ["a", "what", "freqdays", "daysopen", "things", "m", "forwhat", "y", "s", "num", "rel", "freqdays1", "units", "n1", "freqdays2", "r", "norm1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Calculate relative percentage frequencies from table of data", "functions": {"revsort": {"type": "list", "language": "jme", "definition": "list(-1*vector(sort(list(-1*vector(a)))))", "parameters": [["a", "list"]]}}, "variable_groups": [], "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[0]", "minValue": "rel[0]", "showCorrectAnswer": true, "marks": 1}, {"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[1]", "minValue": "rel[1]", "showCorrectAnswer": true, "marks": 1}, {"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[2]", "minValue": "rel[2]", "showCorrectAnswer": true, "marks": 1}, {"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[3]", "minValue": "rel[3]", "showCorrectAnswer": true, "marks": 1}, {"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[4]", "minValue": "rel[4]", "showCorrectAnswer": true, "marks": 1}, {"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[5]", "minValue": "rel[5]", "showCorrectAnswer": true, "marks": 1}, {"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "rel[6]", "minValue": "rel[6]", "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "prompt": " <table border=\"1\">\n        <tbody>\n        <th>{things}</th> <th>{num}</th> <th>Relative Percentages</th>\n        <tr><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><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><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><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><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><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><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>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>The following table shows {what}, $X$, {units} {forwhat}.</p>\n  <p>Calculate the relative percentage frequencies (to one decimal place for all).</p>", "tags": ["checked2015", "MAS1403"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "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>"}, "advice": "<p>We show how to calculate the relative percentage frequency for one range of values for &nbsp;$\\var{a[r]} \\le X \\lt \\var{a[r+1]}$ &nbsp; &nbsp;- you can then check the rest.</p>\n  <p>Note that there were&nbsp;$\\var{daysopen}$&nbsp;days &nbsp;in the year when sales took place.&nbsp;</p>\n  <p>There were $\\var{norm1[r]}$ days out of the&nbsp;&nbsp;$\\var{daysopen}$ when&nbsp;there were between $\\var{a[r]}$&nbsp;and&nbsp;$\\var{a[r+1]}$ thousand pounds worth of&nbsp;sales (including &nbsp;$\\var{a[r]}$ thousand&nbsp;but not&nbsp;$\\var{a[r+1]}$ thousand) .</p>\n  <p>Hence the relative frequency percentage for such sales is given by \\[100 \\times \\frac{\\var{norm1[r]}}{\\var{daysopen}}\\%=\\var{rel[r]}\\%\\]&nbsp;to one decimal place.</p>\n  <p>&nbsp;</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}