// Numbas version: finer_feedback_settings
{"name": "BS1.3", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"revsort": {"definition": "list(-1*vector(sort(list(-1*vector(a)))))", "type": "list", "language": "jme", "parameters": [["a", "list"]]}}, "name": "BS1.3", "tags": ["frequencies", "percentages", "relative percentage frequencies", "statistics"], "advice": "\n  <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>\n  ", "rulesets": {}, "parts": [{"prompt": "\n       <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>\n      ", "gaps": [{"minvalue": "rel[0]", "type": "numberentry", "maxvalue": "rel[0]", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "rel[1]", "type": "numberentry", "maxvalue": "rel[1]", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "rel[2]", "type": "numberentry", "maxvalue": "rel[2]", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "rel[3]", "type": "numberentry", "maxvalue": "rel[3]", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "rel[4]", "type": "numberentry", "maxvalue": "rel[4]", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "rel[5]", "type": "numberentry", "maxvalue": "rel[5]", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "rel[6]", "type": "numberentry", "maxvalue": "rel[6]", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "extensions": ["stats"], "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  ", "variable_groups": [], "progress": "testing", "type": "question", "variables": {"a": {"definition": "map(s*x,x,0..7)", "name": "a"}, "what": {"definition": "'daily sales'", "name": "what"}, "freqdays": {"definition": "freqdays1+freqdays2", "name": "freqdays"}, "daysopen": {"definition": "sum(norm1)", "name": "daysopen"}, "things": {"definition": "'Sales'", "name": "things"}, "m": {"definition": "max(freqdays1)", "name": "m"}, "forwhat": {"definition": "'for a large retailer in '+random(2010,2011,2012)", "name": "forwhat"}, "units": {"definition": "'in thousands of pounds'", "name": "units"}, "s": {"definition": "random(5..15#5)", "name": "s"}, "num": {"definition": "'Number of days'", "name": "num"}, "rel": {"definition": "map(precround(100*norm1[x]/daysopen,1),x,0..2*n1-2)", "name": "rel"}, "n1": {"definition": 4.0, "name": "n1"}, "y": {"definition": "random(300..320)", "name": "y"}, "freqdays1": {"definition": "sort(repeat(random(2..50),n1))", "name": "freqdays1"}, "freqdays2": {"definition": "revsort(repeat(random(2..m-1),n1-1))", "name": "freqdays2"}, "r": {"definition": "random(0..5)", "name": "r"}, "norm1": {"definition": "map(round(x),x,list((y/sum(freqdays))*vector(freqdays)))", "name": "norm1"}}, "metadata": {"notes": "", "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>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}