// Numbas version: exam_results_page_options
{"name": "Numerical reasoning - average salary", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"commanumber": {"definition": "var parts=n.toString().split(\".\");\n        if(parts[1] && parts[1].length<2) {\n      parts[1]+='0';\n        }\n        return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");", "type": "string", "language": "javascript", "parameters": [["n", "number"]]}}, "name": "Numerical reasoning - average salary", "tags": ["average", "maths-aid", "mean", "money", "numerical reasoning", "percentage", "weighted"], "advice": "<p>This is a weighted average.</p>\n    <p>The average value is given by multiplying each salary value by the frequency with which it occurs amongst the staff (in fraction form), and adding the resulting numbers together.</p>\n    <p>For example, the salary &pound;{commanumber(salary[0])} has a frequency of {per[0]}% which is $\\frac{\\var{per[0]}}{100} = \\var{per[0]/100}$. When we multiply these together we get \\[ &pound;\\var{latex(commanumber(salary[0]))} \\times \\frac{\\var{per[0]}}{100} = \\var{salary[0]*per[0]/100}. \\]</p>\n    <p>For this question we have 4 salary values and the weighted average is \\[\\begin{align} &amp; \\frac{\\var{per[0]}}{100} \\times \\var{latex(commanumber(salary[0]))} + \\frac{\\var{per[1]}}{100} \\times \\var{latex(commanumber(salary[1]))} + \\frac{\\var{per[2]}}{100} \\times \\var{latex(commanumber(salary[2]))} + \\frac{\\var{per[3]}}{100} \\times \\var{latex(commanumber(salary[3]))} \\\\ &amp;= &pound;\\var{latex(commanumber(salary[0]*per[0]/100))} +&nbsp;&pound;\\var{latex(commanumber(salary[1]*per[1]/100))} + &pound;\\var{latex(commanumber(salary[2]*per[2]/100))} + &pound;\\var{latex(commanumber(salary[3]*per[3]/100))} \\\\ &amp;= &pound;\\var{latex(commanumber(average))} \\end{align} \\]</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the average salary?</p>\n        <p>&pound; [[0]]</p>", "gaps": [{"minvalue": "average", "type": "numberentry", "maxvalue": "average", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<p>In a department {per[0]}% of the staff have a salary of &pound;{commanumber(salary[0])}, {per[1]}% a salary of &pound;{commanumber(salary[1])}, {per[2]}% a salary of &pound;{commanumber(salary[2])}, and {per[3]}% a salary of &pound;{commanumber(salary[3])}.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"salary": {"definition": "shuffle([salary0,salary1,salary2,salary3])", "name": "salary"}, "salary1": {"definition": "random(15000..50000#5000 except salary0)", "name": "salary1"}, "salary0": {"definition": "random(15000..50000#5000)", "name": "salary0"}, "salary3": {"definition": "random(15000..50000#5000 except [salary0,salary1,salary2])", "name": "salary3"}, "salary2": {"definition": "random(15000..50000#5000 except [salary0,salary1])", "name": "salary2"}, "average": {"definition": "(per[0]*salary[0]+per[1]*salary[1]+per[2]*salary[2]+per[3]*salary[3])/100", "name": "average"}, "per": {"definition": "shuffle([per0,per1,per2,per3])", "name": "per"}, "per3": {"definition": "100-per0-per1-per2", "name": "per3"}, "per2": {"definition": "random(10..min(50,90-per0-per1)#10)", "name": "per2"}, "per1": {"definition": "random(10..min(50,80-per0)#10)", "name": "per1"}, "per0": {"definition": "random(10..50#10)", "name": "per0"}}, "metadata": {"notes": "", "description": "<p>Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}