// Numbas version: exam_results_page_options
{"name": "Lois's copy of 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"]]}}, "ungrouped_variables": ["salary", "salary1", "salary0", "salary3", "salary2", "average", "per", "per3", "per2", "per1", "per0", "per0dec", "per1dec", "per2dec", "per3dec", "department"], "name": "Lois's copy of Numerical reasoning - average salary", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>We need to calculate a weighted mean.</p>\n<p>We can do this by multiplying each salary by the proportion of people who earn it and then adding these amounts.</p>\n<p>$&pound; \\var{commanumber(salary0)} \\times \\var{per0}\\% = &pound;\\var{commanumber(salary0)} \\times \\var{per0dec} =&pound;\\var{salary0*per0/100}. $</p>\n<p>$&pound; \\var{commanumber(salary1)} \\times \\var{per1}\\% = &pound;\\var{commanumber(salary1)} \\times \\var{per1dec} =&pound;\\var{salary1*per1/100}. $</p>\n<p>$&pound; \\var{commanumber(salary2)} \\times \\var{per2}\\% = &pound;\\var{commanumber(salary2)} \\times \\var{per2dec} =&pound;\\var{salary2*per2/100}. $</p>\n<p>$&pound; \\var{commanumber(salary3)} \\times \\var{per3}\\% = &pound;\\var{commanumber(salary3)} \\times \\var{per3dec} =&pound;\\var{salary3*per3/100}. $</p>\n<p></p>\n<p>If we add these we get &pound;{commanumber(average)}.</p>\n<p>(For a weighted mean we need to divide the total &nbsp;by the sum of the weights, but in this case the weights add to 1.)</p>\n<p>For more information about calculating a mean from a frequency table see the Statstutor&nbsp;leaflet at <a href=\"http://www.statstutor.ac.uk/resources/uploaded/meangroupeddata.pdf\">http://www.statstutor.ac.uk/resources/uploaded/meangroupeddata.pdf</a></p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the mean&nbsp;salary of the people working in {department}?</p>\n<p>&pound; [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "average", "minValue": "average", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>In a {department} department {per0}% of the staff have a salary of &pound;{commanumber(salary0)}, {per1}% a salary of &pound;{commanumber(salary1)}, {per2}% a salary of &pound;{commanumber(salary2)}, and {per3}% a salary of &pound;{commanumber(salary3)}.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"salary": {"definition": "shuffle([salary0,salary1,salary2,salary3])", "templateType": "anything", "group": "Ungrouped variables", "name": "salary", "description": ""}, "per1dec": {"definition": "per1/100", "templateType": "anything", "group": "Ungrouped variables", "name": "per1dec", "description": ""}, "per3dec": {"definition": "per3/100", "templateType": "anything", "group": "Ungrouped variables", "name": "per3dec", "description": ""}, "salary1": {"definition": "random(15000..50000#5000 except salary0)", "templateType": "anything", "group": "Ungrouped variables", "name": "salary1", "description": ""}, "salary0": {"definition": "random(15000..50000#5000)", "templateType": "anything", "group": "Ungrouped variables", "name": "salary0", "description": ""}, "salary3": {"definition": "random(15000..50000#5000 except [salary0,salary1,salary2])", "templateType": "anything", "group": "Ungrouped variables", "name": "salary3", "description": ""}, "salary2": {"definition": "random(15000..50000#5000 except [salary0,salary1])", "templateType": "anything", "group": "Ungrouped variables", "name": "salary2", "description": ""}, "average": {"definition": "(per0*salary0+per1*salary1+per2*salary2+per3*salary3)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "average", "description": ""}, "department": {"definition": "random( \"marketing\", \"sales\",\"advertsing\", \"accounting\")", "templateType": "anything", "group": "Ungrouped variables", "name": "department", "description": ""}, "per": {"definition": "shuffle([per0,per1,per2,per3])", "templateType": "anything", "group": "Ungrouped variables", "name": "per", "description": ""}, "per3": {"definition": "100-per0-per1-per2", "templateType": "anything", "group": "Ungrouped variables", "name": "per3", "description": ""}, "per2": {"definition": "random(10..min(50,90-per0-per1)#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "per2", "description": ""}, "per1": {"definition": "random(10..min(50,80-per0)#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "per1", "description": ""}, "per0": {"definition": "random(10..50#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "per0", "description": ""}, "per0dec": {"definition": "per0/100\n", "templateType": "anything", "group": "Ungrouped variables", "name": "per0dec", "description": ""}, "per2dec": {"definition": "per2/100", "templateType": "anything", "group": "Ungrouped variables", "name": "per2dec", "description": ""}}, "metadata": {"description": "<p>Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.</p>\n<p>(Added to calculator test.)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}