// Numbas version: exam_results_page_options
{"name": "Descriptive Stats (P): find sample mean, range and variance", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["Mon", "Tues", "Wed", "Thurs", "Fri", "Sat", "Sun", "data", "range", "variance", "mean"], "name": "Descriptive Stats (P): find sample mean, range and variance", "tags": [], "advice": "<h4>a)</h4>\n<p>The&nbsp;<em>mean</em>&nbsp;of a set of data is the sum of the data, divided by the number of values in the set. In this case, the mean is</p>\n<p>\\[ \\simplify[]{({mon}+{tues}+{wed}+{thurs}+{fri}+{sat}+{sun})/7} = \\var{precround(mean,2)} \\text{ (to 2 d.p.)}\\]</p>\n<h4>b)</h4>\n<p>The&nbsp;<em>range</em> of a set of data is the difference between the greatest and least values in the set. In this case, the range is</p>\n<p>\\[&nbsp;\\simplify[]{{max(data)}-{min(data)} = {range}} \\]</p>\n<h4>c)</h4>\n<p>The variance of a sample&nbsp;$x_1,x_2, \\dots, x_n$ is&nbsp;given by the following formula:</p>\n<p>\\[ \\text{Variance} = \\sum \\frac{(x_i-\\mu)^2}{n}\\]</p>\n<p>{table([['\\$x_i\\$']+data,['\\$x_i-\\\\mu\\$']+map(x-mean,x,data),['\\$(x_i-\\\\mu)^2\\$']+map((x-mean)^2,x,data)],[])}</p>\n<p>Now,</p>\n<p>\\[ \\text{Variance} = \\frac{1}{7} \\sum (x_i-\\mu)^2 = \\var{precround(variance,2)} \\text{ (to 2 d.p.)} \\]</p>", "rulesets": {}, "parts": [{"prompt": "<p>Mean: [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "mean", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "mean", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Range:&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "range", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "range", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Variance: [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "variance", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "90", "scripts": {}, "marks": 1, "minValue": "variance", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Joe makes a variable number of visits to the toilet&nbsp;each day. He recorded his activities as follows:</p>\n<p>{table([data],['Monday','Tuesday','Wednesday','Thursday','Friday','Saturday','Sunday'])}</p>\n<p>Compute the following descriptive statistics of the data. Round&nbsp;your answers to <strong>2 decimal places</strong>.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"Wed": {"definition": "random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Wed", "description": ""}, "Sun": {"definition": "random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Sun", "description": ""}, "Fri": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "Fri", "description": ""}, "Thurs": {"definition": "random(1..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Thurs", "description": ""}, "Tues": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "Tues", "description": ""}, "range": {"definition": "max(data)-min(data)", "templateType": "anything", "group": "Ungrouped variables", "name": "range", "description": ""}, "Mon": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "Mon", "description": ""}, "variance": {"definition": "variance(data)", "templateType": "anything", "group": "Ungrouped variables", "name": "variance", "description": ""}, "Sat": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "Sat", "description": ""}, "data": {"definition": "[mon,tues,wed,thurs,fri,sat,sun]", "templateType": "anything", "group": "Ungrouped variables", "name": "data", "description": ""}, "mean": {"definition": "mean(data)", "templateType": "anything", "group": "Ungrouped variables", "name": "mean", "description": ""}}, "metadata": {"notes": "", "description": "<p>Calculate the mean, range, and variance of a small sample.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "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/"}, {"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}