// Numbas version: exam_results_page_options
{"name": "Find mean, standard deviation, median and interquartile range of sample, ", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"av": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(mean(r),2)", "description": "", "name": "av"}, "sig": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4#0.2)", "description": "", "name": "sig"}, "std": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(stdev(r,true),2)", "description": "", "name": "std"}, "these": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'specialist camera equipment'", "description": "", "name": "these"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(n=2,12,random(7,5))", "description": "", "name": "m"}, "this": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'an online warehouse' ", "description": "", "name": "this"}, "med": {"templateType": "anything", "group": "Ungrouped variables", "definition": "median(r)", "description": "", "name": "med"}, "tble1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(repeat(max(round(normalsample(me,sig)),random(4..6)),m),n)", "description": "", "name": "tble1"}, "whatever": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'number of orders per ' + period", "description": "", "name": "whatever"}, "interq": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(uquartile(r)-lquartile(r),2)", "description": "", "name": "interq"}, "shortform": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'orders'", "description": "", "name": "shortform"}, "r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "flattenint(tble1)", "description": "", "name": "r"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2,3)", "description": "", "name": "n"}, "tble": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(n=2,map(['Year '+x+':']+tble1[x-1],x,1..2),map(['Week '+ x+':']+tble1[x-1],x,1..3))", "description": "", "name": "tble"}, "units": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'over a '+ n + ' '+p+ ' period,'", "description": "", "name": "units"}, "note": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(mean(r)=av,' ','Note that we used the more accurate value $(\\\\var{mean(r)})^2$ for $\\\\bar{x}^2$.')", "description": "", "name": "note"}, "me": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(7..12)", "description": "", "name": "me"}, "p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(m=12,'year','week')", "description": "", "name": "p"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(m=12,[' ','J','F','M','A','M','J','J','A','S','O','N','D'],m=5,[' ','M','T','W','T','F'],[' ','M','T','W','T','F','S','S'])", "description": "", "name": "t"}, "period": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(m=7,'day',m=12,'month',m=5,'weekday')", "description": "", "name": "period"}}, "ungrouped_variables": ["me", "tble1", "tble", "p", "shortform", "med", "this", "m", "interq", "whatever", "n", "note", "these", "std", "r", "sig", "t", "av", "units", "period"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Find mean, standard deviation, median and interquartile range of sample, ", "functions": {"flattenint": {"type": "list", "language": "javascript", "definition": "/*only for integer arrays*/ \n      array.toString().split(',').forEach( function (item, i) \n      {array[i] = parseInt(item);\n      }\n      );        \n       return array;", "parameters": [["array", "list"]]}, "uquartile": {"type": "number", "language": "jme", "definition": "interpolate(a,3*(length(a)+1)/4)", "parameters": [["a", "list"]]}, "interpolate": {"type": "number", "language": "jme", "definition": "(1-fract(r))*sort(a)[floor(r)-1]+fract(r)*sort(a)[ceil(r)-1]", "parameters": [["a", "list"], ["r", "number"]]}, "lquartile": {"type": "number", "language": "jme", "definition": "interpolate(a,(length(a)+1)/4)", "parameters": [["a", "list"]]}}, "showQuestionGroupNames": false, "parts": [{"prompt": "<p>Sample mean = [[0]]{shortform}. Give your answer to &nbsp;$2$ decimal places (include trailing zeros if required).</p>\n<p>Sample Standard Deviation = [[1]] {shortform}. Give your answer to $2$ decimal places&nbsp;(include trailing zeros if required).</p>\n<p>Sample Median = [[2]] (Input as an exact decimal).</p>\n<p>The interquartile range= [[3]] (Input as an exact decimal).</p>", "scripts": {}, "gaps": [{"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "av-0.01", "maxValue": "av+0.01", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"precisionPartialCredit": 0, "allowFractions": false, "correctAnswerFraction": false, "minValue": "std-0.01", "maxValue": "std+0.01", "precision": "2", "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "med", "minValue": "med", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}, {"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "interq", "minValue": "interq", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "statement": "<p>The following data are the {whatever} for {these}, {units} taken by {this}</p>\n    <p>{table(tble,t)}</p>\n    <p>Answer the following questions:</p>\n    <p>&nbsp;</p>\n    <p>&nbsp;</p>", "tags": ["ACE2013", "checked2015", "interquartile range", "lower quartile", "MAS1403", "mean", "mean ", "median", "quartiles", "sample data", "sample mean", "sample standard deviation", "standard deviation", "statistics", "upper quartile"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p>Note that the uquartile and lquartile are calculated as given by the functions below these may change!</p>\n    <p>&nbsp;<strong>21/12/2012:</strong></p>\n    <p>Three user defined functions. Added tag udf.</p>\n    <p>flattenint, takes an array of arrays with integers leaves and converts to an integer array by flattening the array. Other two functions, uquartile and lquartile find the lower and upper quartiles.</p>\n    <p>Scenarios possible, added sc.</p>\n    <p><strong>22/10/2013:</strong></p>\n    <p><strong><br /></strong>Redefined functions uquartile and lquartile to fit new definitions. Added helper udf interpolate.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given sample data find mean, standard deviation, median, interquartile range,</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>As we have to find the median and the interquartile range it is a good idea to order the data and also to total up the data (for the mean) and find the total of the squares of the data (for the variance).</p>\n    <p>{table([['Data']+sort(r),['Squared data']+map(x^2,x,sort(r)),['Index']+map(x,x,1..m*n)],[])}</p>\n    <p>Note that from the above table:</p>\n    <p>$n=\\var{m*n}$.</p>\n    <p>$\\displaystyle &nbsp;\\sum x_i = \\var{sum(r)}$ and&nbsp;</p>\n    <p>$\\displaystyle &nbsp;\\sum x^2_i = \\var{sum(map(x^2,x,r))}$ .</p>\n    <p>The sample mean is $\\bar{x}=\\displaystyle \\frac{ \\sum x_i}{n}=\\frac{\\var{sum(r)}}{\\var{m*n}}=\\var{mean(r)}=\\var{av}$ to 2 decimal places.</p>\n    <p>The sample deviation is the square root of the sample variance.</p>\n    <p>Sample variance:\\[\\begin{eqnarray*}\\frac{1}{ n -1}\\left(\\sum x_i ^ 2 - n \\bar{x} ^ 2\\right)&amp;=&amp;&nbsp;\\frac{1}{\\var{m*n-1}}\\left(\\var{sum(map(x^2,x,r))}-\\var{m*n}\\times\\var{mean(r)^2}\\right)\\\\&amp;=&amp;\\var{variance(r,true)}\\end{eqnarray*}\\]&nbsp;{Note}&nbsp;</p>\n    <p>So the sample standard deviation = $\\sqrt{\\var{variance(r,true)}}=\\var{std}$&nbsp;to 2 decimal places.</p>\n    <p>The median is $\\var{median(r)} $.</p>\n    <p>The lower quartile is : $\\var{lquartile(r)}$.</p>\n    <p>The upper quartile is : $\\var{uquartile(r)}$.</p>\n    <p>The interquartile range is the difference between these quartiles =$\\var{uquartile(r)}-\\var{lquartile(r)}=\\var{uquartile(r)-lquartile(r)}$</p>\n    <p>&nbsp;</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/"}]}