// Numbas version: exam_results_page_options
{"name": "PRAC Averages (frequency table)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "PRAC Averages (frequency table)", "tags": [], "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Use the frequency table below to calculate mean, median and and mode.</p>\n<table border=\"0.1\" style=\"border: solid;\">\n<tbody>\n<tr>\n<td>Class</td>\n<td>0</td>\n<td>1</td>\n<td>2</td>\n<td>3</td>\n<td>4</td>\n<td>5</td>\n</tr>\n<tr>\n<td>Frequency</td>\n<td>{f1}</td>\n<td>{f2}</td>\n<td>{f3}</td>\n<td>{f4}</td>\n<td>{f5}</td>\n<td>{f6}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p>See \"show steps\" within this question for more help.</p>", "rulesets": {}, "extensions": [], "variables": {"f1": {"name": "f1", "group": "Frequencies", "definition": "random(5..20)", "description": "", "templateType": "anything"}, "f2": {"name": "f2", "group": "Frequencies", "definition": "f1+a", "description": "", "templateType": "anything"}, "f3": {"name": "f3", "group": "Frequencies", "definition": "f1-1", "description": "", "templateType": "anything"}, "f4": {"name": "f4", "group": "Frequencies", "definition": "f1-a", "description": "", "templateType": "anything"}, "f5": {"name": "f5", "group": "Frequencies", "definition": "f1-b", "description": "", "templateType": "anything"}, "f6": {"name": "f6", "group": "Frequencies", "definition": "a", "description": "", "templateType": "anything"}, "mp5": {"name": "mp5", "group": "Median calculations", "definition": "tot/2", "description": "", "templateType": "anything"}, "tot": {"name": "tot", "group": "Cumulative", "definition": "cf5+f6", "description": "", "templateType": "anything"}, "sfx": {"name": "sfx", "group": "Mean calculations", "definition": "0*f1+1*f2+2*f3+3*f4+4*f5+5*f6", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Median calculations", "definition": "switch(f1<mp5,1,f1=mp5,0.5,f1>mp5,0)", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "group": "Median calculations", "definition": "switch(cf3<mp5,1,cf3=mp5,0.5,cf3>mp5,0)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Median calculations", "definition": "switch(cf2<mp5,1,cf2=mp5,0.5,cf2>mp5,0)", "description": "", "templateType": "anything"}, "a5": {"name": "a5", "group": "Median calculations", "definition": "switch(cf5<mp5,1,cf5=mp5,0.5,cf5>mp5,0)", "description": "", "templateType": "anything"}, "a4": {"name": "a4", "group": "Median calculations", "definition": "switch(cf4<mp5,1,cf4=mp5,0.5,cf4>mp5,0)", "description": "", "templateType": "anything"}, "cf4": {"name": "cf4", "group": "Cumulative", "definition": "cf3+f4", "description": "", "templateType": "anything"}, "cf5": {"name": "cf5", "group": "Cumulative", "definition": "cf4+f5", "description": "", "templateType": "anything"}, "cf2": {"name": "cf2", "group": "Cumulative", "definition": "f1+f2", "description": "", "templateType": "anything"}, "cf3": {"name": "cf3", "group": "Cumulative", "definition": "cf2+f3", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..f1-1)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(a..f1)", "description": "", "templateType": "anything"}, "mn": {"name": "mn", "group": "Mean calculations", "definition": "sfx/tot", "description": "", "templateType": "anything"}, "median": {"name": "median", "group": "Median calculations", "definition": "a1+a2+a3+a4+a5", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [{"name": "Frequencies", "variables": ["f1", "f2", "f3", "f4", "f5", "f6"]}, {"name": "Cumulative", "variables": ["cf2", "cf3", "cf4", "cf5", "tot"]}, {"name": "Median calculations", "variables": ["a1", "a2", "a3", "a4", "a5", "mp5", "median"]}, {"name": "Mean calculations", "variables": ["sfx", "mn"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the mean value (correct to 2 decimal places)?</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>To find the mean use the formula $\\frac{\\Sigma fx}{\\Sigma f}$</p>\n<p>In other words $\\frac{(0\\times\\var{f1})+(1\\times \\var{f2})+(2\\times\\var{f3})+(3\\times\\var{f4}) +(4\\times\\var{f5})+(5\\times\\var{f6})}{\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}+\\var{f5}+\\var{f6}}$</p>"}], "answer": "{mn}", "showPreview": false, "checkingType": "dp", "checkingAccuracy": "2", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the median value?</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The median is the \"middle\" value.&nbsp;</p>\n<p>In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.</p>\n<p>First add up the frequencies to find $n$.</p>\n<p>Case 1. When the sum of the frequencies is odd, then the median is the value at the $\\frac{n+1}{2}^{th}$ position.<br/>Case 2. When the sum of the frequencies is even, then the median is the average of values at the positions $\\frac{n}{2}^{th}$ and $\\frac{n+1}{2}^{th}$.</p>\n<p><br/>We need to add up the frequencies until we reach this value and then the class we land in is the median.</p>"}], "minValue": "{median}", "maxValue": "{median}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the mode? <em>(If there is no mode, enter \"0\".)</em></p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The mode is the number which occurs most often. In other words the class&nbsp;with the &nbsp;highest frequency.</p>"}], "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}]}