// Numbas version: finer_feedback_settings
{"name": "Averages (frequency table)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b"], "name": "Averages (frequency table)", "tags": ["average", "frequency table", "REBEL", "rebel", "Rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>See \"show steps\" within this question for more help.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "1", "vsetrangepoints": 5, "prompt": "<p>What is the mean value (correct to 2 decimal places)?</p>", "expectedvariablenames": [], "checkingaccuracy": "2", "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "{mn}", "marks": "4", "checkvariablenames": false, "checkingtype": "dp", "type": "jme"}, {"stepsPenalty": "1", "prompt": "<p>What is the median value?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "{median}", "minValue": "{median}", "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "<p>What is the mode? (If it is undefined, enter \"0\".)</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "1", "minValue": "1", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The mode is the number which occurs most often. In other words the class&nbsp;with the &nbsp;highest frequency.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>Calculate the mean, the median and the mode for the following frequency table:</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>", "variable_groups": [{"variables": ["f1", "f2", "f3", "f4", "f5", "f6"], "name": "Frequencies"}, {"variables": ["cf2", "cf3", "cf4", "cf5", "tot"], "name": "Cumulative"}, {"variables": ["a1", "a2", "a3", "a4", "a5", "mp5", "median"], "name": "Median calculations"}, {"variables": ["sfx", "mn"], "name": "Mean calculations"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f1": {"definition": "random(5..20)", "templateType": "anything", "group": "Frequencies", "name": "f1", "description": ""}, "f2": {"definition": "f1+a", "templateType": "anything", "group": "Frequencies", "name": "f2", "description": ""}, "f3": {"definition": "f1-1", "templateType": "anything", "group": "Frequencies", "name": "f3", "description": ""}, "f4": {"definition": "f1-a", "templateType": "anything", "group": "Frequencies", "name": "f4", "description": ""}, "f5": {"definition": "f1-b", "templateType": "anything", "group": "Frequencies", "name": "f5", "description": ""}, "f6": {"definition": "a", "templateType": "anything", "group": "Frequencies", "name": "f6", "description": ""}, "mp5": {"definition": "tot/2", "templateType": "anything", "group": "Median calculations", "name": "mp5", "description": ""}, "tot": {"definition": "cf5+f6", "templateType": "anything", "group": "Cumulative", "name": "tot", "description": ""}, "sfx": {"definition": "0*f1+1*f2+2*f3+3*f4+4*f5+5*f6", "templateType": "anything", "group": "Mean calculations", "name": "sfx", "description": ""}, "a1": {"definition": "switch(f1<mp5,1,f1=mp5,0.5,f1>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a1", "description": ""}, "a3": {"definition": "switch(cf3<mp5,1,cf3=mp5,0.5,cf3>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a3", "description": ""}, "a2": {"definition": "switch(cf2<mp5,1,cf2=mp5,0.5,cf2>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a2", "description": ""}, "a5": {"definition": "switch(cf5<mp5,1,cf5=mp5,0.5,cf5>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a5", "description": ""}, "a4": {"definition": "switch(cf4<mp5,1,cf4=mp5,0.5,cf4>mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a4", "description": ""}, "cf4": {"definition": "cf3+f4", "templateType": "anything", "group": "Cumulative", "name": "cf4", "description": ""}, "cf5": {"definition": "cf4+f5", "templateType": "anything", "group": "Cumulative", "name": "cf5", "description": ""}, "cf2": {"definition": "f1+f2", "templateType": "anything", "group": "Cumulative", "name": "cf2", "description": ""}, "cf3": {"definition": "cf2+f3", "templateType": "anything", "group": "Cumulative", "name": "cf3", "description": ""}, "a": {"definition": "random(1..f1-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(a..f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "mn": {"definition": "sfx/tot", "templateType": "anything", "group": "Mean calculations", "name": "mn", "description": ""}, "median": {"definition": "a1+a2+a3+a4+a5", "templateType": "anything", "group": "Median calculations", "name": "median", "description": ""}}, "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}