// Numbas version: finer_feedback_settings
{"name": "Relative Frequency", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Relative Frequency", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculate relative frequencies in a variety of scenarios.</p>"}, "statement": "<p>The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.</p>", "rulesets": {}, "advice": "<p>The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.</p>\n<h4>a)</h4>\n<p>To calculate the relative frequency of people who performed static stretches we need the number of trials, which is&nbsp;$\\var{no_people}$, and the&nbsp;number of people who said that they&nbsp;they performed static stretches, which is $\\var{stretch}$.</p>\n<p></p>\n<p>Therefore, the relative frequency of people who perform static stretches is</p>\n<p>\\[<br/>\\frac{\\var{stretch}}{\\var{no_people}} = \\var{dpformat({stretch/no_people}, 2)} \\; (\\text{rounded to $2$ decimal places}).<br/>\\]&nbsp;</p>\n<h4>b)</h4>\n<p>We are told that the relative frequency of the number of femurs that break when $4000N$ is applied&nbsp;to them is&nbsp;$\\var{rel_freq}$,&nbsp;so we assume&nbsp;that the relative frequency is the same across all samples of femurs exposed to the same $4000N$ force. Therefore, in our sample of $\\var{no_students}$ femurs we expect that</p>\n<p>\\[<br/>\\begin{align}<br/>&nbsp;\\var{rel_freq} \\times&nbsp;\\var{no_students} = \\var{{rel_freq}*{no_students}}<br/>\\end{align}<br/>\\]</p>\n<p>femurs will break.</p>\n<p>As this result represents a number of femurs, if the answer&nbsp;is not an integer, we must round&nbsp;it to the nearest integer.</p>\n<h4>c)</h4>\n<p><em> </em></p>\n<p>i)&nbsp;</p>\n<p>Using the frequency table given in the question, we can calculate the sample size of the survey by adding together the frequencies of each of the different types of $3D$ motion analysis systems.</p>\n<p>So, the sample size of the survey is&nbsp;</p>\n<p>\\[<br/>\\var{Vicon}+\\var{qualysis}+\\var{Optotrak} = \\var{Vicon + qualysis + Optotrak}.<br/>\\]</p>\n<p>ii)&nbsp;</p>\n<p>To calculate the relative frequency of using Vicon as a type of $3D$ motion anaylsis system, we divide the frequency of Vicon by the sample size of the survey.</p>\n<p>So, the relative frequency is&nbsp;</p>\n<p>\\[<br/>\\frac{\\var{Vicon}}{\\var{n}} = \\var{dpformat({Vicon/n}, 2)} \\; (\\text{rounded to $2$ decimal places}).<br/>\\]</p>\n<p></p>", "variable_groups": [], "functions": {}, "extensions": [], "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["no_people", "stretch", "no_students", "rel_freq", "Vicon", "qualysis", "Optotrak", "n"], "parts": [{"showCorrectAnswer": true, "precisionPartialCredit": 0, "strictPrecision": true, "prompt": "<p>$\\var{no_people}$ track and field athletes were asked whether they perform static stretches before they competed. $\\var{stretch}$ athletes said that they performed static stretches.</p>\n<p>What is the relative frequency of athletes who perform static stretches before competing?</p>\n<p></p>", "correctAnswerStyle": "plain", "precisionMessage": "<p>You must give your answer as a decimal to 2 decimal places.</p>", "unitTests": [], "maxValue": "{stretch}/{no_people}", "type": "numberentry", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showPrecisionHint": true, "mustBeReduced": false, "precisionType": "dp", "scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "{stretch}/{no_people}", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "precision": "2", "customMarkingAlgorithm": ""}, {"showCorrectAnswer": true, "precisionPartialCredit": 0, "strictPrecision": false, "prompt": "<p>The force required to break a femur during a simulated lateral fall was measured on multiple samples. The relative frequency of a femur breaking when $4000N$ was applied was estimated to be $\\var{rel_freq}$.</p>\n<p>Estimate the number of femurs that would break in a sample of&nbsp;$\\var{no_students}$ when a $4000N$ force is applied to them.</p>", "correctAnswerStyle": "plain", "precisionMessage": "<p>Round your answer to the nearest integer.</p>", "unitTests": [], "maxValue": "{no_students}*{rel_freq}", "type": "numberentry", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showPrecisionHint": true, "mustBeReduced": false, "precisionType": "dp", "scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "{no_students}*{rel_freq}", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "precision": 0, "customMarkingAlgorithm": ""}, {"marks": 0, "showCorrectAnswer": true, "gaps": [{"marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "mustBeReduced": false, "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "{Vicon} + {qualysis} + {Optotrak}", "unitTests": [], "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "maxValue": "{Vicon} + {qualysis} + {Optotrak}", "correctAnswerFraction": false, "customMarkingAlgorithm": "", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": []}, {"showCorrectAnswer": true, "precisionPartialCredit": 0, "strictPrecision": true, "correctAnswerStyle": "plain", "precisionMessage": "<p>Round your answer to 2 decimal places.</p>", "unitTests": [], "maxValue": "{Vicon}/({Vicon} + {qualysis} + {Optotrak})", "type": "numberentry", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showPrecisionHint": true, "mustBeReduced": false, "precisionType": "dp", "scripts": {}, "extendBaseMarkingAlgorithm": true, "minValue": "{Vicon}/({Vicon} + {qualysis} + {Optotrak})", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "precision": "2", "customMarkingAlgorithm": ""}], "sortAnswers": false, "prompt": "<p>A survey was conducted to find out what type of $3D$ motion analysis system is the most commonly used. The results are given in the table below.</p>\n<table style=\"width: 365px; height: 183px;\" border=\"-\" cellspacing=\"1\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 104px; height: 17px; text-align: center;\"><strong>Type of $3D$ motion anaylsis system</strong></td>\n<td style=\"width: 100px; height: 17px; text-align: center;\"><strong>Frequency</strong></td>\n</tr>\n<tr style=\"height: 39px;\">\n<td style=\"width: 104px; height: 39px; text-align: center;\">Vicon</td>\n<td style=\"width: 100px; height: 39px; text-align: center;\">$\\var{vicon}$</td>\n</tr>\n<tr style=\"height: 39px;\">\n<td style=\"width: 104px; height: 39px; text-align: center;\">Qualysis</td>\n<td style=\"width: 100px; height: 39px; text-align: center;\">$\\var{qualysis}$</td>\n</tr>\n<tr style=\"height: 43.5px;\">\n<td style=\"width: 104px; height: 43.5px; text-align: center;\">Optotrak</td>\n<td style=\"width: 100px; height: 43.5px; text-align: center;\">$\\var{optotrak}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>i)<em>&nbsp;</em></p>\n<p>What was the sample size for the survey?</p>\n<p>[[0]]</p>\n<p>ii)</p>\n<p>What is the relative frequency of using Vicon as a $3D$ motion analysis system?</p>\n<p>[[1]]</p>", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": []}], "variables": {"qualysis": {"group": "Ungrouped variables", "name": "qualysis", "description": "<p>Frequency of cat in part c.</p>", "definition": "random(5..15 except vicon)", "templateType": "anything"}, "Optotrak": {"group": "Ungrouped variables", "name": "Optotrak", "description": "<p>Frequency of hamster in part c</p>", "definition": "random(1..10 except vicon except qualysis) ", "templateType": "anything"}, "no_people": {"group": "Ungrouped variables", "name": "no_people", "description": "<p>Number of people asked in part a)</p>", "definition": "random(50..150 #10)", "templateType": "anything"}, "stretch": {"group": "Ungrouped variables", "name": "stretch", "description": "<p>Number of people who prefer free-range eggs in part a)</p>", "definition": "random(10..40)", "templateType": "anything"}, "Vicon": {"group": "Ungrouped variables", "name": "Vicon", "description": "", "definition": "random(20..40)", "templateType": "anything"}, "n": {"group": "Ungrouped variables", "name": "n", "description": "<p>Sample size for part c</p>", "definition": "Vicon + qualysis + Optotrak", "templateType": "anything"}, "rel_freq": {"group": "Ungrouped variables", "name": "rel_freq", "description": "<p>Relative frequency for part b</p>", "definition": "random(0.3..0.5 # 0.01)", "templateType": "anything"}, "no_students": {"group": "Ungrouped variables", "name": "no_students", "description": "<p>Number of students in the class for part b</p>", "definition": "random(20..40 #10)", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "type": "question", "contributors": [{"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}, {"name": "Lauren Frances Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2490/"}]}]}], "contributors": [{"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}, {"name": "Lauren Frances Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2490/"}]}