// Numbas version: exam_results_page_options
{"name": "Relative Frequency ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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>We are told that&nbsp;$\\var{no_people}$ people were asked whether they preferred to buy free-range eggs or caged eggs in supermarkets and that&nbsp;$\\var{free_range}$ of these people said that they preferred to buy free-range eggs.&nbsp;</p>\n<p>To calculate the relative frequency of people who prefer buying free-range eggs we need the number of trials and the frequency of people who said that they preferred buying free-range eggs.</p>\n<p>So, the number of trials in this situation is the number of people who were asked the question, which is $\\var{no_people}$.</p>\n<p>The frequency of people who said that they preferred to buy free-range eggs is&nbsp;$\\var{free_range}$.</p>\n<p>Therefore, the relative frequency of people who prefer buying free-range eggs is&nbsp;</p>\n<p>\\[<br/>\\frac{\\var{free_range}}{\\var{no_people}} = \\var{dpformat({free_range/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 a student being taller than $150$&nbsp;cm is&nbsp;$\\var{rel_freq}$.</p>\n<p>Here, we must use the formula for relative frequency in reverse in order to estimate the number of students in the class who are taller than $150$ cm.</p>\n<p>As we are using relative frequency to calculate this number, our answer may not be completely accurate, therefore our answer will be an estimate of the actual number.</p>\n<p>If we let $n$ denote the number of students in the class who are taller than $150$&nbsp;cm and if there&nbsp;are&nbsp;$\\var{no_students}$ students in the class then</p>\n<p>\\[<br/>\\begin{align}<br/>\\frac{n}{\\var{no_students}} &amp;=&nbsp;\\var{rel_freq}\\\\<br/>n &amp;=&nbsp;\\var{rel_freq} \\times&nbsp;\\var{no_students}\\\\<br/>&amp;= \\var{{rel_freq}*{no_students}}.<br/>\\end{align}<br/>\\]</p>\n<p>As $n$ represents a number of people we must round our value of $n$ to the nearest integer.</p>\n<p>So, the estimated number of students in the class who are taller than $150$&nbsp;cm is $\\var{dpformat({rel_freq}*{no_students},0)}$.</p>\n<h4>c)</h4>\n<p><em> </em></p>\n<p><em>i)&nbsp;</em></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 pets.</p>\n<p>So, the sample size of the survey is&nbsp;</p>\n<p>\\[<br/>\\var{dog}+\\var{cat}+\\var{hamster}+\\var{parrot} = \\var{{dog}+{cat}+{hamster}+{parrot}}.<br/>\\]</p>\n<p><em>ii)&nbsp;</em></p>\n<p>To calculate the relative frequency of a person having a dog as a pet, we divide the frequency of people in the survey who had a dog as a pet by the sample size of the survey.</p>\n<p>So, the relative frequency is&nbsp;</p>\n<p>\\[<br/>\\frac{\\var{dog}}{\\var{n}} = \\var{dpformat({dog/n}, 2)} \\; (\\text{rounded to $2$ decimal places}).<br/>\\]</p>\n<p></p>", "statement": "<p>The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.</p>", "variables": {"dog": {"name": "dog", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Frequency of dog in part c</p>", "definition": "random(10..50)"}, "free_range": {"name": "free_range", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Number of people who prefer free-range eggs in part a)</p>", "definition": "random(10..40)"}, "cat": {"name": "cat", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Frequency of cat in part c.</p>", "definition": "random(10..50 except dog)"}, "parrot": {"name": "parrot", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Frequency of guinea pig in part c.</p>", "definition": "random(10..50 except dog except cat except hamster)"}, "rel_freq": {"name": "rel_freq", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Relative frequency for part b</p>", "definition": "random(0.1..0.9 # 0.01)"}, "n": {"name": "n", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Sample size for part c</p>", "definition": "dog+cat+hamster+parrot"}, "no_students": {"name": "no_students", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Number of students in the class for part b</p>", "definition": "random(20..40 #10)"}, "no_people": {"name": "no_people", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Number of people asked in part a)</p>", "definition": "random(50..150 #10)"}, "hamster": {"name": "hamster", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Frequency of hamster in part c</p>", "definition": "random(10..40 except dog except cat) "}}, "tags": ["Experimental Probability", "Relative Frequency", "taxonomy"], "ungrouped_variables": ["no_people", "free_range", "no_students", "rel_freq", "dog", "cat", "hamster", "parrot", "n"], "functions": {}, "name": "Relative Frequency ", "preamble": {"js": "", "css": ""}, "extensions": [], "type": "question", "variable_groups": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>Calculate relative frequencies in a variety of scenarios.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "strictPrecision": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "precision": "2", "scripts": {}, "maxValue": "{free_range}/{no_people}", "prompt": "<p>$\\var{no_people}$ people were asked whether they preferred to buy free-range eggs or caged eggs in supermarkets. $\\var{free_range}$ people said that they preferred to buy free-range eggs. What is the relative frequency of people who prefer buying free-range eggs? Give your answer as a decimal, to $2$ decimal places.&nbsp;</p>\n<p></p>", "marks": 1, "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerFraction": false, "minValue": "{free_range}/{no_people}", "precisionType": "dp", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": true, "showFeedbackIcon": true, "precisionMessage": "<p>You must give your answer as a decimal to 2 decimal places.</p>"}, {"notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "precision": 0, "scripts": {}, "maxValue": "{no_students}*{rel_freq}", "prompt": "<p>The heights of a class of students were measured. The relative frequency of a student being taller than $150$&nbsp;cm&nbsp;is&nbsp;known to be $\\var{rel_freq}$. If there&nbsp;are $\\var{no_students}$ students in the class, estimate the number of students who&nbsp;are taller than $150$ cm.</p>", "marks": 1, "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerFraction": false, "minValue": "{no_students}*{rel_freq}", "precisionType": "dp", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": true, "showFeedbackIcon": true, "precisionMessage": "<p>Round your answer to the nearest integer.</p>"}, {"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "{dog}+{cat}+{hamster}+{parrot}", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "scripts": {}, "maxValue": "{dog}+{cat}+{hamster}+{parrot}", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst"}, {"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "precisionPartialCredit": 0, "strictPrecision": true, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "minValue": "{dog}/({dog}+{cat}+{hamster}+{parrot})", "allowFractions": false, "correctAnswerStyle": "plain", "precisionType": "dp", "scripts": {}, "maxValue": "{dog}/({dog}+{cat}+{hamster}+{parrot})", "showCorrectAnswer": true, "precision": "2", "type": "numberentry", "showPrecisionHint": true, "marks": 1, "showFeedbackIcon": true, "precisionMessage": "<p>Round your answer to 2 decimal places.</p>"}], "type": "gapfill", "prompt": "<p>A survey was conducted to find out what type of pet is the most common. 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;\">Type of Pet</td>\n<td style=\"width: 100px; height: 17px; text-align: center;\">Frequency</td>\n</tr>\n<tr style=\"height: 39px;\">\n<td style=\"width: 104px; height: 39px; text-align: center;\">Dog</td>\n<td style=\"width: 100px; height: 39px; text-align: center;\">$\\var{dog}$</td>\n</tr>\n<tr style=\"height: 39px;\">\n<td style=\"width: 104px; height: 39px; text-align: center;\">Cat</td>\n<td style=\"width: 100px; height: 39px; text-align: center;\">$\\var{cat}$</td>\n</tr>\n<tr style=\"height: 43.5px;\">\n<td style=\"width: 104px; height: 43.5px; text-align: center;\">Hamster</td>\n<td style=\"width: 100px; height: 43.5px; text-align: center;\">$\\var{hamster}$</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 104px; height: 17px; text-align: center;\">Parrot</td>\n<td style=\"width: 100px; height: 17px; text-align: center;\">\n<p style=\"text-align: center;\">$\\var{parrot}$</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><em>i)&nbsp;</em></p>\n<p>What was the sample size for the survey?</p>\n<p>[[0]]</p>\n<p><em>ii)</em></p>\n<p>What is the relative frequency of a person having a dog as a pet? Give your answer as a decimal, to $2$ decimal places.</p>\n<p>[[1]]</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "showFeedbackIcon": true}], "contributors": [{"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}]}], "contributors": [{"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}