// Numbas version: exam_results_page_options
{"name": "kopie mediaan gemiddelde aantal 20", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>A random sample of 20 residents from Newcastle were asked about the number of times they&nbsp;went&nbsp;to see a play at&nbsp;the&nbsp;theatre&nbsp;last year.</p>\n<p>Here is the list of their answers:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$\\var{a[0]}$</td>\n<td>$\\var{a[1]}$</td>\n<td>$\\var{a[2]}$</td>\n<td>$\\var{a[3]}$</td>\n<td>$\\var{a[4]}$</td>\n<td>$\\var{a[5]}$</td>\n<td>$\\var{a[6]}$</td>\n<td>$\\var{a[7]}$</td>\n<td>$\\var{a[8]}$</td>\n<td>$\\var{a[9]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[10]}$</td>\n<td>$\\var{a[11]}$</td>\n<td>$\\var{a[12]}$</td>\n<td>$\\var{a[13]}$</td>\n<td>$\\var{a[14]}$</td>\n<td>$\\var{a[15]}$</td>\n<td>$\\var{a[16]}$</td>\n<td>$\\var{a[17]}$</td>\n<td>$\\var{a[18]}$</td>\n<td>$\\var{a[19]}$</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>", "name": "kopie mediaan gemiddelde aantal 20", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>This question provides a list of data to the student. They are asked to find the&nbsp;mean, median, mode and range.</p>"}, "tags": ["mean", "measures of average and spread", "median", "mode", "range", "taxonomy"], "functions": {}, "rulesets": {}, "variables": {"modea2": {"name": "modea2", "group": "Ungrouped variables", "definition": "mode(a2)", "templateType": "anything", "description": ""}, "as": {"name": "as", "group": "final list", "definition": "sort(a)", "templateType": "anything", "description": "<p>Sorted list.</p>"}, "range": {"name": "range", "group": "final list", "definition": "max(a) - min(a)", "templateType": "anything", "description": ""}, "a": {"name": "a", "group": "final list", "definition": "if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))", "templateType": "anything", "description": "<p>The final list.</p>"}, "modea1": {"name": "modea1", "group": "Ungrouped variables", "definition": "mode(a1)", "templateType": "anything", "description": ""}, "modetimes": {"name": "modetimes", "group": "final list", "definition": "map(\nlen(filter(x=j,x,a)),\nj, 0..8)", "templateType": "anything", "description": "<p>The vector of&nbsp;number of times of each value in the data.</p>"}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "shuffle([ random(0..1),\n  2, \n  random(4..6),\n  random(0..3 except 2), \n  random(0..3 except 2),\n  random(4..6),\n  2,\n  2,\n  random(4..6),\n  random(7..8),\n  random(0..3 except 2 except 1), \n  random(4..6),\n  2,\n  random(1..3 except 2), \n  random(7..8),\n  2,\n  random(7..8),\n  random(4..6), \n  random(0..3 except 2), \n  2\n])", "templateType": "anything", "description": "<p>Option 3 for the list. Ensures there is only one mode (2) while still randomising the data.</p>"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "repeat(random(0..8), 20)", "templateType": "anything", "description": "<p>Option 1 for the list. Only used if there is only one mode.</p>"}, "mean": {"name": "mean", "group": "final list", "definition": "mean(a)", "templateType": "anything", "description": ""}, "mode1": {"name": "mode1", "group": "final list", "definition": "mode[0]", "templateType": "anything", "description": "<p>Mode as a value.</p>"}, "mode": {"name": "mode", "group": "final list", "definition": "mode(a)", "templateType": "anything", "description": "<p>Mode as a vector.</p>"}, "median": {"name": "median", "group": "final list", "definition": "median(a)", "templateType": "anything", "description": ""}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "repeat(random(0..8), 20)", "templateType": "anything", "description": "<p>Option&nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.</p>"}}, "parts": [{"correctAnswerFraction": false, "mustBeReducedPC": 0, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "prompt": "<p>Find the mean.</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "unitTests": [], "minValue": "mean", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 1, "variableReplacements": [], "scripts": {}, "maxValue": "mean"}, {"correctAnswerFraction": false, "mustBeReducedPC": 0, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "prompt": "<p>Find the median.</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "unitTests": [], "minValue": "median", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 1, "variableReplacements": [], "scripts": {}, "maxValue": "median"}, {"correctAnswerFraction": false, "mustBeReducedPC": 0, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "prompt": "<p>Find the mode.</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "unitTests": [], "minValue": "mode1", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 1, "variableReplacements": [], "scripts": {}, "maxValue": "mode1"}, {"correctAnswerFraction": false, "mustBeReducedPC": 0, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "prompt": "<p>Find the range.</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "unitTests": [], "minValue": "range", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 1, "variableReplacements": [], "scripts": {}, "maxValue": "range"}], "extensions": ["stats"], "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "<h4>a)</h4>\n<p>The mean is the sum of all the&nbsp;responses ($\\sum x$) divided by the number of responses ($n$).</p>\n<p>Here, $n = 20$.</p>\n<p>\\begin{align} <br/>\\sum x &amp;= \\var{a[0]} + \\var{a[1]} +\\var{a[2]} +\\var{a[3]} +\\var{a[4]} +\\var{a[5]} +\\var{a[6]} +\\var{a[7]} +\\var{a[8]} +\\var{a[9]} + \\var{a[10]} + \\var{a[11]} +\\var{a[12]} +\\var{a[13]} +\\var{a[14]} +\\var{a[15]} +\\var{a[16]} +\\var{a[17]} +\\var{a[18]} +\\var{a[19]}&nbsp;\\\\<br/>&amp;= \\var{sum(a)} \\text{.}<br/>\\end{align}</p>\n<p><span face=\"Courier New\">Therefore we calculate the mean</span></p>\n<p><span face=\"Courier New\">\\begin{align} <br/>\\overline{x} &amp;= \\frac{\\sum x}{n}&nbsp;\\\\[0.5em]<br/>&amp;= \\frac{\\var{sum(a)}}{20}&nbsp;\\\\[0.5em]<br/>&amp;= \\var{mean} \\text{.}<br/>\\end{align}</span></p>\n<p><span face=\"Courier New\">&nbsp;</span></p>\n<h4>b)</h4>\n<p>The median is&nbsp;the middle value. We need to sort the list in order:</p>\n<p style=\"text-align: center;\">\\[ \\var{as[0]}, \\quad \\var{as[1]}, \\quad&nbsp;\\var{as[2]}, \\quad \\var{as[3]}, \\quad \\var{as[4]}, \\quad \\var{as[5]}, \\quad \\var{as[6]}, \\quad \\var{as[7]}, \\quad \\var{as[8]}, \\quad \\var{as[9]}, \\quad \\var{as[10]}, \\quad \\var{as[11]}, \\quad&nbsp;\\var{as[12]}, \\quad \\var{as[13]}, \\quad \\var{as[14]}, \\quad \\var{as[15]}, \\quad \\var{as[16]}, \\quad \\var{as[17]}, \\quad \\var{as[18]}, \\quad \\var{as[19]} \\]</p>\n<p>There is an even number of responses, so there are&nbsp;two numbers in the middle (10<sup>th</sup> and 11<sup>th</sup> place). To&nbsp;find the median, we need to&nbsp;find the mean of these two numbers $\\var{as[9]}$ and $\\var{as[10]}$:</p>\n<p>\\begin{align} <br/>\\frac{\\var{as[9]} + \\var{as[10]}}{2} &amp;= &nbsp;\\frac{\\var{as[9] + as[10]}}{2} \\\\<br/>&amp;= \\var{median} \\text{.}&nbsp;<br/>\\end{align}</p>\n<p>&nbsp;</p>\n<h4>c)</h4>\n<p>The mode is the value that occurs the most often in the data.</p>\n<p>To find a mode, we can look at our sorted list:</p>\n<p style=\"text-align: center;\">$\\var{as[0]}, \\var{as[1]}, \\var{as[2]}, \\var{as[3]}, \\var{as[4]}, \\var{as[5]}, \\var{as[6]}, \\var{as[7]}, \\var{as[8]}, \\var{as[9]}, \\var{as[10]}, \\var{as[11]}, \\var{as[12]}, \\var{as[13]}, \\var{as[14]}, \\var{as[15]}, \\var{as[16]}, \\var{as[17]}, \\var{as[18]}, \\var{as[19]}$.</p>\n<p>We&nbsp;notice that $\\var{mode1}$ occurs the most ($\\var{modetimes[mode1]}$ times) so $\\var{mode1}$ is the mode.</p>\n<p>&nbsp;</p>\n<h4>d)</h4>\n<p>Range is the difference between the highest and the lowest value in the data.</p>\n<p>To find this, we subtract the lowest value from the highest value:</p>\n<p>\\[ \\var{max(a)} - \\var{min(a)} = \\var{range} \\text{.}\\]</p>", "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["modea1", "modea2", "a1", "a2", "a3"], "variable_groups": [{"variables": ["a", "as", "mean", "median", "mode", "mode1", "range", "modetimes"], "name": "final list"}], "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}