// Numbas version: finer_feedback_settings
{"name": "SM09 Range and Interquartile Range", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "SM09 Range and Interquartile Range", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Here are the ages of 7 people:</p>\n<p>{a1}, {a2}, {a3}, {a4}, {a5}, {a6}, {a7}.</p>", "advice": "<p>First we should order our list of ages from smallest to largest:</p>\n<p>$\\var{list[0]}, \\var{list[1]}, \\var{list[2]}, \\var{list[3]}, \\var{list[4]}, \\var{list[5]}, \\var{list[6]}$.</p>\n<p><strong>a)</strong></p>\n<p>To find the range of ages we must subtract the smallest age from the largest age,</p>\n<p>$\\var{max(list)} - \\var{min(list)} = \\var{range}$.</p>\n<p>Hence, the range is $\\var{range}$.</p>\n<p><strong>b)&nbsp;</strong></p>\n<p>To calculate the interquartile range we subtract the lower quartile from the upper quartile.</p>\n<p><span style=\"text-decoration: underline;\">To calculate the lower quartile:</span></p>\n<p>Since we have an odd number of ages we had one to the total and divide by 4,</p>\n<p>$\\frac{7+1}{4} = \\frac{8}{4} = 2.$</p>\n<p>So we are looking for the $2^{nd}$ value in our list which is $\\var{lq}$.</p>\n<p>Hence the lower quartile is $\\var{lq}$.</p>\n<p><span style=\"text-decoration: underline;\">To find the upper quartile:</span></p>\n<p>We still add one to the number of ages because this number is odd and then we find $75$% of it,</p>\n<p>$\\frac{3\\times(7+1)}{4} = \\frac{3\\times8}{4} = \\frac{24}{4} = 6.$</p>\n<p>So we are looking for the $6^{th}$ value in our list which is $\\var{uq}$.</p>\n<p>Hence the lower quartile is $\\var{uq}$.</p>\n<p>Now we can calculate the interquartile range by subtracting the lower quartile from the upper quartile,</p>\n<p>$\\var{uq}-\\var{lq} = \\var{iqr}.$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 1</p>", "templateType": "randrange", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 2</p>", "templateType": "randrange", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 3</p>", "templateType": "randrange", "can_override": false}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 4</p>", "templateType": "randrange", "can_override": false}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", 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{"name": "uq", "group": "Ungrouped variables", "definition": "list[(((3*8)/4)-1)]", "description": "<p>Upper quartile</p>", "templateType": "anything", "can_override": false}, "iqr": {"name": "iqr", "group": "Ungrouped variables", "definition": "uq-lq", "description": "<p>Interquartile range</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "a5", "a6", "a7", "list", "range", "lq", "uq", "iqr"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Work out the range of ages.</p>", "minValue": "range", "maxValue": "range", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Work out the interquartile range of the ages.</p>", "minValue": "iqr", "maxValue": "iqr", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": 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