// Numbas version: finer_feedback_settings
{"name": "SD06 Reading a Histogram", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "SD06 Reading a Histogram", "tags": [], "metadata": {"description": "<p>Reading a value from a histogram.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The histogram shows information about distances run on a Sunday by some randomly asked people in a park.&nbsp;</p>\n<div id=\"dragpoint\"></div>\n<p></p>", "advice": "<p><strong>a)</strong></p>\n<p>To calculate the frequencies using the following formula:</p>\n<p style=\"padding-left: 40px;\">frequency = class width $\\times$ frequency density&nbsp;</p>\n<p>Hence our table becomes:</p>\n<table style=\"width: 439px; height: 106px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 148.969px; height: 18px;\"><strong>Distance, $km$</strong></td>\n<td style=\"width: 257.031px; height: 18px;\"><strong>Frequency&nbsp;</strong></td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$0 &lt; t \\leq 10$</td>\n<td style=\"width: 257.031px; height: 22px;\">$10 \\times \\var{yo0} = \\var{freq0}$</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$10 &lt; t \\leq 15$</td>\n<td style=\"width: 257.031px; height: 22px;\">$5 \\times \\var{yo1} = \\var{freq1}$</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$15 &lt; t \\leq 20$</td>\n<td style=\"width: 257.031px; height: 22px;\">$5 \\times \\var{yo2} = \\var{freq2}$</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$20 &lt; t \\leq 30$</td>\n<td style=\"width: 257.031px; height: 22px;\">$10 \\times \\var{yo3} = \\var{freq3}$</td>\n</tr>\n</tbody>\n</table>\n<p>Hence, to find the total number of people that ran that day:</p>\n<p>$\\var{freq0} + \\var{freq1} + \\var{freq2} + \\var{freq3} = \\var{total}.$</p>\n<p><strong>b)&nbsp;</strong></p>\n<p>The frequency of runners that ran less than $10km$ is found by calculating the frequency from the first bar on the histogram:</p>\n<p>class width $\\times$ frequency density $= 10 \\times \\var{yo0} = \\var{freq0}$.</p>\n<p><strong>c)</strong></p>\n<p>The frequency of runners that ran between $15km$ and $20km$ is found by calculating the frequency from the third bar on the histogram:</p>\n<p>class width $\\times$ frequency density $= 5 \\times \\var{yo2} = \\var{freq2}$.</p>\n<p><strong>d)</strong></p>\n<p>To estimate how many runners ran more than $25km$ we need again need to use the frequency = class width \\times frequency density formula.</p>\n<p>Here the class width is $5$ because we are looking for the frequency of runners that ran between $25km$ and $30km$ from the college.</p>\n<p>Frequency $= 5 \\times \\var{yo3} = \\var{5*yo3}.$</p>\n<p>If this number is a decimal we round up to get $\\var{m25}$.</p>\n<p><strong>e)</strong></p>\n<p>As in part <strong>d)</strong>,to estimate how many runners ran less than $7km$ we use the frequency = class width \\times frequency density formula.</p>\n<p>Here the class width is $7$ because we are looking for the frequency of runners that ran between 0 and 7 km.</p>\n<p>Frequency $= 7 \\times \\var{yo0} = \\var{7*yo0}.$</p>\n<p>If this number is a decimal we round up to get $\\var{l7}$.</p>\n<p><strong>f)</strong></p>\n<p>To estimate how many runners ran between $5km$ and $12.5km$ we use a method similar to that in part <strong>d)</strong> and <strong>e)</strong> but, this time, we need to use information from both the first and second bar on the histogram.&nbsp;</p>\n<p>Let's first calculate how many runners ran between $5km$ and $10km$:</p>\n<p>frequency $=$ class width $\\times$ frequency density $= 5 \\times \\var{yo0} = \\var{5*yo0}$.</p>\n<p>Now we need to calculate how many runners ran between $10km$ and $12.5km$:</p>\n<p>frequency $=$ class width $\\times$ frequency density $= 2.5 \\times \\var{yo1} = \\var{2.5*yo1}$.</p>\n<p>Putting this together the number of runners that ran between $5km$ and $12.5km$ is $\\var{5*yo0} + \\var{2.5*yo1} = \\var{5*yo0 + 2.5*yo1}.$</p>\n<p>If this number is a decimal we round up to get $\\var{ef}.$</p>\n<p><strong>g)</strong></p>\n<p>The number of runners that ran between $10km$ and $14km$ is $4 \\times \\var{yo1} = \\var{4*yo1}.$<br/><br/>If this number is a decimal we round up to get $\\var{eh}.$</p>\n<p><strong>i)</strong></p>\n<p>The number of runners that ran further than $18km$ is:</p>\n<p>$2 \\times \\var{yo2} + 10 \\times \\var{yo3} = \\var{2*yo2} + \\var{freq3} = \\var{2*yo2+freq3}.$<br/><br/>If this number is a decimal we round up to get $\\var{ej}.$</p>\n<p><strong>Did you get a decimal </strong><strong>answer? 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Look at the context of the question, you cannot have $0.5$ of a student so we round our answers up to the next whole number!</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {"std": ["all", "fractionNumbers"]}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"yo2": {"name": "yo2", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": "<p>Frequency Density</p>", "templateType": "randrange", "can_override": false}, "yo1": {"name": "yo1", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": "<p>Frequency Density</p>", "templateType": "randrange", "can_override": false}, "yo3": {"name": "yo3", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": 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