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Plots </span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <div class="intro-card" readonly="false"><img class="intro-image" readonly="true" src="../../files/Stats/CFBP/CFBP-1.jpeg" style="width: 100px; height: 100px; float: left;">Looking at the Spread of Data - This topic is all about these two related tools for helping us look at how a data set is spread out. Learn about filling in cumulative frequency tables, plotting the corresponding curves and using the curves to draw box plots and answer questions about the data set. See below for some short, specific video lessons, some revision slides and practice questions.</div> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p>In this unit you should learn to...</p> <ul> <li>Construct cumulative frequency tables and diagrams</li> <li>Use them to find the median, quartile, percentiles, range and Interquartile range</li> <li>Produce and understand box plots </li> <li>Use all of the above to describe, interpret and compare data sets</li> </ul> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <h4>Slide Gallery</h4> <p>Look at the topic at a glance with these overview slides about cumulative frequency and box plots</p> <div id="carousel-235" class="dynamic-gallery carousel slide" data-id="235"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-235/cfbp2001.jpeg" data-fancybox="gallery-235" title="" data-caption=""><img alt="" src="../../../std-galleries/15-235/cfbp2001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-235/cfbp2002.jpeg" data-fancybox="gallery-235" title="" data-caption=""><img alt="" src="../../../std-galleries/15-235/cfbp2002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-235/cfbp2003.jpeg" data-fancybox="gallery-235" title="" data-caption=""><img alt="" src="../../../std-galleries/15-235/cfbp2003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-235/cfbp2004.jpeg" data-fancybox="gallery-235" title="" data-caption=""><img alt="" src="../../../std-galleries/15-235/cfbp2004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-235/cfbp2005.jpeg" data-fancybox="gallery-235" title="" data-caption=""><img alt="" src="../../../std-galleries/15-235/cfbp2005.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-235" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-235" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-235/cfbp2001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-235/cfbp2002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-235/cfbp2003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-235/cfbp2004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-235/cfbp2005-thumb128.jpg"><li></li></ol> <h4>Video Lessons</h4> <p>This section offers a series of video tutorials on this topic. They are carefully paced and ordered to help you step by step through the idea. You can use them to teach yourself from scratch or to review all or any part of the topic as and when you need to.</p> <div class="panel panel-yellow panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. What is Cumulative Frequency</p> </div> </div> <div class="panel-body"> <div> <p>This is an introduction to the concept and purpose of this subtopic.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543956786"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Drawing and using cumulative Frequency curves</p> </div> </div> <div class="panel-body"> <div> <p>In this video we will go through the stages of how to construct the cumulative frequency diagram, from plotting the points to drawing the curve. Then we will have a look at how the diagram can be used.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543970734"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. Interpreting cumulative frequency curves</p> </div> </div> <div class="panel-body"> <div> <p>Once we have the cumulative frequency diagrams, this is a video about how to interpret them.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543971364"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. Curves to box plots</p> </div> </div> <div class="panel-body"> <div> <p>This video covers going from cumulative frequency curves to box plots.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543972501"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div id="carousel-236" class="dynamic-gallery carousel slide" data-id="236"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-236/cfbprc001.jpeg" data-fancybox="gallery-236" title="" data-caption=""><img alt="" src="../../../std-galleries/15-236/cfbprc001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-236/cfbprc002.jpeg" data-fancybox="gallery-236" title="" data-caption=""><img alt="" src="../../../std-galleries/15-236/cfbprc002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-236/cfbprc003.jpeg" data-fancybox="gallery-236" title="" data-caption=""><img alt="" src="../../../std-galleries/15-236/cfbprc003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-236/cfbprc004.jpeg" data-fancybox="gallery-236" title="" data-caption=""><img alt="" src="../../../std-galleries/15-236/cfbprc004.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-236" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-236" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-236/cfbprc001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-236/cfbprc002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-236/cfbprc003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-236/cfbprc004-thumb128.jpg"><li></li></ol> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self Checking Quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the worked solutions when you get stuck. If you find there are still some gaps in your understanding then go back to the videos above<em>.</em></p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-312-2099"><p>The following is a cumulative frequency table for a survey that measured the length of TV programs in minutes.<img alt="" src="../../files/Stats/CFBP/Table-1.jpg" style="text-align: center; width: 690px; height: 266px;"></p><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>Work out what should go in the table below instead of the letter A</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="76"> <span class="review"></span> </p></div><div class="q-explanation"><p>A = 39 + 37, A is 76</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Work out what should go in the table below instead of the letter B</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="18"> <span class="review"></span> </p></div><div class="q-explanation"><p>94 - B = A, B is 18</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>Work out what should go in the table below instead of the letter C</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="11"> <span class="review"></span> </p></div><div class="q-explanation"><p>120 - C = 109, C is 11</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>How many TV programs were in the survey above?</p></div><div class="q-answer"><p><input type="text" style="height: auto;" data-c="120"> <span class="review"></span> </p></div><div class="q-explanation"><p>This will always be the last number in the cumulative frequency column. It is always important to be clear about this.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>The lower quartile in the survey is the item that is one quarter of the way through the total. What frequency is one quarter of the way through this data set?</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="30"> <span class="review"></span> </p></div><div class="q-explanation"><p>The total frequency is 120.. One quarter, or 25%, of the way through is 30. We say that the lower quartile is where the frequency is 30 (in this case)</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>The following is a cumulatve frequency graph of the data above.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/CFBP/Graph-1.jpg" style="width: 500px; height: 377px;"></p><p style="text-align: center;"> </p><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following could be the lower quartile?</p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> 39 minutes</label></p><p><label class="checkbox"><input type="checkbox"> 30 minutes</label></p><p><label class="checkbox"><input type="checkbox"> 45 minutes</label></p><p><label class="checkbox"><input class="c" type="checkbox"> 43 minutes</label></p></div><div class="q-explanation"><p>Reading across from 30 on the frequency axis and down to the x- axis, the answer is greater than 40, but less than 45. </p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>Use your graph to decide which of the following could be the median length of a TV program.</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 62 minutes</label></p><p><label class="radio"><input type="radio"> 64 minutes</label></p><p><label class="radio"><input type="radio"> 60 minutes</label></p><p><label class="radio"><input type="radio"> 70 minutes</label></p></div><div class="q-explanation"><p>Reading across from 60 (50% of 120) on the frequency axis and down to the x- axis, the answer is greater than 60, but less than 64. </p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>Use the graph to decide which of the following is the best estimate of how many programs were less than 100 minutes long?</p></div><div class="q-answer"><p><label class="checkbox"><input class="c" type="checkbox"> 103</label></p><p><label class="checkbox"><input type="checkbox"> 105</label></p><p><label class="checkbox"><input type="checkbox"> 101</label></p><p><label class="checkbox"><input type="checkbox"> 107</label></p></div><div class="q-explanation"><p>Reading up from 100 minutes on the x - axis and then across to the y - axis, 103 is the best estimate.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>What percentage of the TV programs were <em>longer</em> than 100 minutes? Give your answer to 3 sf (eg, 32.1%)</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="14.2%"> <span class="review"></span> </p></div><div class="q-explanation"><p>103 programs were less than 100 minutes long, so 17 were longer. <img align="middle" alt="17 over 120 cross times 100 space equals space 14.2 space left parenthesis 3 s f right parenthesis" class="Wirisformula" data-mathml="«math style=¨font-family:Arial¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»17«/mn»«mn»120«/mn»«/mfrac»«mo»§#215;«/mo»«mn»100«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»14«/mn»«mo».«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»(«/mo»«mn»3«/mn»«mi»s«/mi»«mi»f«/mi»«mo»)«/mo»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-31.php?formula=44dc3bcea16f1b2ec11d91c40e1a5676.png"></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>Use the following box plot of the data to work out the best answer for the Interquartile range of the data.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/CFBP/IQR.jpg" style="width: 500px; height: 112px;"></p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> 18 minutes</label></p><p><label class="checkbox"><input type="checkbox"> 53 minutes</label></p><p><label class="checkbox"><input type="checkbox"> 120 minutes</label></p><p><label class="checkbox"><input class="c" type="checkbox"> 43 minutes</label></p></div><div class="q-explanation"><p>Read the Lower quartile as 43 minutes and the upper quartiles as 86 minutes. The interquartile range is the difference so is 43 minutes.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following are exam style questions on this topic that you should try on your own before checking against the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/Stats/CFBP/cfbpq1.jpg" style="width: 600px; height: 288px;"></p> <p>See the solution in the hidden box</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543974934"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-default"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p style="text-align: center;"><img alt="" src="../../files/Stats/CFBP/cfbpq2.jpg" style="width: 600px; height: 350px;"></p> <p>See the solution in the hidden box</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543975332"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-expandable panel-default"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p style="text-align: center;"><img alt="" src="../../files/Stats/CFBP/cfbpq3.jpg" style="width: 600px; height: 580px;"></p> <p>See the solution in the hidden box</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/543975835"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="2099"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>4.2 & 4.3 Cumulative Frequency & Box Plots </strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider 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