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class="fa fa-fw"></i><a href="../2259/411-chi-squared-independence-tests.html">4.11 Chi Squared Independence tests</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../2413/411-chi-squared-goodness-of-fit-and-the-t-test.html">4.11 Chi Squared Goodness of Fit and the T-Test</a></label></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> 4.1 Statistical concepts <a href="#" class="mark-page-favorite pull-right" data-pid="2188" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1065/statistics-and-probability.html">Statistics and Probability</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">4.1 Statistical concepts</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="../../football-crowd-1.png" style="width: 532px; height: 387px;"> <div class="content" readonly="true">Statistics are so powerful because they allow us to create meaning from data. In this chapter we will learn the differences between types of data, how to choose useful samples, and how to recognise outliers in data.</div> </div> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-486de6ee-7fff-a9d1-4896-02e9367973d0"></span></p> <p dir="ltr"><span id="docs-internal-guid-486de6ee-7fff-a9d1-4896-02e9367973d0">In this unit you should learn to…</span></p> <ul style="list-style-type:disc;"> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">recognise the difference between discrete and continuous data</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">be able to minimise the bias in your data</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">take a sample of data in order to analyse it</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">recognise difference types of sampling</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">find outliers of a set of data</p> </li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. Types of Data</p> </div> </div> <div class="panel-body"> <div> <p>Discrete and Continuous Data, what is a data, how do we ensure we minimise bias in our data?<iframe allow="autoplay; fullscreen" allowfullscreen="" frameborder="0" height="480" src="https://player.vimeo.com/video/461511555" width="640"></iframe></p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Sampling vs Population</p> </div> </div> <div class="panel-body"> <div> <p>Why might you want to take a sample of your data? How do we collect a representative sample? What types of sample are there?</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/461513998"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. Outliers and Anomalies</p> </div> </div> <div class="panel-body"> <div> <p>What is the difference between an outlier and an anomaly? How could you recognise one? What are some examples of potential outliers?<iframe allow="autoplay; fullscreen" allowfullscreen="" frameborder="0" height="564" src="https://player.vimeo.com/video/461515810" width="640"></iframe></p> </div> </div> </div> </div> </div> </div> <h4> </h4> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <ul class="gallery layout-row thumb48"><li class=""><a href="../../../std-galleries/15-213/11.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/11-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/12.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/12-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/13.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/13-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/14.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/14-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/15.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/15-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/16.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/16-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/17.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/17-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/18.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/18-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/19.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/19-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/20.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/20-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/21.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/21-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/22.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/22-thumb128.jpg" class="thumb"></a></li><li class=""><a href="../../../std-galleries/15-213/23.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/23-thumb128.jpg" class="thumb"></a></li><li><a href="../../../std-galleries/15-213/24.png" data-fancybox="gallery-213" class="fancy"><img src="../../../std-galleries/15-213/24-thumb128.jpg" class="thumb"></a></li></ul> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <p>Self Checking Quiz</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="15-534-2188"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of these are examples of discrete data?</p></div><div class="q-answer"><p><label class="checkbox"><input class="c" type="checkbox"> <span>The number of students in a class</span></label> </p><p><label class="checkbox"><input class="c" type="checkbox"> <span>Results of rolling a dice</span></label> </p><div class="ck-mark" id="right-mark" style="display:none;"> </div><p><label class="checkbox"><input type="checkbox"> <span>A cat's weight</span></label> </p><p><label class="checkbox"><input type="checkbox"> <span>The length of a leaf</span></label> </p><p><label class="checkbox"><input type="checkbox"> <span>Time taken to run a race</span></label> </p><div class="ck-mark" id="wrong-mark" style="display:none;"> </div></div><div class="q-explanation"><p>Discrete data is data that can be counted, continuous data is data that can be measured</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>Which of these are examples of continuous data?</p></div><div class="q-answer"><p><label class="checkbox"><input class="c" type="checkbox"> <span class="checkbox"><span>The length of a leaf</span></span></label> </p><p><label class="checkbox"><input class="c" type="checkbox"> <span class="checkbox"> <span>A cat's weight</span></span></label> </p><div class="ck-mark" id="right-mark" style="display:none;"> </div><p><label class="checkbox"><input type="checkbox"> <span class="checkbox"><span>Results of rolling a dice</span></span></label> </p><p><label class="checkbox"><input type="checkbox"> <span class="checkbox"><span>The number of students in a class</span></span></label> </p><p><label class="checkbox"><input type="checkbox"> Colours in a rainbow</label></p><div class="ck-mark" id="wrong-mark" style="display:none;"> </div></div><div class="q-explanation"><p>Discrete data is data that can be counted, continuous data is data that can be measured</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>Which type of data is data that can be measured, and can take an infinite number of values?</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="continuous"> <span class="review"></span> data</p></div><div class="q-explanation"><p>continuous data is data that can be measured, whereas discrete data is data that is counted</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>Which type of data is data that can be counted, and could only take a finite number of values?</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="discrete"> <span class="review"></span> data</p></div><div class="q-explanation"><p>continuous data is data that can be measured, whereas discrete data is data that is counted</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>An <input type="text" style="height: auto;" data-c="outlier"> <span class="review"></span> is a value that lies outside other values.</p></div><div class="q-answer"></div><div class="q-explanation"></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">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>Below is a table of students' test results. One of these results is an outlier.</p><table border="0" cellpadding="0" cellspacing="0" style="width:100%;"><tbody><tr><td>Craig</td><td>45%</td></tr><tr><td>Laura</td><td>36%</td></tr><tr><td>Luisa</td><td>56%</td></tr><tr><td>Josh</td><td>98%</td></tr><tr><td>Maia</td><td>40%</td></tr><tr><td>Becca</td><td>42%</td></tr></tbody></table><p>a. Whose test result is the outlier?</p><p>b. What is the mean if you remove the outlier?</p></div><div class="q-answer"><p>a. <input type="text" style="height: auto;" data-c="Josh"> <span class="review"></span></p><p>b. <input type="text" style="height: auto;" data-c="43.8"> <span class="review"></span> %</p></div><div class="q-explanation"></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>An outlier is a piece of data that is distant from the other data in a data set. It can occur because of inaccurate data collection, but also just through variation in the data that is collected. As statisticians, we can choose to either include or exlude outliers, depending on whether we think they contribute to our analysis. This decision can change how we interpret a data set, as it impacts how we calculate central tendency, especially the <span style="background-color: rgb(240, 240, 240);"><input type="text" style="height: auto;" data-c="mean"> <span class="review"></span> </span></p></div><div class="q-answer"></div><div class="q-explanation"></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>Match the word to the correct description:</p><table border="0" cellpadding="0" cellspacing="0" style="width:100%;"><tbody><tr><td>The whole group we are interested in</td><td> <input type="text" style="height: auto;" data-c="Population"> <span class="review"></span></td></tr><tr><td>A collection of data from the whole population</td><td> <input type="text" style="height: auto;" data-c="Census"> <span class="review"></span></td></tr><tr><td>A collection of data from part of the population</td><td> <input type="text" style="height: auto;" data-c="Sample"> <span class="review"></span></td></tr></tbody></table><p style="text-align: center;"> </p></div><div class="q-answer"><span class="q-text-draggable draggable" draggable="true">Census</span> <span class="q-text-draggable draggable" draggable="true">Population</span> <span class="q-text-draggable draggable" draggable="true">Sample</span></div><div class="q-explanation"><p>Use this optional field for teacher explanations.</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>Match the word to the correct description of different types of sampling</p><table border="0" cellpadding="0" cellspacing="0" style="width:100%;"><tbody><tr><td>Randomly chosen data, but in the ratio of group size</td><td> <input type="text" style="height: auto;" data-c="Stratified"> <span class="review"></span></td></tr><tr><td>Data chosen from a random starting point, and then at even intervals</td><td> <input type="text" style="height: auto;" data-c="Systematic"> <span class="review"></span></td></tr><tr><td>Data picked randomly from a list</td><td> <input type="text" style="height: auto;" data-c="Simple"> <span class="review"></span></td></tr><tr><td>A sample created from individuals that fit certain required characteristics</td><td> <input type="text" style="height: auto;" data-c="Quota"> <span class="review"></span></td></tr><tr><td>A sample chosen by ease of collection</td><td> <input type="text" style="height: auto;" data-c="Convenience"> <span class="review"></span></td></tr></tbody></table></div><div class="q-answer"><span class="q-text-draggable draggable" draggable="true">Systematic</span> <span class="q-text-draggable draggable" draggable="true">Quota</span> <span class="q-text-draggable draggable" draggable="true">Simple</span><span class="q-text-draggable draggable" draggable="true">Convenience</span> <span class="q-text-draggable draggable" draggable="true">Stratified</span></div><div class="q-explanation"><p>Use this optional field for teacher explanations.</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>What type of sampling are you using if you survey every fifth person who enters the room?</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>Systematic</span></label> </p><p><label class="radio"> <input type="radio"> <span>Stratified</span></label> </p><p><label class="radio"> <input type="radio"> <span>Quota</span></label> </p><p><label class="radio"> <input type="radio"> <span>Simple</span></label> </p></div><div class="q-explanation"><p>Use this field for hidden/teacher's explanations</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> <h4> </h4> <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>Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with 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"> <p dir="ltr" id="docs-internal-guid-05171221-7fff-abed-2445-3126902af9cb">A headteacher wants to find out in how many subjects students have Internal Assessments (IA). He conducts a survey:</p> <table align="left" dir="ltr" style="width:718px;"> <colgroup> <col> <col> <col> <col> <col> <col> <col> <col> </colgroup> <tbody> <tr> <td> <p dir="ltr">Number of subjects with IAs</p> </td> <td> <p dir="ltr">0</p> </td> <td> <p dir="ltr">1</p> </td> <td> <p dir="ltr">2</p> </td> <td> <p dir="ltr">3</p> </td> <td> <p dir="ltr">4</p> </td> <td> <p dir="ltr">5</p> </td> <td> <p dir="ltr">6</p> </td> </tr> <tr> <td> <p dir="ltr">Number of students</p> </td> <td> <p dir="ltr">15</p> </td> <td> <p dir="ltr">20</p> </td> <td> <p dir="ltr">20</p> </td> <td> <p dir="ltr">32</p> </td> <td> <p dir="ltr">30</p> </td> <td> <p dir="ltr">17</p> </td> <td> <p dir="ltr">16</p> </td> </tr> </tbody> </table> <div style="clear:both;"> </div> <ol style="list-style-type:lower-alpha;"> <li dir="ltr"> <p dir="ltr" role="presentation">State whether the data is discrete or continuous (1)</p> </li> <li dir="ltr"> <p dir="ltr" role="presentation">It was not possible to ask the whole school, so he conducts a survey. The school is 55% boys and 45% girls, so he makes sure his sample includes 55% boys and 45% girls. What type of sampling does he use? (1)</p> </li> <li dir="ltr"> <p dir="ltr" role="presentation">He then wants to investigate further, so asks all the students that are studying Geography. What type of sampling is this? (1)</p> </li> <li dir="ltr"> <p dir="ltr" role="presentation">The coursework marks of the students studying Geography are listed below. </p> <ol style="list-style-type:lower-roman;"> <li dir="ltr"> <p dir="ltr" role="presentation">Identify the outlier</p> </li> <li dir="ltr"> <p dir="ltr" role="presentation">By removing the outlier, calculate the new mean (3)</p> </li> </ol> </li> </ol> <table align="left" dir="ltr" style="width:718px;"> <colgroup> <col> <col> <col> <col> <col> <col> <col> <col> <col> <col> </colgroup> <tbody> <tr> <td> <p dir="ltr">45%</p> </td> <td> <p dir="ltr">39%</p> </td> <td> <p dir="ltr">46%</p> </td> <td> <p dir="ltr">29%</p> </td> <td> <p dir="ltr">39%</p> </td> <td> <p dir="ltr">43%</p> </td> <td> <p dir="ltr">42%</p> </td> <td> <p dir="ltr">48%</p> </td> <td> <p dir="ltr">39%</p> </td> <td> <p dir="ltr">41%</p> </td> </tr> </tbody> </table> <div style="clear:both;"> </div> <p dir="ltr" style="margin-left: 72pt; text-align: right;">(6 marks)</p> <p dir="ltr" style="margin-left: 72pt;">Video Solution</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/598249992?badge=0&autopause=0&player_id=0&app_id=58479&h=e71ab97965"></iframe></div> <script src="../../../api/player.js"></script><script src="../../../api/player.js"></script></section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr" id="docs-internal-guid-276ff59f-7fff-3f50-4a3f-d240eda5c594">A reservoir contains 3 types of fish. There are estimated to be 700 carp, 500 bass and 300 pike. A survey of the fish is taken, and a sample of 50 is used. </p> <p dir="ltr">a)Explain why a simple random sample would not be appropriate (1)</p> <p dir="ltr">b)Name a potential sampling method that could be used (1)</p> <p dir="ltr">c) Give one advantage and one disadvantage of this method (2)</p> <p dir="ltr">d) Explain briefly how you could conduct this survey (3)</p> <p dir="ltr" style="text-align: right;">(7 marks)</p> <p dir="ltr">Video Solution</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/594695468?badge=0&autopause=0&player_id=0&app_id=58479&h=c5eb816760"></iframe></div> <script src="../../../api/player.js"></script></section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr" id="docs-internal-guid-ab30b9ae-7fff-d0a5-c22c-c22d8cc67b70">A survey of hours taken revising for a test is conducted by a teacher. She asks all the students in her Grade 12 class: “Revising hard will make you do better in this exam. How many hours did you revise?”</p> <p dir="ltr">a)What type of sampling did the teacher use? (1)</p> <p dir="ltr">b) Her question might have made her results unreliable. Suggest what change could be made, and why. (2)</p> <p dir="ltr">The table shows the answers that her students gave. </p> <table align="left" dir="ltr" style="width:718px;"> <colgroup> <col> <col> <col> <col> <col> <col> <col> <col> <col> <col> </colgroup> <tbody> <tr> <td> <p dir="ltr">0</p> </td> <td> <p dir="ltr">0</p> </td> <td> <p dir="ltr">1</p> </td> <td> <p dir="ltr">1</p> </td> <td> <p dir="ltr">2</p> </td> <td> <p dir="ltr">5</p> </td> <td> <p dir="ltr">5</p> </td> <td> <p dir="ltr">8</p> </td> <td> <p dir="ltr">9</p> </td> <td> <p dir="ltr">50</p> </td> </tr> </tbody> </table> <div style="clear:both;"> </div> <p dir="ltr">c)Showing your working, identify the outlier and explain whether or not you think the value should be included in the teacher’s analysis. (5)</p> <p dir="ltr"> (8 marks)</p> <p dir="ltr">Video Solution</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/594704680?badge=0&autopause=0&player_id=0&app_id=58479&h=4247e2a7e3"></iframe></div> <script src="../../../api/player.js"></script></section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="2188"> <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>4.1 Statistical concepts</strong> have you understood?</p><div class="slider-container 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