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186 lines
6.8 KiB
HTML
186 lines
6.8 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/median.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:41:48 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>How to Find the Median Value</title>
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<meta name="description" content="It's the middle of a sorted list of numbers">
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<script src="data/images/median.js" type="text/javascript"></script>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="search" role="search"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">How to Find the Median Value</h1>
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<div class="center"><i>It's the middle of a sorted list of numbers.</i></div>
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<h2>Median Value</h2>
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<p>The Median is the <i><b>"middle"</b></i> of a sorted list of numbers.</p>
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<p class="center"><img src="data/images/median.svg" alt="middle number in a list of numbers"></p>
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<h2>How to Find the Median Value</h2>
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<p>To find the Median, place the numbers in <b>value order</b> and find the <b>middle</b>.</p>
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<div class="example">
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<h3>Example: find the Median of <b>12, 3 and 5</b></h3>
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<p>Put them in order:</p>
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<p class="center large">3, 5, 12</p>
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<p>The middle is <b>5</b>, so the median is <b>5</b>.</p>
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</div>
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<h3> </h3>
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<div class="example">
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<h3>Example:<span class="largemono"> 3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29</span></h3>
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<p class="center"><span class="largemono"></span></p>
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<p> When we put those numbers in order we have:
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</p>
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<p class="largemono" align="center">3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56</p>
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<p> </p>
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<p>There are <b>fifteen</b> numbers. Our middle is the <b>eighth</b> number:</p>
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<p class="largemono" align="center">3, 5, 7, 12,
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13, 14, 21, <span class="largest">23</span>, 23, 23, 23, 29,
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39, 40, 56</p>
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<p class="center larger"> </p>
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<p class="center larger">The median value of this set of numbers is <b>23</b>.</p>
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<p> </p>
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<p>(It doesn't matter that some numbers are the same in the list.)</p>
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</div>
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<h2>Two Numbers in the Middle</h2>
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<p>BUT, with an <b>even amount of numbers</b> things are
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slightly different.<br>
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<br>
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In that case we find the <b>middle
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pair</b> of numbers, and then find the value that is <b>half
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way</b> between them. This is easily done by adding them together
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and dividing by two.</p>
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<div class="example">
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<h3>Example: 3, 13,
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7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29</h3>
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<p class="center largemono"></p>
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<p> When we put those numbers in order we have:</p>
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<p class="largemono" align="center">3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56</p>
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<p> </p>
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<p>There are now <b>fourteen</b> numbers and so we don't have just one middle number, we have a <b>pair of middle numbers</b>:</p>
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<p class="largemono" align="center">3, 5, 7, 12, 13, 14, <span class="largest">21</span>, <span class="largest">23</span>, 23, 23, 23, 29, 40, 56</p>
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<p> </p>
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<p>In this example the middle numbers are <b>21 and 23</b>.</p>
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<p>To find the value halfway between them, add them together and
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divide by 2:</p>
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<p class="center"><b>21 + 23 = 44</b><br>
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then <b>44 ÷ 2 = 22</b></p>
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<p class="center larger"> </p>
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<p class="center larger">So the <b>Median</b> in this example is <b>22</b>.</p>
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<p> </p>
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<p>(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)</p>
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</div>
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<h2>Your Turn</h2>
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<script>medianMain();</script>
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<!--<div class="flash">
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<script>putFlash6(500,200,'numbers/images/median.swf','','#FFFFFF');</script>
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<noscript>
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<object type="application/x-shockwave-flash" width="500" height="200" data="numbers/images/median.swf" align="middle">
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<param name="allowScriptAccess" value="sameDomain" /><param name="allowFullScreen" value="true" /><param name="movie" value="numbers/images/median.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#FFFFFF" /></object>
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</noscript>
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</div>
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-->
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<h2>Where is the Middle?</h2>
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<p>A quick way to find the middle:</p>
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<p class="center"><b>Count how many numbers, add 1, then divide by 2</b></p>
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<div class="example">
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<h3>Example: There are 45 numbers</h3>
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<p>45 plus 1 is 46, then divide by 2 and we get <b>23</b></p>
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<p>So the median is the <b>23rd number</b> in the sorted list.</p>
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</div>
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<div class="example">
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<h3>Example: There are 66 numbers</h3>
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<p>66 plus 1 is 67, then divide by 2 and we get <b>33.5</b></p>
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<p><b>33 and a half?</b> That means that the <b>33rd and 34th</b> numbers in the sorted list are the two middle numbers.</p>
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<p>So to find the median: add the <b>33rd and 34th</b> numbers together and
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divide by 2.</p>
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</div>
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<p> </p>
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<div class="questions">693, 1457,739, 1458, 1459, 3055, 3056, 3057, 3792, 3793</div>
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<div class="related">
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<a href="mean.html">Mean</a>
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<a href="mode.html">Mode</a>
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<a href="data/central-measures.html">Central Measures</a>
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</div>
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</article>
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