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<p align="justify">When data is arranged in ascending or descending order, it can be divided into various parts by different values such as quartiles, deciles and percentiles. These values are collectively called quantiles and are the extension of median formula which divides data into two equal parts. Since the basic purpose of these partition values is to divide data into different parts therefore a relationship exists between them. This relationship is given below and is elaborated with the help of simple problem. </p>
<p align="justify">&#160;</p>
<p align="justify"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image53.png"><img title="image" style="border-top-width: 0px; display: inline; border-left-width: 0px; border-bottom-width: 0px; border-right-width: 0px" height="254" alt="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb53.png" width="450" border="0" /></a> </p>
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<p align="justify"><strong>Problem:</strong> Following are the number of defective items produced in a month by a machine for the last 24 months. 45, 30, 36, 26, 16, 21 33, 40, 32, 14, 10, 29, 23, 39, 17, 11, 18, 34, 19, 24, 21, 35, 42, 37</p>
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Prove that Second Quartile= Fifth Decile = 50th Percentile = Median</p>
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<p align="justify">&#160;</p>
<p> <strong>Solution:<br />
</strong></p>
<p> Arrange data in ascending order:<br />
10, 11, 14, 16, 17, 18, 19, 21, 21, 23, 24, 26, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 42, 45 </p>
<p align="justify">&#160;</p>
<h3 align="justify">Second Quartile Q2</h3>
<p align="justify">
Since the data given in the problem is ungrouped therefore following formula will be used for the calculation of second quartile. </p>
<p align="justify">&#160;</p>
<p align="justify"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image54.png"><img title="image" style="border-top-width: 0px; display: inline; border-left-width: 0px; border-bottom-width: 0px; border-right-width: 0px" height="336" alt="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb54.png" width="400" border="0" /></a> </p>
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<h3>5th Decile</h3>
<p>The calculation of 5th decile for ungrouped data is given below:</p>
<p align="justify">&#160;</p>
<p align="justify"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image55.png"><img title="image" style="border-top-width: 0px; display: inline; border-left-width: 0px; border-bottom-width: 0px; border-right-width: 0px" height="292" alt="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb55.png" width="400" border="0" /></a> </p>
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<p align="justify">
</p>
<h3>50th Percentile (P50)</h3>
<p>
The calculation of 50th percentile for ungrouped data is given below:</p>
<p> &#160;</p>
<p> <a href="http://mba-lectures.com/wp-content/uploads/2010/06/image56.png"><img title="image" style="border-top-width: 0px; display: inline; border-left-width: 0px; border-bottom-width: 0px; border-right-width: 0px" height="297" alt="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb56.png" width="400" border="0" /></a> </p>
<p> &#160;</p>
<h3>Median </h3>
<p>If the observations are Even in numbers, then median is the arithmetic mean of two central values. These two central values are calculated as:</p>
<p> &#160;
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View Comments
also mention here for even no. of integers in ungrouped data
computation of decile for grouped data.. please.. :D
its good...........
how i can calculate P99(percentile99) with ungroup data
can u find percentile p99 with ungrouped
tnk-u so much 4 ds website....8 helps me a lot. 8 makes me knowledgeable in terms of statistic subject..
thnx alot 4 dis...its realy helped me
thank you so much for giving the formulas of quartile, decile and percentile i was looking all over the web but no one was giving this much clearly the formulas with example so once again thank you so much
great idea....congratulation sir
please help...what is the practical application of quantiles