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<p style="text-align: justify;">Quartile deviation or semi-interquartile range is the dispersion which shows the degree of spread around the middle of a set of data. Since the difference between third and first quartiles is called interquartile range therefore half of interquartile range is called semi-interquartile range also known as quartile deviation. For both grouped and ungrouped data, quartile deviation can be calculated by using the formula: </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image62.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb62.png" border="0" alt="image" width="300" height="79" /></a></p>
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<h3 style="text-align: justify;">Coefficient of Quartile Deviation:</h3>
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<p style="text-align: justify;">Coefficient of Quartile Deviation is used to compare the variation in two data. Since quartile deviation is not affected by the extreme values therefore it is widely used in the data containing extreme values. Coefficient of Quartile Deviation can be calculated by using the formula: </p>
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<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image63.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb63.png" border="0" alt="image" width="300" height="49" /></a> </p>
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<p style="text-align: justify;">The concept of quartile deviation and coefficient of quartile deviation can be explained with the help of simple problems for grouped data. </p>
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<h3 style="text-align: justify;">For Grouped Data</h3>
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<p style="text-align: justify;"><strong>Problem:</strong> Following are the observations showing the age of 50 employees working in a whole sale center. Find the quartile deviation and coefficient of quartile deviation. </p>
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<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image64.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb64.png" border="0" alt="image" width="500" height="60" /></a> </p>
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<p style="text-align: justify;"><strong>Solution:</strong> </p>
<p style="text-align: justify;">In case of frequency distribution, quartiles can be calculated by using the formula: </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image65.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb65.png" border="0" alt="image" width="400" height="270" /></a> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image66.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb66.png" border="0" alt="image" width="400" height="240" /></a> </p>
<p style="text-align: justify;"> </p>
<h3 style="text-align: justify;">First Quartile (Q1)</h3>
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<p style="text-align: justify;">In case of frequency distribution first quartile can be calculated by using the formula given below: </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image67.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb67.png" border="0" alt="image" width="300" height="355" /></a> </p>
<p style="text-align: justify;"> </p>
<h3 style="text-align: justify;">Third Quartile (Q3)</h3>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Like first and second quartile, the third quartile can be calculated by using the formula: </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image68.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb68.png" border="0" alt="image" width="300" height="365" /></a> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">By putting the values into the formulas of quartile deviation and coefficient of quartile deviation we get: </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/wp-content/uploads/2010/06/image69.png"><img style="display: inline; border: 0px;" title="image" src="http://mba-lectures.com/wp-content/uploads/2010/06/image_thumb69.png" border="0" alt="image" width="400" height="110" /></a> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><a href="http://mba-lectures.com/statistics/313/quartile-deviation-or-semi-inter-quartile-range-ungrouped-data.html" target="_blank" rel="noopener">See also calculation of quartile deviation for ungrouped data</a>
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View Comments
its a good lesson,thanks for this one
its a good lesson, it helps to understand the topic.thanks much for this
I have enjoyed a lot in this lesson, you helps many who have problems in maths. Thanks alot
Thanks!
thanks for the lesson
thanks so much. but i have a little bit of correction
in the computation for the third quartile, should it be 60.4375 not 60.63...
but THANKS SO MUCH. i had a hard time understanding this because the formula of my prof is a bit different from yours but when I look at it, they're just the same. :D
Nice one I like it and it help me a lot
it is very good lesson for solving problem
Thanks a lot bro! :D
nice topic keep it up