Quartile deviation for Grouped Data

by | Jun 15, 2010 | Descriptive statistics | 43 comments

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: 

 

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Coefficient of Quartile Deviation:

  

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: 

 

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The concept of quartile deviation and coefficient of quartile deviation can be explained with the help of simple problems for grouped data. 

 

For Grouped Data

  

Problem: 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. 

 

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Solution: 

In case of frequency distribution, quartiles can be calculated by using the formula: 

 

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First Quartile (Q1)

  

In case of frequency distribution first quartile can be calculated by using the formula given below: 

 

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Third Quartile (Q3)

  

Like first and second quartile, the third quartile can be calculated by using the formula: 

 

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By putting the values into the formulas of quartile deviation and coefficient of quartile deviation we get: 

 

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See also calculation of quartile deviation for ungrouped data

43 Comments

  1. ?????
    ????? on December 25, 2010 at 6:13 am

    its a good lesson,thanks for this one

  2. mpeli mwasumbi
    mpeli mwasumbi on March 31, 2011 at 8:00 am

    its a good lesson, it helps to understand the topic.thanks much for this

  3. Tindwa John
    Tindwa John on May 7, 2011 at 6:09 pm

    I have enjoyed a lot in this lesson, you helps many who have problems in maths. Thanks alot

  4. John Isaac Piccio
    John Isaac Piccio on August 15, 2011 at 4:09 am

    Thanks!

  5. magnu dutta
    magnu dutta on August 18, 2011 at 4:15 pm

    thanks for the lesson

  6. charles
    charles on September 19, 2011 at 6:56 pm

    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. 😀

  7. Carlos
    Carlos on October 16, 2011 at 1:30 pm

    Nice one I like it and it help me a lot

  8. pranja
    pranja on November 3, 2011 at 5:10 am

    it is very good lesson for solving problem

  9. Daniel
    Daniel on January 11, 2012 at 12:34 pm

    Thanks a lot bro! 😀

  10. chipofya elias
    chipofya elias on January 29, 2012 at 11:26 pm

    nice topic keep it up

  11. M.raza shah
    M.raza shah on April 24, 2012 at 6:42 pm

    Its very easy to understand but if the data is give as…
    5_10=3
    10_15=5
    15_20=7 then how will we find commulative frequecy for such data please iam confused in this i need to know its solution. Thanks

  12. irfan shah
    irfan shah on May 10, 2012 at 5:17 pm

    Dear friend , i learn a lot of things , because it was easy to understand. thank you

  13. Kondo Jared
    Kondo Jared on July 2, 2012 at 3:00 pm

    thanks for assisting me

  14. anam
    anam on November 11, 2012 at 4:41 pm

    thanks sooooooo much, i learn a lot about this topic because its fully explan.

  15. Joly Kenny
    Joly Kenny on November 12, 2012 at 10:31 am

    Thanks a lot!!!!!!!!!!!!! you helped me to solve the problem with all the steps…..

  16. Faith E
    Faith E on November 19, 2012 at 2:19 pm

    It was of great help. Thanks so much. Please the correct answer for Q3 is 60.4375.

  17. Samuel M. Johnson
    Samuel M. Johnson on December 2, 2012 at 7:17 am

    Thanks. This presentation makes the calculations very simple. Even a high school student can follow through. I now have a good insight on quartile deviation for grouped and ungrouped data.

  18. urooj
    urooj on April 9, 2013 at 11:59 am

    its very nice…now i’ve got it

  19. sana
    sana on April 14, 2013 at 8:20 pm

    awsome explanation…

  20. justine mauredi(sheema uganda)
    justine mauredi(sheema uganda) on May 1, 2013 at 4:32 am

    thanks a lot dear,i will do my assignment easily

  21. danish
    danish on November 9, 2013 at 4:42 pm

    Very helpful

  22. chesebe john
    chesebe john on January 14, 2014 at 2:00 pm

    Nyc vry helpful

  23. Zuniya
    Zuniya on March 2, 2014 at 2:52 am

    Solved my problem……thanks…..:):):)

  24. Utsab Barman
    Utsab Barman on March 21, 2014 at 1:29 am

    Thanks a lot …

  25. Afghan
    Afghan on March 23, 2014 at 5:18 am

    Thank You so much Mr. Admin
    It really helped me alot, keep ur good work up, we appreciate it.

  26. collorizy
    collorizy on November 11, 2014 at 7:42 pm

    Very helpfull,keep it up guys….

  27. rex
    rex on December 17, 2014 at 8:39 am

    thanks i learned much

  28. dray
    dray on January 2, 2015 at 9:32 pm

    Brother u av really done a good job,tnks 4 assisting me……luv ya

  29. Babylayne V. Dinero
    Babylayne V. Dinero on August 7, 2015 at 1:53 am

    nice!!! and thank you i’ve done my activities with the help of your examples and formulas…..

  30. francis wambua
    francis wambua on August 7, 2015 at 6:04 am

    it has been a friendly lesson…thanks for the lesson

  31. paro
    paro on August 26, 2015 at 8:09 am

    huh too long but too easy thnx for given this on net ????

  32. Muhammad Murad
    Muhammad Murad on October 6, 2015 at 2:04 pm

    thanks alot…. its really help me….. Good keep it up

  34. Uchenna
    Uchenna on November 3, 2015 at 2:19 pm

    It made the understanding of quartiles simple, thanks

  35. fm special
    fm special on February 13, 2016 at 9:14 am

    The last step I.e while calculating the coefficient of quartile deviation, is faulty…How can 60.63-50.016 =110.60…

  36. Kidia
    Kidia on May 28, 2016 at 11:09 pm

    Thanks i understand it now

  37. Mohammad Aslam
    Mohammad Aslam on October 16, 2016 at 8:18 am

    Jazakullah Khairull jazah

  38. wanjau
    wanjau on November 16, 2016 at 5:49 am

    kudos! Deserves a part on ya back. Can see light.

  39. justine
    justine on November 18, 2016 at 12:33 pm

    thnx so much 4 the help am so grateful

  40. george
    george on March 2, 2017 at 6:17 pm

    thanks so very much for the information

  41. Caleb ogola
    Caleb ogola on May 22, 2017 at 1:09 pm

    I have really enjoyed the lesson

  42. cliffe morgan
    cliffe morgan on February 15, 2018 at 8:54 am

    thanks for the lesson

  43. cass
    cass on March 1, 2018 at 11:36 am

    you can teach better than my teacher. lol.

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