How to find an interquartile range in statistics

Descriptive Statistics, The Basics 46 Comments

In statistics, finding the difference between the biggest and smallest values in the middle fifty percent of data–can be a tricky concept to grasp at first. However, this article breaks it down into a couple of easy steps, so you’ll have the answer in no time!

Probability and statistics: Interquartile range (IQR)

  • Step 1: Put the numbers in order
    1,2,5,6,7,9,12,15,18,19,27
  • Step 2: Find the median (How to find a median)
    1,2,5,6,7,9,12,15,18,19,27
  • Step 3: Place parentheses around the numbers above and below the median.
    Not necessary statistically–but it makes Q1 and Q3 easier to spot.
    (1,2,5,6,7),9,(12,15,18,19,27)
  • Step 4: Find Q1 and Q3
    Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data.
    (1,2,5,6,7),  9, ( 12,15,18,19,27). Q1=5 and Q3=18.
  • Step 5:Subtract Q1 from Q3 to find the interquartile range.
    18-5=13.

That’s the easy way to find the interquartile range in statistics!

Tips: This article does tell you the steps. However, if you want to find an IQR quickly, check out the interquartile range calculator.
If you have a boxplot, see this article to find the interquartile range.

Feel like Cheating at Statistics? This is the Statistics Handbook that your professor doesn't want you to see. So easy, it's Practically Cheating. Find out more »
Need more help? Ask on our free forums »

You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.

46 Responses to “How to find an interquartile range in statistics”

  1. How to find an interquartile range on a boxplot « How to Do Everything Statistics said:

    Aug 22, 09 at 8:27 am

    [...] an interquartile range on a boxplot is easy! (If you only have numbers, see How to  find an interquartile range from a set of numbers). This how-to will show you how to find an interquartile range in a couple of easy [...]

  2. Cathy Flanagan said:

    Sep 07, 09 at 2:32 pm

    This article really helped me to understand interquartile range. I really like the hint of using parentheses to find Q1 and Q3! I will definently try it on my next problem.

  3. Philip Smith said:

    Sep 09, 09 at 8:41 am

    You make it all seem so easy. I really like the way you break it all down into easy-to-follow steps. More importantly, after reading the article and studying the steps, I feel like it’s something I will be able to remember.

  4. Evelyn Snyder said:

    Sep 12, 09 at 8:06 am

    Subtract Q1 from Q3 to find the interquartile range.
    The online textbook in MathZone helps, but your explanation on what the IQR represents and how it is found, makes it easier to grasp and solve the problem. The IQR is the middle point between Q1 and Q3. Now when I am asked to find the IQR for a report, I will have some knowledge as to “what?” I am being asked. In the past we have charted our ups and downs with a histrogram; but with this class, I will be able to use more pertinent charts to show a more realistic annual report, thanks!

  5. Lisa Barcomb said:

    Oct 04, 09 at 8:24 pm

    Yeah you do make it seem easy but I worked these problems out and I did get them right and then when I went to take my test well that was a different story. I don’t know what happened with my thought process, but it went out the window. I also have a problem with those histograms.

  6. Vanessa DuBarry said:

    Dec 14, 09 at 10:25 pm

    I loved how everything is in order and done step by step! this was really helpful thanks for these blogs!

  7. Shannon M said:

    Dec 16, 09 at 7:16 pm

    Many thanks to the author of this page has helped me greatly, unfortunately I found it hard to believe that there is no decent standard deviation pages on this site yet the rest is so thorough….

    Regards

    Shannon

  8. How to Do Everything Statistics » How to Find Q1, Q3 and the Interquartile Range on the TI-89 calculator said:

    Jan 04, 10 at 1:54 pm

    [...] It’s the distance between the 75th percentile and the 25th percentile. In order to calculate the interquartile range by hand, you would have to do a few separate calculations, including finding the mean. Or you could use the [...]

  9. Ela said:

    Dec 19, 10 at 6:01 pm

    If you say in step 4 that: Q1=5 and Q3=18.
    then in Step 5. (Subtract Q1 from Q3 to find the interquartile range) You should get 5-18 = -13

  10. shawa Dominic said:

    Jan 04, 11 at 4:34 am

    Thanks for the help given

  11. dwomoh kennedy said:

    Mar 12, 11 at 8:08 pm

    Thank you for providing me with such a wonderful explanation.

  12. desperate student said:

    Jun 09, 11 at 12:26 pm

    frst of all
    thankyou
    ive got exams tomaro n irealy had trouble with IQR
    n now i think ive becum n expert wen it comes to iqr..lol thanku again

  13. Statistics How To» Blog Archive » How to find an interquartile range in statistics « Gregory Reese Research said:

    Sep 03, 11 at 1:50 pm

    [...] Statistics How To» Blog Archive » How to find an interquartile range in statistics. Advertisement LD_AddCustomAttr("AdOpt", "0"); LD_AddCustomAttr("Origin", "other"); [...]

  14. Molly said:

    Oct 13, 11 at 1:00 am

    Makes sense sort of, this way doesnt account for even numbers. but lets say for this set of data…. 1,1,2,2,3,3,4,4,5,5 the median is 3, Q1-2 and Q3- 4, so the IQR by your definition would be 2, but according to my statistics textbook the IQR is 2.5…. ????? So what do you do?

  15. Stephanie said:

    Oct 13, 11 at 3:11 pm

    the IQR is subtracting Q1 from Q3. If you have a list of whole numbers, I don’t know why your text would come up with a fraction. Perhaps you could post your question in the forum (along with exactly what your book says).

  16. Dylan said:

    Oct 15, 11 at 7:10 pm

    Very intuitive, but what if you have even amount of numbers.
    For example: 12, 15, 15, 22, 45, 45, 45, 60, 80, 200.

    The median is 45 because it’s between 45 and 45. Do I now add 12, 15, 15, 22 and 45 and divide by 5 to find Q1?

  17. Stephanie said:

    Nov 01, 11 at 1:06 pm

    Dylan,

    Tricky question! the simple answer is to follow whatever your text/instructor says. In a basic stats class (at least, in mine) — you’ll never be “tricked” by being given an even number of figures to throw you off. In most textbooks you will be guided by an odd number, or a pair of numbers in the center that are similar (as in your question). If they are different, the median is *sometimes* the number you get by dividing the left and right numbers from the center. However, this doesn’t always work. for example, if you are talking about people — a median of 45.5 people doesn’t always make sense (because you can’t get half of a person).

    Q1 could be that middle figure — 15 — or it could be what you said (divide by 5). Again, it depends on the text — and whether the answer makes sense or not (depending upon the figures in the question).

    Think of it like a kindergarten question: if Bob has 10 apples and gives Maria 1 apple, how many apples does Bob have? The Kindergarten answer is — of course — 9. However, the answer depends upon whether Bob takes a bite, drops an apple or makes an apple pie.

    Stephanie

  18. jannat iman said:

    Nov 06, 11 at 4:46 am

    thanx!
    ds data help me alot…..

  19. jannat iman said:

    Nov 06, 11 at 4:47 am

    ds data helps me alot…bt need mre explaination,,,…..thnx

  20. Pramit said:

    Nov 09, 11 at 3:32 am

    I’m not sure if I’m correct, but here is my calculation:

    The given series is: 1,1,2,2,3,3,4,4,5,5
    Q1: 0.25(count+1)= 0.25*11 =2.75
    Q3: 0.75(count+1)= 0.75*11 =8.25

    now following the position, we get Q1p= 1.75 & Q3p= 4.25
    So IQR: Q3p- Q1p = 4.25-2.75 = 2.5

    Let me know if I did it wrong.

  21. Statistical Terms about Variation | CRE preparation notes said:

    Nov 27, 11 at 11:24 am

    [...] based on work of Stephanie at Statistics How To at http://www.statisticshowto.com/articles/how-to-find-an-interquartile-range-in-statistics/  on Nov 20th, [...]

  22. Said said:

    Jan 24, 12 at 11:53 pm

    Easy peasy . . . thanks!

  23. Tony said:

    Feb 17, 12 at 5:27 pm

    This is great to learn, how do I find the interquartile range?
    If I had the same numbers 0,1,3,5,0,2,8,2,1,3 and I had a list of names but the numbers would say something like the number of arrest. How do I figure this one out.

  24. Andale said:

    Mar 19, 12 at 12:57 pm

    I used the Interquartile Range Calculator and got the following results:
    25th Percentile: 2
    50th Percentile: 3
    75th Percentile: 4
    Interquartile Range: 2

    It’s a good way to check your work :)

    Stephanie

  25. How to find an interquartile range TI 83 | said:

    Apr 15, 12 at 4:49 pm

    [...] How to Find an Interquartile Range by Hand Feel like Cheating at Statistics? This is the Statistics Handbook that your professor doesn't want you to see. So easy, it's Practically Cheating. Find out more » Need more help? Ask on our free forums » [...]

  26. submit URL said:

    Apr 24, 12 at 6:17 pm

    submit URL…

    [...]How to find an interquartile range in statistics |[...]…

  27. DIONNA MAYFIELD said:

    May 20, 12 at 11:33 am

    omg soo easyy thankyou

  28. Jawaher said:

    May 26, 12 at 9:42 am

    These tips are very helpful. Thanks a lot

  29. Jarrod Page said:

    Jun 09, 12 at 7:10 pm

    thanks a heap, shopuld be abble to get through my maths mid year now :D

  30. Godwin yohanna said:

    Jun 29, 12 at 12:04 pm

    Thanks i learn how to find interquartile range. what is the secret behind the use of percentile

  31. Jules Lee said:

    Jul 19, 12 at 7:46 pm

    Thank you! I found your blog as the best alternative to my book. My book suck at explaining!

  32. Andale said:

    Jul 20, 12 at 11:05 am

    Glad it helped!

    Stephanie

  33. charnay said:

    Aug 10, 12 at 5:41 am

    Thanks so much. This was a clear,understandable, answer on how to solve inter-quartile range.

  34. pooh said:

    Sep 20, 12 at 7:20 pm

    how do i get interquartile range and standard deviation for 112,111,107,92,80,81,84,118,106,103,94

  35. Andale said:

    Sep 21, 12 at 4:19 pm

    Pooh…just use the IQ and std dev calculators on this site. It isn’t just a calculator…it shows you the answer step-by-step too :)

    http://www.statisticshowto.com/calculators/

  36. kayla said:

    Oct 31, 12 at 1:07 pm

    this was so helpful thank you so much!

  37. Carol said:

    Nov 01, 12 at 5:43 pm

    Ella
    the directions are right…..careful how you read them….subtract the Q1 FROM Q3…..18-5=13

  38. What is an Interquartile Range? | said:

    Nov 05, 12 at 7:09 am

    [...] Range Calculator on this site can calculate that interval for you. Alternatively, you may want to calculate the IQR manually. But if you want to know that the IQR is in formal terms, the interquartile range is calculated as [...]

  39. Captain Falcon said:

    Nov 27, 12 at 5:46 am

    Thanks that actually really helped, and you break it down so easy. love your work and keep it up

  40. Brian Ombisa said:

    Dec 05, 12 at 11:16 pm

    How about in cases where the data is big that you can not arrange it all. Also where they are in classes how do you go about with that.

  41. Andale said:

    Dec 10, 12 at 5:57 am

    Brian…large data, you can use MS Excel. As for classes….my first thought would be that’s impossible (unless you have the raw data).

  42. Darlene said:

    Dec 12, 12 at 11:47 pm

    This method doesnt work at certain questions

  43. Andale said:

    Dec 13, 12 at 7:03 am

    Hi, Darlene,

    What kinds of questions?

    Stephanie

  44. Kris Keyes said:

    Jan 21, 13 at 11:38 am

    How do you find the interquartile range for a set with an even amount of values?

  45. Andale said:

    Jan 22, 13 at 6:29 am

    Kris,

    Time constraints prevent me from answering stats questions in the comments…but post on our forums and our mod will be happy to help :)

    Stephanie

  46. Cassi said:

    Apr 19, 13 at 8:11 pm

    Simplified and easy to follow – Thankyou so much!