How to find an interquartile range in statistics
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! (If you have a boxplot, see this article to find the interquartile range).
*Note: This article does tell you the steps. However, if you want to find an IQR quickly, check out the interquartile range calculator.*
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!
Related posts:
- How to find an interquartile range on a boxplot
- How to Find Q1, Q3 and the Interquartile Range on the TI-89 calculator
- How to Find the TI 83 Interquartile Range
- How to find a five number summary in statistics
- How to find the mean, mode and median in statistics
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 [...]
Cathy Flanagan said:
Sep 07, 09 at 2:32 pmThis 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.
Philip Smith said:
Sep 09, 09 at 8:41 amYou 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.
Evelyn Snyder said:
Sep 12, 09 at 8:06 amSubtract 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!
Lisa Barcomb said:
Oct 04, 09 at 8:24 pmYeah 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.
Vanessa DuBarry said:
Dec 14, 09 at 10:25 pmI loved how everything is in order and done step by step! this was really helpful thanks for these blogs!
Shannon M said:
Dec 16, 09 at 7:16 pmMany 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
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 [...]
Ela said:
Dec 19, 10 at 6:01 pmIf 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
shawa Dominic said:
Jan 04, 11 at 4:34 amThanks for the help given
dwomoh kennedy said:
Mar 12, 11 at 8:08 pmThank you for providing me with such a wonderful explanation.
desperate student said:
Jun 09, 11 at 12:26 pmfrst 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
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"); [...]
Molly said:
Oct 13, 11 at 1:00 amMakes 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?
Stephanie said:
Oct 13, 11 at 3:11 pmthe 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).
Dylan said:
Oct 15, 11 at 7:10 pmVery 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?
Stephanie said:
Nov 01, 11 at 1:06 pmDylan,
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
jannat iman said:
Nov 06, 11 at 4:46 amthanx!
ds data help me alot…..
jannat iman said:
Nov 06, 11 at 4:47 amds data helps me alot…bt need mre explaination,,,…..thnx
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, [...]
Said said:
Jan 24, 12 at 11:53 pmEasy peasy . . . thanks!