## How to find an interquartile range in statistics

Main Index> Basic Statistics>Find an interquartile range

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 would prefer to view a video on how to find the IQR, click here (opens a new window).

## 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.

Have an even set of numbers? How to Find an Interquartile Range, Part 2

## 48 thoughts on “How to find an interquartile range in statistics”

1. Cathy Flanagan

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.

2. Philip Smith

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.

3. Evelyn Snyder

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!

4. Lisa Barcomb

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.

5. Vanessa DuBarry

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

6. Shannon M

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

7. Ela

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

8. desperate student

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

9. Molly

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?

10. Stephanie

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).

11. Dylan

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?

12. Stephanie

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

13. Pramit

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.

14. Tony

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.

15. Godwin yohanna

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

16. Jules Lee

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

17. charnay

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

18. Captain Falcon

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

19. Andale

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).

20. Andale

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