Statistics How To

Box Plot interquartile range: How to find it

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Box Plot interquartile range: Overview

The interquartile range(IQR) is a measure of spread in statistics. the mean (average) tells you where the center of data is; the IQR tells you where the average set of numbers is — the set of numbers in the middle. This can give you a better idea of where the middle set of scores are, and that’s why it’s sometimes called the middle fifty. It excludes high scores (the top 25%) and the bottom scores (the bottom 25%).
A boxplot is a type of graph in statistics. It’s sometimes called a box and whiskers chart, because there is a central box and two lines emitting from the left and right that look like whiskers. A box plot gives you a five number summary — the mean, the minimum, the maximum, the first quartile (25%) and the third quartile (75%).

This how-to will show you how to find a box plot interquartile range in a couple of easy steps.

box plot interquartile range

Box Plot interquartile range: How to find it

Sample question: Find the interquartile range for the above box plot.

  • Step 1: Find Q1.Q1 is represented on a boxplot by the left hand edge of the “box” (at the point where the whisker stops).
    finding q1 on the boxplot graph

    In the above graph, Q1 is approximately at 2.5. If you are interested, a complete explanation of what Q1 is here: The five number summary.)

  • Step 2: Find Q3.
    Q3 is represented on a boxplot by the right hand edge of the “box”.
    finding q3 on the boxplot
    Q3 is approximately 12 in this graph.
  • Step 3: Subtract the number you found in step 1 from the number you found in step 3.
    This will give you the interquartile range. 12 – 2.5 = 9.5.

That’s it!

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11 thoughts on “Box Plot interquartile range: How to find it

  1. Christine Mao

    This article was simple to comphrehend. The diagram and the steps explain everything you would need to know. I was able to understand more of the interquartile range on a boxplot. The book helped, but the article was more helpful.

  2. Lisa Barcomb

    I understood this article it was easy because of the diagram, its nice when you have the diagrams to look at and see what you are doing. But the interquartile range is alittle difficult by plotting it on the boxplot.

  3. Vanessa DuBarry

    Very easy to learn this. Thanks for this blog!, its just way easier than the book explains it.

  4. crystal lydick

    Our book does not seem to explain innterequartile range as easily to me as our practically cheating book has. I do not understand our book as I do the practically cheating book.