How to read a boxplot and find the five number summary including Q1 and Q3

Descriptive Statistics, The Basics 11 Comments

This article will help you find the five number summary (minimum, Q1, median, Q3, and maximum) by reading a boxplot.

five number summary boxplot

Step 1: Find the minumum.
The minimum is the far left hand side of the graph, at the tip of the left whisker. For this graph, the left whisker end is at approximately 0.75.

Step 2:Find Q1.
Q1 is represented by the far left hand side of the box. In this case, about 2.5.

Step 3:  Find the median.
The median is represented by the vertical bar. In this boxplot, it can be found at about 6.5.

boxplot4

Step 4: Find Q3.
Q3 is the far right hand edge of the box, at about 12 in this graph.

Step 5: Find the maximum.
The maximum is the end of the “whiskers”: in this graph, at approximately 16.

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11 Responses to “How to read a boxplot and find the five number summary including Q1 and Q3”

  1. Cathy Flanagan said:

    Sep 10, 09 at 5:00 pm

    I didn’t know if this would help other people remember 5 number sequence on a box plot. They way I think of it is as a dog…the median is the middle of the dog’s nose, Q1 is the left nostril, Q3 is the right nostril,and minimum is the left wiskers and maximum is the right wiskers. Hope this helps!

  2. Stephanie said:

    Sep 12, 09 at 5:32 am

    Sounds like you are a visual learner :)

  3. Evelyn Snyder said:

    Sep 12, 09 at 8:13 am

    My biggest challenge is the heighth of the boxplot. In this example I understand how the minimum, Q1, median, Q3 and the maximum were plotted on the boxplot; however, I don’t understand how we are to determine the heighth of the boxplot OR does that matter as long as the min, Q1, median, Q3 and max are plotted correctly?
    Thanks

  4. Christine Mao said:

    Sep 12, 09 at 7:02 pm

    I think Cathy’s response to the boxplot is a good example to remember. The article is also easy to understand because the example and diagram tells you straight forward where to find the minimun, maximum, median, Q1, and Q3.

  5. Stephanie said:

    Sep 13, 09 at 5:12 am

    Evelyn,
    Sometimes the height can give information about the sample size. However, in elementary statistics, that topic isn’t covered (in other words, for this class, height does not matter).
    Stephanie

  6. Vanessa DuBarry said:

    Dec 14, 09 at 9:41 pm

    Very helpful, I like the way that it showed the two different boxes and examples.and I liked that it was labeled and that it explained everything.

  7. Louise said:

    Sep 29, 11 at 9:46 pm

    The lengths of the tails are very easy to calculate. You find your IQR and multiply it by 1.5. Then you add to your Q3 and subtract from your Q1. This gives your fences. Your legs, extend from the ends off the boxes to all the data values within your fences. Every number outside your fences are outliers.

    Q3 + 1.5*IQR = Upper fence
    Q1 – 1.5*IQR = Lower fence

  8. Brian Ombisa said:

    Dec 05, 12 at 11:10 pm

    Its sounds like a visual learning.

  9. Joshua said:

    Feb 16, 13 at 8:38 pm

    It should probably be mentioned that if there is an outlier, your minimum/maximum is not contained within a “whisker” but is the outlier. Just to avoid confusion.

  10. Andale said:

    Feb 18, 13 at 7:42 am

    Joshua,

    Very true! I did mention more on outliers here: http://www.statisticshowto.com/articles/what-is-a-boxplot/

    Thanks for dropping by,
    Stephanie

  11. What is a boxplot? | said:

    Mar 18, 13 at 10:54 pm

    [...] How to get a five number summary by reading a boxplot. [...]