Statistics How To

How to read a box plot and find the five number summary

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How to read a box plot

A box plot is a way to show a five number summary in a chart. The main part of the chart (the “box”) shows where the middle portion of the data is: the interquartile range. The ends of the box show the first quartile (the 25% mark) and the third quartile (the 75% mark). The far left of the chart (at the end of the left “whisker”) is the minimum and the far right is the maximum. The median is represented by a vertical bar in the center of the box. Box plots (sometimes called box and whiskers charts) aren’t used that much in statistics. However, they can be a useful tool for getting a quick summary of data.

How to read a box plot

How to read a box plot: Steps

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.

All done. That’s how to read a box plot!

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11 thoughts on “How to read a box plot and find the five number summary

  1. Cathy Flanagan

    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. Evelyn Snyder

    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

  3. Christine Mao

    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.

  4. Stephanie

    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

  5. Vanessa DuBarry

    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.

  6. Louise

    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

  7. Joshua

    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.