Using Box Plots to Visualize Variation

Contributor: Lynn Ellis. Lesson ID: 13748

Box plots are a compact way to show variation in data. Learn how to draw and how to interpret a box plot.


Measurement and Data, Statistics and Probability

learning style
personality style
Grade Level
High School (9-12)
Lesson Type
Quick Query

Lesson Plan - Get It!

  • What does this picture look like to you?

The picture above looks like pistons to me, but it is actually a picture of box plots.

After you complete this lesson, you will be able to construct a box plot and interpret what a box plot is telling you.

(You should understand the median and the quartiles before this lesson. If you need a refresher, check out our lessons under Additional Resources in the right-hand sidebar.)

The US Census Bureau collects information about the population of each state and the District of Columbia. That's 50 states plus the District of Columbia, all with different populations.

  • If I list them all out for you here, could you easily picture how spread out those populations are or how clustered they are around a central value?

Probably not. Making sense of a list of numbers is not easy, so we use tools to help us.

One tool in the statistician's toolbox is a box plot.

A box plot is simply a way to represent a data set in a picture. Instead of giving you a list of all 51 state (and DC) populations, I could show you this picture:

box plot us population by state

This picture gives you a significant amount of information about the data set.

  • How do you draw a box plot?
  • What can you learn about your data from a box plot?

Watch How to Draw a Boxplot, from Parabola Magic, and remeber to take notes:

Now that you have learned how to draw a box plot, watch Box Plot Examples, from Parabola Magic, to practice with an example and to learn more about interpreting box plots:

Now, try matching number summaries and box plots yourself.

First, look at each box plot shown below. Then, drag and drop the correct number summary into the matching data box.

Feel free to watch the video again if you need to.

When you are ready, move on to the Got It? section for some practice.

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