Boxplots

On the
Side

Boxplots

Introduction

The text on this page in a form suitable for copying and pasting.

Activities

STEPS
Tutorials

Interactive computer-based tutorials

Worksheets

Boxplots Worksheet

Featuring Real Live Data!

Matching Histograms and Boxplots

Codeine Concentration in the Body

Datasets
Visit the Datasets page for more datasets and stories to support this topic.

Or, get some ideas on how students can gather their own data

FYI

How to Construct
a Boxplot

Ticky-Tacky Boxes

Ozone and Outliers

The 1970 Draft Lottery

You had to be in it to win it!

The treatment of boxplots in current senior secondary textbooks highlights the need for Queensland high school teachers to use resources other than the textbook when teaching introductory statistics.

There are two basic flavours of boxplot. The 'simple' boxplot has the whiskers drawn out to the maximum and minimum values. While this is suitable for a quick analysis, it doesn't give as much information about the data as the standard boxplot, which draws the whiskers no longer than 1.5 IQRs from the box and locates points beyond that individually. Such points are called outliers.

Unfortunately boxplots in our texts tend to only be simple boxplots. This shouldn't be surprising as the Mathematics A syllabus only makes mention of simple boxplots. It could have been worse - an early model of a graphical calculator available in Queensland used the mean rather than the median to mark the centre of the dataset. Even the TI-83 graphical calculator, the calculator of choice for AP-Statistics students in the US, draws boxplots two ways, and the default boxplot ignores outliers.

Nonetheless statisticians almost exclusively draw boxplots with outliers, if they exist. The process isn't difficult, even if done by hand, so I recommend that your students learn to draw standard boxplots as well as simple ones. The article How to Construct a Boxplot explains how to do it.

When to Choose the Boxplot

Boxplots are most useful when comparing two or more sets of sample data. Differences in the centres and spread of the datasets are clearly visible with a boxplot.

A boxplot also gives a picture of the symmetry of a dataset, and shows outliers very clearly. Both of these features are important when deciding which summary statistics would best describe the dataset. A condition of many hypothesis tests is that the data is approximately normally distributed and a boxplot can assist in determining this. Prior to conducting a hypothesis test, a statistician looks at the data, and histograms and a boxplot would be the displays most often chosen.

The Boxplots worksheet contains data drawn from physics, cricket and biology. The Codeine Concentrations worksheet has some data suitable for displaying using boxplots. There is assessment available from the Assessment page, where a variety of graphical displays, including boxplots, may be needed for a solution.

STEPS

The STEPS modules are a collection of hypertext-based tutorials covering a wide range of statistics topics, including the graphical display of data. Visit the STEPS page for further information and a list of the modules available.

Matching Histograms and Boxplots

Students will improve their ability to interpret the information given in a boxplot by matching boxplots of sample data drawn from different distributions with their associated histograms.

Constructing Boxplots

It is interesting that there is general agreement among statisticians about how to construct the whiskers and determine outliers (which is where the problem lies with our texts) but very little agreement on how to construct the box. Using the KISS principle, I teach students a method that is easy to remember and easy to do. Read the article How to Construct a Boxplot for details.

Ticky-Tacky Boxes

If you are interested in learning about different methods of calculating the 1^st and 3^rd quartiles (and the angst this has caused among AP-Stats teachers), you may find the article Ticky-Tacky Boxes interesting. The article is based on emails from the AP-Stat and Edstat mailing lists. Warning - whatever you do, please don't try to tell your students about all of this. You will only confuse the cherubs.

Thanks to Bob Hayden, who has provided much of the information for this article.

Ozone and Outliers

The 'ozone hole' above Antarctica provides the setting for one of the most infamous outliers in recent history. It is a great story to tell students who wantonly delete outliers from a dataset merely because they are outliers. Visit the Ozone and Outliers page for all of the fascinating details.

The 1970 Draft Lottery

No discussion of boxplots should leave out the story of the 1970 Draft Lottery, the first lottery held to select those chosen to serve in Vietnam, which gave rise to possibly the single most famous set of boxplots in existence. Yours truly was given a free ticket in the lottery, so the story on this page is of uncommon interest to me. Based on what the boxplots show, it turns out that this October-born lad was even luckier than was thought at the time.