From the
Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997
Introduction to Boxplots
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.
In the examples and exercises in our texts the boxplots are often drawn without reference to outliers. Even worse, the datasets are all fake and usually are set in a trivial context. And frequently for the dataset given a boxplot isn't the most appropriate graphical display.
The Queensland textbook authors can be partly forgiven for incorrectly constructing boxplots (though not for using fake data), given the resources that were available at the time. Appendix 2 in the back of the Mathematics A syllabus draws the whiskers out to the largest and smallest values in the dataset, and makes no mention of outliers. 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.
David Moore in Statistics - Concepts and Controversies, an introductory statistics book for liberal arts students, ignores outliers and draws the whiskers to the extreme values of the dataset. I was disappointed to see this, but only one page of the text is devoted to boxplots so maybe there wasn’t space to develop the topic to greater depth.
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 Coedine 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.
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 1st and 3rd 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 truely 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.