Summarizing Quantitative Data: Boxplots and Outliers (Lesson 1.8)
Chapter 1 - Day 9
Use the 1.5 × IQR rule to identify outliers.
Make and interpret boxplots of quantitative data.
Compare distributions of quantitative data with boxplots.
To start, let students talk in groups about their favorite concert they have attended. Next, students will record the total number of concerts they have been to on the white board. Eliminate any of the 0 values, otherwise you might end up with a funny boxplot.
Identify any potential high outliers and ask students whether they think it should be considered an outlier. The purpose of this lesson is to establish a mathematical rule for deciding if a value is an outlier. Sidenote – one of the Stats Medic has been to 100+ Phish concerts (definitely an outlier!)
Students will be using this applet to find summary statistics and to make a boxplot.
Note that the outlier rule used in this lesson is not the only outlier rule. Another common one is to say that any value that is more than two standard deviations from the mean is considered an outlier.
Note that the shape of a distribution is hard to determine from a boxplot. We don’t know how values are distributed within each quartile, and a boxplot often hides large gaps. As a general rule if the stretch from the median to one end of the boxplot is much larger on one side than the other, we can at least say the boxplot suggests the distribution is skewed.