While this support activity is designed for a face-to-face, synchronous delivery, it should be noted that supporting text and interactive examples have been embedded in the digital assignment page to assist asynchronous or hybrid course delivery and to be made more accessible to students performing make-up work.

Suggested instructional plan for synchronous active-learning

Use this corequisite support activity to prepare students for interpreting and comparing boxplots. The next preview assignment and in-class activity presume an understanding of the five-number summary and what it tells us about a dataset. Have students work in pairs or small groups throughout this support activity. Question 1 is meant to introduce the idea of outliers informally. Give pairs or groups time to formulate their answers, and then have a few volunteers share their answers. Students will probably identify Japan and the United States as “unusual.” Hopefully, there will be some questions as to whether Japan is an outlier. Use this gray area as an opportunity to motivate students to engage in the support activity; the point of the activity is to begin to understand which values are considered unusual in a statistical sense. Let students know that they will revisit this question at the end of the support activity.

Have students continue working in pairs or small groups to answer Questions 2–11. The goal of these questions is to introduce the idea of quartiles and the five-number summary. Use Question 5 to gauge students’ understanding of median, and then hold a brief check-in with the whole class after Question 11 to ensure students’ understanding of quartiles. If time permits, have a few students summarize quartiles and the idea of the five-number summary.

The goal of Questions 12 and 13 is to introduce the interquartile range (IQR). The IQR will be used in the preview assignment to determine values that are outliers. The focus in this support activity is on the procedural fluency required to compute the interquartile range. However, depending on how quickly students move through this support activity, you can apply the IQR to determine if Japan and the United States are outliers in a statistical sense. See the optional extension below.

Use Question 14 as a way to launch a discussion. Highlight the idea that some outliers seem quite simple to spot (such as the GDP per capita of the United States), but others are harder to identify (such as Japan’s GDP per capita). Prompt students to come up with their own rules for determining outliers. This discussion is an opportunity to interject the idea that statistics is a field that requires interpretation. The study of quantitative data does not imply certainty or lack subtlety. Students will learn a formal method for determining which values are outliers in the preview assignment.

Optional Extension: If time permits, discuss elements of this article: https://towardsdatascience.com/why-1-5-in-iqr-method-of-outlier-detection-5d07fdc82097. Have students compute 1.5(IQR) and determine if Japan is an outlier.

Note that students are given the task above to computer 1.5(IQR) to determine if Japan is an outlier, with a discussion but without the article linked, in the final Interactive Example in the digital activity page. This is done to facilitate asynchronous or hybrid delivery and to accommodate students working alone on the activity.