Lesson 1.8: Summarizing Quantitative Data: Boxplots and Outliers
- Use the 1.5 x IQR rule to identify outliers.
- Make and interpret boxplots of quantitative data.
- Compare distributions of quantitative data with boxplots.
Activity: How many concerts have you been to?
Our data question was fun for students to discuss but it led to a bit of a problem. With our first class, there were quite a few students who had been to zero concerts. This made the distribution strongly right skewed and it was really hard to see any spread. Even worse, the minimum and first quartile were both zero so the box plot was missing a whisker. To remedy this for the following classes, we did not use the zeros in the data set. We weren’t huge fans of doing this though because it could have made some students feel unimportant. We will probably change this question for next year or maybe have students find a total in pairs. We did have outliers in all classes so that was great! If you don’t, you could add in an outlier, preferably it is someone the students know like yourself or another teacher.
Application 1.8: Which is best in reducing stress?
We really liked this application because it gave students an opportunity to create a narrative for the data. When the boxplots were created students compared the distributions. They concluded that the presence of a pet reduced stress level while the presence of a friend would increase stress level. When asked why they thought that was, they discussed lots of possibilities like how the pressure of having a person watching over your shoulder could make you nervous so you may make more mistakes. We felt students were beginning to understand that statistics is not just about memorization and computation, but it’s about the story the data tells.
The data set we used on our note page is slightly different than the data in the text. Since students had to type all the data into the applet, we truncated the decimals and made all the data whole numbers.