Displaying Quantitative Data: Stemplots (Lesson 1.4)

Chapter 1 - Day 4

Learning Targets
  • Make stemplots of quantitative data.
  • Interpret or describe stemplots.
  • Compare distributions of quantitative data with stemplots.
Activity: How Many Pairs of Shoes Do You Own?
Activity:
jpg.jpg
pdf.jpg
pdf.jpg

Experience First

Start the activity with a quick quiz. Can students identify the three pairs of shoes pictured in the activity?

1. Reebok Pump (1989)

2. Toms (2006)

3. Air Jordan (1984)

 

For some students identifying the number of pairs of shoes will be easy, but for others they might just have to provide an estimate. Yes, Crocs count as shoes. No, sandals and flip flops do not count.

 

Students will use this applet to create stemplots.

Formalize Later

Common student errors when making stemplots is forgetting empty stems (stems with no leaves) and forgetting to include a KEY. The empty stems are necessary to show the true shape (that includes gaps). The KEY is necessary in case the numbers might have a decimal. For example, the numbers 324 and 32.4 would look the same in a stemplot, but would be clearly differentiated in the KEY.

 

Notice that the third learning target from this lesson is essentially the same as the third learning target in Lesson 1.3, asking students to compare distributions of quantitative data. Hint: it will be the same again in Lessons 1.5 and 1.8, just with different types of displays.

 

In the Check Your Understanding #3, you will see a back-to-back stemplot. Here, identifying the shape of the distributions can be a bit challenging (one of the Stats Medics even got this wrong on a college exam). It’s easy for the distribution on the right, but it is backwards for the distribution on the left. Turn your head to the left and if the distribution looks skewed left, it is actually skewed right. Have students think about where most of the values fall. Do we have most values that are large with fewer and fewer as we get smaller (skewed left) or is it that most values are small with fewer and fewer as we get larger (skewed right).