2. Describing Data with Tables and Graphs
Stemplots (Stem-and-Leaf Plots)
2:34 minutesProblem 2.2.42a
Textbook Question
Yoga Classes The data sets at the left show the ages of all participants in two yoga classes.
a. Make a back-to-back stem-and-leaf plot as described in Exercise 41 to display the data.
Verified step by step guidance1
Step 1: Understand the concept of a back-to-back stem-and-leaf plot. This type of plot is used to compare two data sets side by side. The 'stem' represents the leading digits (e.g., tens place), while the 'leaves' represent the trailing digits (e.g., ones place). The stems are shared between the two data sets, with one set's leaves displayed to the left and the other's to the right.
Step 2: Organize the data for both classes into stems and leaves. For example, for the 3:00 P.M. class, the ages include numbers like 40, 60, 73, etc. The stems will be the tens digits (e.g., 4, 6, 7, etc.), and the leaves will be the ones digits (e.g., 0, 0, 3, etc.). Similarly, for the 8:00 P.M. class, organize the ages into stems and leaves.
Step 3: Create a shared stem column. Write the stems in ascending order (e.g., 1, 2, 3, etc.) in the center of the plot. The leaves for the 3:00 P.M. class will be displayed to the left of the stems, and the leaves for the 8:00 P.M. class will be displayed to the right.
Step 4: Populate the back-to-back stem-and-leaf plot. For each stem, list the leaves for the 3:00 P.M. class on the left side and the leaves for the 8:00 P.M. class on the right side. Ensure the leaves are ordered numerically within each stem.
Step 5: Review the completed plot for accuracy. Verify that all data points are included and correctly placed. The plot should visually compare the distribution of ages between the two yoga classes, allowing for easy interpretation of differences or similarities.
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