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 guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stem-and-Leaf Plot

A stem-and-leaf plot is a method of displaying quantitative data in a graphical format, similar to a histogram, to retain the original data values while showing their distribution. Each number is split into a 'stem' (the leading digit or digits) and a 'leaf' (the trailing digit). This allows for easy visualization of the data's shape and helps identify the distribution, central tendency, and spread.

Data Distribution

Data distribution refers to how values are spread or arranged across a dataset. Understanding the distribution helps in identifying patterns, trends, and anomalies within the data. Common distributions include normal, skewed, and uniform distributions, which can be visualized using plots like histograms or stem-and-leaf plots, providing insights into the data's characteristics.

Comparative Analysis

Comparative analysis involves evaluating two or more datasets to identify similarities, differences, and trends. In the context of the yoga classes, comparing the ages of participants in the 3:00 P.M. and 8:00 P.M. classes can reveal insights about the demographics of each class. This analysis can be effectively visualized using back-to-back stem-and-leaf plots, facilitating a clear comparison of the two groups.

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