Questions: Part A: Create a stem-and-leaf plot for each set of data. Justify your reasoning for split or non-split stems. (10 points)

Solution Steps

To create a stem-and-leaf plot, we need to first determine the stems and leaves from the given data set. The stems represent the leading digits, while the leaves represent the trailing digits. If the data range is large, we might consider splitting the stems to provide a clearer view of the data distribution. The decision to split or not depends on the data's spread and the number of data points.

The data set provided is \([12, 15, 22, 24, 25, 31, 32, 33, 35, 41, 42, 43, 44, 45, 46, 47, 48, 49]\). We first sort the data, which is already sorted in this case.

For a stem-and-leaf plot, we separate each number into a stem and a leaf. The stem is the leading digit(s), and the leaf is the trailing digit. For example, the number 12 has a stem of 1 and a leaf of 2.

We group the numbers by their stems and list the leaves in ascending order for each stem. The plot is as follows:

• Stem 1: \(1 | 2, 5\)
• Stem 2: \(2 | 2, 4, 5\)
• Stem 3: \(3 | 1, 2, 3, 5\)
• Stem 4: \(4 | 1, 2, 3, 4, 5, 6, 7, 8, 9\)

Final Answer