Graphing Data Sets In Exercises 17–32, organize the data using the indicated type of graph. Describe any patterns.

Nursing Use a stem-and-leaf plot to display the data, which represent the number of hours 24 nurses work per week.
40 40 35 48 38 40 36 50 32 36 40 35
30 24 40 36 40 36 40 39 33 40 32 38

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Step 1: Understand the problem. The task is to create a stem-and-leaf plot for the given data set, which represents the number of hours 24 nurses work per week. A stem-and-leaf plot organizes data by separating each value into a 'stem' (all but the last digit) and a 'leaf' (the last digit).

Step 2: Organize the data in ascending order. Arrange the data set in increasing order to make it easier to construct the stem-and-leaf plot. The ordered data set is: 24, 30, 32, 32, 33, 35, 35, 36, 36, 36, 36, 38, 38, 39, 40, 40, 40, 40, 40, 40, 40, 40, 48, 50.

Step 3: Identify the stems and leaves. The 'stem' will be the tens digit of each number, and the 'leaf' will be the ones digit. For example, for the number 24, the stem is 2, and the leaf is 4. For the number 36, the stem is 3, and the leaf is 6.

Step 4: Construct the stem-and-leaf plot. Create a vertical list of stems (2, 3, 4, 5) and write the corresponding leaves next to each stem. For example, under the stem '3', write the leaves 0, 2, 2, 3, 5, 5, 6, 6, 6, 6, 8, 8, 9. Repeat this process for all stems.

Step 5: Analyze the plot for patterns. Look for clusters, gaps, or any other patterns in the data. For example, you might notice that the majority of the data is concentrated around the stem '4', indicating that most nurses work around 40 hours per week.

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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, that helps to visualize the distribution of the data. Each number is split into a 'stem' (the leading digit or digits) and a 'leaf' (the trailing digit). This format retains the original data values while allowing for easy identification of patterns, such as clusters or gaps in the data.

Data Organization

Data organization refers to the systematic arrangement of data to facilitate analysis and interpretation. In the context of graphing, it involves categorizing and structuring data points in a way that highlights trends and relationships. Effective organization is crucial for accurately representing the data and drawing meaningful conclusions from visualizations.

Identifying Patterns

Identifying patterns in data involves analyzing the visual representation to discern trends, clusters, or anomalies. Patterns can indicate relationships between variables or highlight significant observations, such as common values or ranges. Recognizing these patterns is essential for making informed decisions based on the data and for communicating findings effectively.

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