Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

2. Describing Data with Tables and Graphs

Stemplots (Stem-and-Leaf Plots)

Statistics

2. Describing Data with Tables and Graphs

Stemplots (Stem-and-Leaf Plots)

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2:13 minutes

Problem 2.2.18

Textbook Question

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

Verified step by step guidance

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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Related Practice

Textbook Question

The overall averages of 12 students in a statistics class prior to taking the final exam are listed.

67 72 88 73 99 85 81 87 63 94 68 87

d. Display the data in a stem-and-leaf plot. Use one line per stem.

Textbook Question

Putting Graphs in Context In Exercises 5–8, match the plot with the description of the sample.

a. Times (in minutes) it takes a sample of employees to drive to work

b. Grade point averages of a sample of students with finance majors

c. Top speeds (in miles per hour) of a sample of high-performance sports cars

d. Ages (in years) of a sample of residents of a retirement home

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Textbook Question

Estimating Standard Deviation Both data sets shown in the stem-and-leaf plots have a mean of 165. One has a standard deviation of 16, and the other has a standard deviation of 24. By looking at the stem-and-leaf plots, which is which? Explain your reasoning.

Multiple Choice

A stemplot contains the row 2|0024555789. List the data points displayed in this row.

Textbook Question

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

Highest-Paid Athletes Use a stem-and-leaf plot that has two rows for each stem to display the data, which represent the incomes (in millions) of the top 30 highest-paid athletes. (Source: Forbes Media LLC)

39 42 41 45 48 48 106 45 88 54 61 37 62 74 40

47 56 57 105 96 37 48 41 64 52 47 45 59 49 104

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.

Textbook Question

The overall averages of 12 students in a statistics class prior to taking the final exam are listed.

67 72 88 73 99 85 81 87 63 94 68 87

d. Display the data in a stem-and-leaf plot. Use one line per stem.

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