/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 These data give the times (in mi... [FREE SOLUTION] | 91Ó°ÊÓ

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These data give the times (in minutes) taken to commute from home to work for 20 workers. \(\begin{array}{llllllllll}10 & 50 & 65 & 33 & 48 & 5 & 11 & 23 & 39 & 26 \\\ 26 & 32 & 17 & 7 & 15 & 19 & 29 & 43 & 21 & 22\end{array}\) Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.

Short Answer

Expert verified
The stem-and-leaf plot arranged in increasing order is: {0 | 51 | 0 1 5 72 | 1 2 3 6 6 93 | 2 3 94 | 3 85 | 06 | 5}

Step by step solution

01

Identify the Stems

This involves identifying the tens digits from the list. The unique tens digits are: 0, 1, 2, 3, 4, 5, 6. These are the stems for the diagram.
02

Attach the Leaves

This involves grouping the commute times based on the tens digits and recording the units digits. This must be done in ascending order. For example, if the stem is '1', the leaves would be commute times from 10 to 19, thus giving us 0,1,5,7. The leaves for each stem are:Stem 0: 5Stem 1: 0,1,5,7Stem 2: 1,2,3,6,6,9Stem 3: 2,3,9Stem 4: 3,8Stem 5: 0Stem 6: 5
03

Arrange the Leaves in Increasing Order

This step involves arranging the leaves for each stem in ascending order. Hence the stem and leaf plot becomes:0 | 51 | 0 1 5 72 | 1 2 3 6 6 93 | 2 3 94 | 3 85 | 06 | 5

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Descriptive Statistics
Descriptive statistics provide a way to summarize and present data in a meaningful way. This technique helps to reveal important patterns and insights in a dataset.
When dealing with commute times, such as in our exercise, you often use different measures like mean, median, mode, range, and standard deviation to describe the data's characteristics.
For instance, examining the mean commute time gives you an average idea of how long workers typically take to commute. Meanwhile, the median can tell you the middle value, showing a central tendency in the dataset.
By understanding these measures, you can gain insights into the commute times of the workers and identify any unusual or outlying data points.
Data Visualization
Data visualization is crucial because it transforms numbers into visuals, making patterns in datasets easy to understand. A stem-and-leaf plot is a straightforward form of data visualization for small datasets, like commute times.
With this plot, you can quickly see data distribution, identify clusters, and spot data trends. The stems represent the 'tens' digit in this plot, helping group data points, while leaves show the ones, providing exact values.
Visual tools like stem-and-leaf plots not only make it easier to communicate data insights but also allow for a quick snapshot view, which simplifies the process of data analysis and helps in making data-driven decisions.
Frequency Distribution
A frequency distribution shows how often each value or range of values occurs in a dataset. It's a way to understand how data points are spread across different categories.
In stem-and-leaf plots, the stems and leaves effectively form a visual frequency distribution. The number of leaves (which are the data points) linked to each stem indicates the frequency of data within that range.
For example, if the stem '2' has more leaves, it tells us that most commute times fall within the 20-29 minutes range. Such insights are important for decision-making and identifying trends.

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Most popular questions from this chapter

The following data give the numbers of orders received for a sample of 30 hours at the Timesaver Mail Order Company. \(\begin{array}{llllllllll}34 & 44 & 31 & 52 & 41 & 47 & 38 & 35 & 32 & 39 \\\ 28 & 24 & 46 & 41 & 49 & 53 & 57 & 33 & 27 & 37 \\ 30 & 27 & 45 & 38 & 34 & 46 & 36 & 30 & 47 & 50\end{array}\) a. Construct a frequency distribution table. Take 23 as the lower limit of the first class and 7 as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. For what percentage of the hours in this sample was the number of orders more than 36 ?

A data set on money spent on lottery tickets during the past year by 200 households has a lowest value of \(\$ 1\) and a highest value of \(\$ 1167\). Suppose we want to group these data into six classes of equal widths. a. Assuming that we take the lower limit of the first class as \(\$ 1\) and the width of each class equal to \(\$ 200\), write the class limits for all six classes. b. What are the class boundaries and class midpoints?

A July 2011 ESPN SportsNation poll asked, "Which is the best Fourth of July weekend sports tradition?" (http://espn.go.com/espn/fp/flashPollResultsState?sportIndex=frontpage\&pollid=116290). The choices were Major League baseball game (B), Nathan's Famous International Hot Dog Eating Contest (H), Breakfast at Wimbledon (W), or NASCAR race at Daytona (N). The following data represent the responses of a random sample of 45 persons who were asked the same question. \(\begin{array}{lllllllll}\text { H } & \text { H } & \text { B } & \text { W } & \text { N } & \text { B } & \text { H } & \text { N } & \text { W } \\\ \text { N } & \text { H } & \text { B } & \text { W } & \text { H } & \text { N } & \text { N } & \text { H } & \text { H } \\ \text { B } & \text { B } & \text { W } & \text { H } & \text { H } & \text { B } & \text { W } & \text { H } & \text { B } \\ \text { H } & \text { B } & \text { B } & \text { H } & \text { B } & \text { H } & \text { B } & \text { N } & \text { H } \\ \text { B } & \text { B } & \text { H } & \text { H } & \text { H } & \text { B } & \text { H } & \text { H } & \text { N }\end{array}\) a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of the respondents mentioned Major League baseball game or Breakfast at Wimbledon? d. Draw a bar graph for the frequency distribution.

Create a dotplot for the following data set. \(\begin{array}{llllllllll}1 & 2 & 0 & 5 & 1 & 1 & 3 & 2 & 0 & 5 \\ 2 & 1 & 2 & 1 & 2 & 0 & 1 & 3 & 1 & 2\end{array}\)

As shown in Exercise \(2.89\), back-to-back stem-and-leaf displays can be used to compare the distribution of a variable for two different groups. Consider the following data, which give the alcohol Flying Dog Brewery: \(\begin{array}{lllllllll}4.7 & 4.7 & 4.8 & 5.1 & 5.5 & 5.5 & 5.6 & 6.0 & 7.1 \\\ 7.4 & 7.8 & 8.3 & 8.3 & 9.2 & 9.9 & 10.2 & 11.5 & \end{array}\) Sierra Nevada Brewery: \(\begin{array}{lllllllllllll}4.4 & 5.0 & 5.0 & 5.6 & 5.6 & 5.8 & 5.9 & 5.9 & 6.7 & 6.8 & 6.9 & 7.0 & 9.6\end{array}\) a. Create a back-to-back stem-and-leaf display of these data. Place the Flying Dog Brewery data to the left of the stems. b. What would you consider to be a typical alcohol content of the beers made by each of the two breweries? c. Does one brewery tend to have higher alcohol content in its beers than the other brewery? If so, which one? Explain how you reach this conclusion by using the stem-and-leaf display. d. Do the alcohol content distributions for the two breweries appear to have the same levels of variability? Explain how you reach this conclusion by using the stem-and-leaf display.

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