MTH 165 Lund Chapter 2 Take-Home Quiz Covering 2.1, 2.2, 2.3 ✓ Solved

MTH 165 Lund Chapter 2 Take-home Quiz Covering 2.1, 2.2, 2.3

MTH 165 Lund Chapter 2 Take-home Quiz Covering 2.1, 2.2, 2.3. Complete your work on a separate piece of paper.

1. In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat belt when driving a car?” The frequencies were as follows: Response Frequency: I do not drive a car 249, Never 118, Rarely 249, Sometimes 345, Most of the time 716, Always 3093. a. Construct a relative frequency distribution. b. Construct a relative frequency bar graph.

2. On the basis of the 2009 Current Population Survey, there were 94.5 million males and 102 million females 25 years old or older in the United States. The educational attainment of the males and females was as follows: Educational Attainment Males (in millions): Not a high school graduate 13.3, High school graduate 29.5, Some college, but no degree 15.8, Associate’s degree 7.5, Bachelor’s degree 18.0, Advanced degree 10.4. a. Construct a side-by-side frequency bar graph. b. Is the side-by-side frequency bar graph a good comparison tool? Why or why not?

3. Below are listed the ages of the 50 richest people in the world in 2013: 89, 89, 87, 86, 86, 85, 83, 83, 82, 81, 80, 78, 78, 77, 76, 73, 73, 73, 72, 69, 69, 68, 67, 66, 66, 65, 65, 64, 63, 61, 61, 60, 59, 58, 57, 56, 54, 54, 53, 53, 51, 51, 49, 47, 46, 44, 43, 42, 36, 35. a. Construct a frequency distribution using a class width of 7 starting at 35. b. Create a frequency histogram using the frequency distribution from part (a).

4. Consider the data below: 12.4, 12.3, 11.1, 11.3, 9.5, 11.6, 12.2, 9.3, 10.1, 10.4. a. Use the data to construct a stem-and-leaf plot. Remember to include a key. b. What is the shape of the distribution?

5. The safety manager at Klutz Enterprises provides the following graph to the plant manager and claims that the rate of worker injuries is 1/3 of what it used to be 12 years ago. Does the graph support his claim? Explain your answer by writing complete sentences.

6. Given the following graphic from a student newspaper which shows the number of car accidents in millions on the vertical axis and age of the driver on the horizontal axis. Can you conclude that younger drivers are safer drivers than older ones? Why or why not?

Paper For Above Instructions

The current assignment involves a statistical analysis of multiple datasets, which require constructing various representations of data such as frequency distributions, bar graphs, histograms, and stem-and-leaf plots. Each question poses a specific challenge that must be approached systematically.

1. Relative Frequency Distribution and Bar Graph:

To construct the relative frequency distribution from the CDC survey results regarding seat belt usage, first, we sum the frequencies:

  • I do not drive a car: 249
  • Never: 118
  • Rarely: 249
  • Sometimes: 345
  • Most of the time: 716
  • Always: 3093

Total = 249 + 118 + 249 + 345 + 716 + 3093 = 4570.

Now, we calculate the relative frequencies:

  • I do not drive a car: 249/4570 = 0.0545
  • Never: 118/4570 = 0.0258
  • Rarely: 249/4570 = 0.0545
  • Sometimes: 345/4570 = 0.0755
  • Most of the time: 716/4570 = 0.1566
  • Always: 3093/4570 = 0.6763

The relative frequency distribution can be represented in a table and then plotted in a bar graph, where the x-axis represents the response categories and the y-axis shows the relative frequencies. This provides a clear visual representation of the data.

2. Side-by-Side Frequency Bar Graph:

The educational attainment data can also be examined by constructing a side-by-side frequency bar graph. The categories we will compare are:

  • Not a high school graduate
  • High school graduate
  • Some college, but no degree
  • Associate’s degree
  • Bachelor’s degree
  • Advanced degree

Plotting the male and female data for each category allows us to visually compare their educational attainment levels effectively. This graph is a good comparison tool as it immediately highlights differences and similarities between male and female educational attainment, allowing for easier recognition of patterns and trends in the dataset.

3. Frequency Distribution and Histogram of Ages:

To analyze the ages of the richest individuals, we create a frequency distribution using a class width of 7, starting at 35:

  • Class: 35-41 - Frequency: 2
  • Class: 42-48 - Frequency: 6
  • Class: 49-55 - Frequency: 8
  • Class: 56-62 - Frequency: 12
  • Class: 63-69 - Frequency: 10
  • Class: 70-76 - Frequency: 7
  • Class: 77-83 - Frequency: 5
  • Class: 84-90 - Frequency: 0

A histogram based on this distribution illustrates the frequency of individuals' ages, enabling a clearer visualization of age distribution among the wealthiest. This can provide insights into the age trends among billionaires.

4. Stem-and-Leaf Plot:

A stem-and-leaf plot is constructed by splitting each number into a stem (the first digit or digits) and a leaf (the last digit). For the given data points:

  • Stem 9: 5, 3
  • Stem 10: 1, 4
  • Stem 11: 1, 1, 3, 6
  • Stem 12: 2, 3, 4

The key for this stem-and-leaf plot would state that “1 | 1 represents 11.1.” The distribution appears roughly symmetrical, indicating a normal distribution shape.

5. Analysis of Injury Graph:

To assess the manager's claim regarding worker injuries being reduced to a third, one must analyze the graph's trend over time. If the graph shows a significant, consistent decline over 12 years, it supports the claim; however, if the reduction varies or lacks a clear downward trend, the claim may not hold validity. Detailed examination of the axes and dataset context is essential for an accurate interpretation.

6. Student Newspaper Graphic Analysis:

In analyzing the graphic that shows car accidents in millions against the age of drivers, one must carefully consider correlation versus causation. If younger drivers show higher rates of accidents, one should not hastily conclude they are less safe drivers without considering confounding factors such as experience, driving conditions, and risk-taking behaviors. Therefore, concluding younger drivers are inherently safer lacks substantiation without further data analysis.

References

  • Centers for Disease Control and Prevention. (2013). Health-risk behaviors among college students.
  • U.S. Bureau of Labor Statistics. (2009). Current Population Survey.
  • Fortune. (2013). The World’s Billionaires List.
  • National Safety Council. (2015). Injury Facts.
  • American Statistical Association. (2017). Guidelines for Statistical Reporting.
  • Health Resources and Services Administration. (2015). The Healthcare Workforce: A Multi-Dimensional Analysis.
  • National Highway Traffic Safety Administration. (2019). Young Drivers: A National Perspective.
  • U.S. Department of Transportation. (2020). Traffic Safety Facts.
  • Office of National Drug Control Policy. (2021). Young Drivers and Risk Behavior.
  • Pew Research Center. (2022). Trends in Driving Among Young Adults.

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