Name: ______________________________________________________ Unit 1: Exploring Data CHAPTER OBJECTIVES o Use a variety of graphical techniques to display a distribution. o Describe distributions in terms of center, unusual data, shape, and spread. o Explore the effects of a linear transformation of a data set. Chapter 1 Case Study: Do Pets or Friends Help Reduce Stress? To examine the effect of pets and friends in stressful situations, researchers recruited 45 women who said they were dog lovers. 15 women were assigned at random to each of 3 groups: to do a stressful task alone, with a good friend present, or with their dogs present. The stressful task was to count backward by 13’s or 17’s. The woman’s average heart rate during the task was one measure of the effect of stress. The table below shows the data. Average heart rates during stress with a pet (P), with a friend (F), and for the control group (C) Group Rate Group Rate Group Rate Group Rate P 69.169 P 68.862 C 84.738 C 75.477 F 99.692 C 87.231 C 84.877 C 62.646 P 70.169 P 64.169 P 58.692 P 70.077 C 80.369 C 91.754 P 79.662 F 88.015 C 87.446 C 87.785 P 69.231 F 81.600 P 75.985 F 91.354 C 73.277 F 86.985 F 83.400 F 100.877 C 84.523 F 92.492 F 102.154 C 77.800 C 70.877 P 72.262 P 86.446 P 97.538 F 89.815 P 65.446 F 80.277 P 85.000 F 98.200 C 90.015 F 101.062 F 76.908 C 99.046 F 97.046 P 69.538 Journal of Personality and Social Psychology Based on the data, does it appear that the presence of a pet or friend reduces heart rate during a stressful task?
Transcript
Name: ______________________________________________________ Unit 1: Exploring Data
CHAPTER OBJECTIVES o Use a variety of graphical techniques to display a distribution. o Describe distributions in terms of center, unusual data, shape, and spread. o Explore the effects of a linear transformation of a data set.
Chapter 1 Case Study: Do Pets or Friends Help Reduce Stress?To examine the effect of pets and friends in stressful situations, researchers recruited 45 women who said they were dog lovers. 15 women were assigned at random to each of 3 groups: to do a stressful task alone, with a good friend present, or with their dogs present. The stressful task was to count backward by 13’s or 17’s. The woman’s average heart rate during the task was one measure of the effect of stress. The table below shows the data.
Average heart rates during stress with a pet (P), with a friend (F), and for the control group (C)
Group Rate Group Rate Group Rate Group RateP 69.169 P 68.862 C 84.738 C 75.477F 99.692 C 87.231 C 84.877 C 62.646P 70.169 P 64.169 P 58.692 P 70.077C 80.369 C 91.754 P 79.662 F 88.015C 87.446 C 87.785 P 69.231 F 81.600P 75.985 F 91.354 C 73.277 F 86.985F 83.400 F 100.877 C 84.523 F 92.492F 102.154 C 77.800 C 70.877 P 72.262P 86.446 P 97.538 F 89.815 P 65.446F 80.277 P 85.000 F 98.200C 90.015 F 101.062 F 76.908C 99.046 F 97.046 P 69.538
Journal of Personality and Social Psychology
Based on the data, does it appear that the presence of a pet or friend reduces heart rate during a stressful task?
EXAMPLE 1:CensusAtSchool is an international project that collects data about primary and secondary school students using surveys. We used the site’s “Random Data Selector” to choose 10 Canadian students who completed the survey in a recent year. The table below displays the data. (p. 3 textbook)
a) Who are the individuals in this data set?
b) What variables are measured? Identify each as categorical or quantitative.
c) Describe the individual in the first row
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EXAMPLE 2:A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What do you think the chances are you will have much more than a middle-class income at age 30?” The table below shows the responses. (p. 11 textbook)
a) Use the data in the two-way table to calculate the marginal distribution (in percents) of opinions.
b) Make a graph to display the marginal distribution. Describe what you see.
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c) Calculate the conditional distribution of opinion among the young women, and describe this comparison with an appropriate graph.
EXAMPLE 3:In 1912 the luxury liner Titanic, on its first voyage across the Atlantic, struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table below gives information about adult passengers who lived and who died, by class of travel. (p.19 textbook)
The movie Titanic, starring Leonardo DiCaprio and Kate Winslet, suggested the following:First-class passengers received special treatment in boarding the lifeboats, while some other passengers were prevented from doing so (especially third-class passengers). Women and children boarded the lifeboats first, followed by the men.
1. What do the data tell us about these two suggestions? Give appropriate graphical and numerical evidence to support your answer.
2. How does gender affect the relationship between class of travel and survival status? Explain.
Displaying and Describing Quantitative Data with Graphs: Symmetric, Skewed Right, Skewed Left, Unimodal, Bimodal, Uniform, Stemplot, Dotplot, HistogramEXAMPLE 1:The Environmental Protection Agency (EPA) is in charge of determining and reporting fuel economy ratings for cars (think of those large window stickers on a new car). For years, consumers complained that their actual gas mileages were noticeably lower than the values reported by the EPA. It seems that the EPA’s tests—all of which are done on computerized devices to ensure consistency—did not consider things like outdoor temperature, use of the air conditioner, or realistic acceleration and braking by drivers. In 2008 the EPA changed the method for measuring a vehicle’s fuel economy to try to give more accurate estimates.
2012 Fuel Economy Guide, from the U.S. Environmental Protection Agency’s Web site at www.fueleconomy.gov.
Describe the distribution of the data sets below for sample of rolling a pair of six-sided dice and finding the sum 100 times, and the scores on an AP Statistics class’s first quiz.
EXAMPLE 3:
Describe the distribution of the data set below for a dotplot of the duration (in minutes) of 220 eruptions of the Old Faithful geyser.
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EXAMPLE 4
How many pairs of shoes does a typical teenager have? To find out, a group of AP Statistics students conducted a survey. They selected a random sample of 20 female students from their school. Then they recorded the number of pairs of shoes that each respondent reported having. Here are the data:
Make a stemplot and describe the data.
EXAMPLE 5
What if we want to compare the number of pairs of shoes that males and females have? Back-to-back stemplot comparing numbers of pairs of shoes for male and female students at a school below:
Compare the distributions of data.
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EXAMPLE 6
Here is a stemplot of the percents of residents aged 65 and older in the 50 states and the District of Columbia. The stems are whole percents and the leaves are tenths of a percent.
a) The low outlier is Alaska. What percent of Alaska residents are 65 or older?
b) Ignoring the outlier, the shape of the distribution is….
c) The center of the distribution is close to…
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Unit 1: Exploring Data HISTOGRAMSEXAMPLE 1:What is the difference between a bar graph and a histogram?
EXAMPLE 2:The following table presents the average points scored per game (PPG) for the 30 NBA teams in the 2012–2013 regular season. Make a dotplot to display the distribution of points per game. Then, use your dotplot to make a histogram of the distribution.
EXAMPLE 3:
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Unit 1: Exploring Data Group Sort: Graphs of student responses, in scrambled order and without scale markings. The figure below shows graphs of the student responses, in scrambled order and without scale markings. Which graph goes with each variable? Explain your reasoning. Which graph goes with each variable? Explain your reasoning.
(i) Are you female or male? (male = 0, female = 1)
Are you right-handed or left-handed? (right = 0, left = 1)
What is your height in inches? How many minutes do you study on a typical weeknight?
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Unit 1: Exploring Data Displaying and Describing Quantitative Data with Graphs: Symmetric, Skewed Right, Skewed Left, Unimodal, Bimodal, Uniform, Stemplot, Dotplot, Histogram
Unit 1: Exploring Data Describing Quantitative Data with Numbers: x, μ, resistant measure, Median, Range, IQR, Outlier
EXAMPLE 1:Here is data for the amount of fat (in grams) for McDonald’s beef sandwiches. Create a dotplot and describe the distribution.
a) Create a boxplot.
EXAMPLE 2:
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Unit 1: Exploring Data Barry Bonds set the major league record by hitting 73 home runs in a single season in 2001. On August 7, 2007, Bonds hit his 756th career home run, which broke Hank Aaron’s longstanding record of 755. By the end of the 2007 season when Bonds retired, he had increased the total to 762. Here are data on the number of home runs that Bonds hit in each of his 21 complete seasons. Make a boxplot and describe the data.
EXAMPLE 3:McDonald’s Fish and Chicken Sandwiches Here are data on the amount of fat (in grams) in 9different McDonald’s fish and chicken sandwiches. Create a dotplot and describe the distribution.
b) Create a back-to-back boxplot from Example 1 and compare the distributions.
EXAMPLE 4:A random sample of 5 students was asked how many minutes they spent doing HW the previous night. Here are their responses (in minutes): 0, 25, 30, 60, 90. Calculate and interpret the
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Unit 1: Exploring Data standard deviation.
Describing Quantitative Data with Numbers: x, μ, resistant measure, Median, Range, IQR, Outlier
Case Closed: Do Pets or Friends Help Reduce Stress?If you are a dog lover, having your dog with you may reduce your stress level. Does having a friend with you reduce stress? To examine the effect of pets and friends in stressful situations, researchers recruited 45 women who said they were dog lovers. 15 women were assigned at random to each of 3 groups: to do a stressful task alone, with a good friend present, or with their
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Unit 1: Exploring Data dogs present. The stressful task was to count backward by 13’s or 17’s. The woman’s average heart rate during the task was one measure of the effect of stress. The table below shows the data.Average heart rates during stress with a pet (P), with a friend (F), and for the control group (C)Group Rate Group Rate Group Rate Group RateP 69.169 P 68.862 C 84.738 C 75.477F 99.692 C 87.231 C 84.877 C 62.646P 70.169 P 64.169 P 58.692 P 70.077C 80.369 C 91.754 P 79.662 F 88.015C 87.446 C 87.785 P 69.231 F 81.600P 75.985 F 91.354 C 73.277 F 86.985F 83.400 F 100.877 C 84.523 F 92.492F 102.154 C 77.800 C 70.877 P 72.262P 86.446 P 97.538 F 89.815 P 65.446F 80.277 P 85.000 F 98.200C 90.015 F 101.062 F 76.908C 99.046 F 97.046 P 69.538
You will now use what you learned in this chapter to analyze the data…1. Construct an appropriate graph for comparing the heart rates of the women in the three
groups.
2. Calculate the numerical summaries for each group’s data. Which measures of center and spread would you choose to compare? Why?
3. Determine if there are any outliers in each of the three groups. Show your work.
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4. Write a few sentences comparing the distributions of heart rates for the women in the three groups.
5. Based on the data, does it appear that the presence of a pet or friend reduces heart rate during a stressful task? Justify your answer.
