demonstrate your knowledge of using statistical thinking
To demonstrate your knowledge of using statistical thinking in the process of data collection, complete the problems from Chapter 1 listed below.
• Section 2.1 – numbers 26a-c
• Section 2.2 – numbers 9a-e, 55, 60
• Section 2.3 – numbers 6, 8a-b
• Section 3.1 – numbers 24a-b, 16, 34
• Section 3.2 – numbers 36, 40
• Section 3.3 – numbers 4, 12
• Section 2.1 – numbers 26a-c
26.President’s State of Birth The following table lists the presidents of the United States (as of October 2010) and their state of birth.
Birthplace of U.S. President
President State of Birth
Washington Virginia
J. Adams Massachusetts
Jefferson Virginia
Madison Virginia
Monroe Virginia
J. Q. Adams Massachusetts
Jackson South Carolina
Van Buren New York
W. H. Harrison Virginia
Tyler Virginia
Polk North Carolina
Taylor Virginia
Fillmore New York
Pierce New Hampshire
Buchanan Pennsylvania
Lincoln Kentucky
A. Johnson North Carolina
Grant Ohio
Hayes Ohio
Garfield Ohio
Arthur Vermont
Cleveland New Jersey
B. Harrison Ohio
Cleveland New Jersey
McKinley Ohio
T. Roosevelt New York
Taft Ohio
Wilson Virginia
Harding Ohio
Coolidge Vermont
Hoover Iowa
F. D. Roosevelt New York
Truman Missouri
Eisenhower Texas
Kennedy Massachusetts
L. B. Johnson Texas
Nixon California
Ford Nebraska
Carter Georgia
Reagan Illinois
George H. Bush Massachusetts
Clinton Arkansas
George W. Bush Connecticut
Barack Obama Hawaii
• (a)Construct a frequency bar graph for state of birth.
• (b)Which state has yielded the most presidents?
• (c)Explain why the answer obtained in part (b) may be misleading.
• Section 2.2 – numbers 9a-e, 55, 60
• ORGANIZING QUANTITATIVE DATA: THE POPULAR DISPLAYS
9.Rolling the Dice An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The following frequency histogram gives the results.
• (a)What was the most frequent outcome of the experiment?
• (b)What was the least frequent?
• (c)How many times did we observe a 7?
• (d)How many more 5’s were observed than 4’s?
• (e)Determine the percentage of time a 7 was observed.
• (f)Describe the shape of the distribution.
55.Walt Disney Company The following data represent the stock price for the Walt Disney Company at the end of each month in 2010. Construct a time-series plot and comment on any trends. What was the percent change in the stock price of Disney from January 2010 to December 2010?
Date Closing Price Date Closing Price
1/10 28.71 7/10 30.72
2/10 28.99 8/10 31.55
3/10 31.34 9/10 32.68
4/10 35.01 10/10 36.13
5/10 31.00 11/10 36.51
6/10 31.36 12/10 37.51
60. Putting It Together: Which Graphical Summary? Suppose you just obtained data from a survey in which you learned the following information about 50 individuals: age, income, marital status, number of vehicles in household. For each variable, explain the type of graphical summary you might be able to draw to provide a visual summary of the data.
• Section 2.3 – numbers 6, 8a-b
6.Car Accidents An article in a student newspaper claims that younger drivers are safer than older drivers and provides the following graph to support the claim. Explain how this graph is misleading.
8.New Homes The time-series plot in the next column shows the number of new homes built in the Midwest from 2000 to 2009.
• (a)Describe how this graph is misleading.
• (b)What is the graph trying to convey?
• Section 3.1 – numbers 24a-b, 16, 34
24. Tour de Lance Lance Armstrong won the Tour de France seven consecutive years (1999-2005). The following table gives the winning times, distances, speeds, and margin of victory.
Year Winning Time (h) Distance (km) Winning Speed (km/h) Winning Margin (min)
1999 91.538 3687 40.28 7.617
2000 92.552 3662 39.56 6.033
2001 86.291 3453 40.02 6.733
2002 82.087 3278 39.93 7.283
2003 83.687 3427 40.94 1.017
2004 83.601 3391 40.56 6.317
2005 86.251 3593 41.65 4.667
Source: cyclingnews.com
• (a)Determine the mean and median of his winning times for the seven races.
• (b)Determine the mean and median of the distances for the seven races.
16.Flight Time The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on Continental Airlines.
282, 270, 260, 266, 257, 260, 267
Compute the mean, median, and mode flight time.
34.Mr. Zuro finds the mean height of all 14 students in his statistics class to be 68.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 65 inches tall. What is the mean height of the 15 students in the class?
• Section 3.2 – numbers 36, 40
36.Chebyshev’s Inequality According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following:
• (a)What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean?
• (b)What minimum percentage of commuters in Boston has a commute time within 1.5 standard deviations of the mean? What are the commute times within 1.5 standard deviations of the mean?
• (c)What is the minimum percentage of commuters who have commute times between 3 minutes and 51.6 minutes?
40. Identical Values Compute the sample standard deviation of the following test scores: 78, 78, 78, 78. What can be said about a data set in which all the values are identical?
• Section 3.3 – numbers 4, 12
4.Living in Poverty (See Problem 3.) The frequency distribution on the following page represents the age of people living in poverty in 2009 (in thousands). In this frequency distribution, the class widths are not the same for each class. Approximate the mean and standard deviation age of a person living in poverty. For the open-ended class 65 and older, use 70 as the class midpoint.
Age Frequency
0-17 15,451
18-24 6071
25-34 6123
35–44 4756
45-54 4421
55–59 1792
60-64 1520
65 and older 3433
12.Nut Mix Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can’t decide among peanuts, cashews, or almonds. They again agree to create a mix. They bought 2.5 pounds of peanuts for $1.30 per pound, 4 pounds of cashews for $4.50 per pound, and 2 pounds of almonds for $3.75 per pound. Determine the price per pound of the mix.