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Statistics for Business Economics

David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

Chapter 2

Descriptive Statistics: Tabular and Graphical Presentations - all with Video Answers

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Chapter Questions

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Problem 1

The response to a question has three alternatives: $A, B,$ and $C . A$ sample of 120 responses provides $60 \mathrm{A}, 24 \mathrm{B},$ and $36 \mathrm{C}$. Show the frequency and relative frequency distributions.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
09:27

Problem 2

A partial relative frequency distribution is given.
a. What is the relative frequency of class D?
b. The total sample size is $200 .$ What is the frequency of class D?
c. Show the frequency distribution.
d. Show the percent frequency distribution.

Mihir Nayar
Mihir Nayar
Numerade Educator
06:45

Problem 3

A questionnaire provides 58 Yes, 42 No, and 20 no-opinion answers.
a. In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers?
b. How many degrees would be in the section of the pie showing the No answers?
c. Construct a pie chart.
d. Construct a bar chart.

Sarah Wallace
Sarah Wallace
Numerade Educator
05:50

Problem 4

The top four prime-time television shows were Law \& Order, CSI, Without a Trace, and Desperate Housewives (Nielsen Media Research, January 1, 2007). Data indicating the preferred shows for a sample of 50 viewers follow.
$$\begin{array}{lllll}
\text { DH } & \text { CSI } & \text { DH } & \text { CSI } & \text { L\&O } \\
\text { Trace } & \text { CSI } & \text { L\&O } & \text { Trace } & \text { CSI } \\
\text { CSI } & \text { DH } & \text { Trace } & \text { CSI } & \text { DH } \\
\text { L\&O } & \text { L\&O } & \text { L\&O } & \text { CSI } & \text { DH } \\
\text { CSI } & \text { DH } & \text { DH } & \text { L\&O } & \text { CSI } \\
\text { DH } & \text { Trace } & \text { CSI } & \text { Trace } & \text { DH } \\
\text { DH } & \text { CSI } & \text { CSI } & \text { L\&O } & \text { CSI } \\
\text { L\&O } & \text { CSI } & \text { Trace } & \text { Trace } & \text { DH } \\
\text { L\&O } & \text { CSI } & \text { CSI } & \text { CSI } & \text { DH } \\
\text { CSI } & \text { DH } & \text { Trace } & \text { Trace } & \text { L\&O }
\end{array}$$
a. Are these data categorical or quantitative?
b. Provide frequency and percent frequency distributions.
c. Construct a bar chart and a pie chart.
d. On the basis of the sample, which television show has the largest viewing audience? Which one is second?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
06:58

Problem 5

In alphabetical order, the six most common last names in the United States are Brown, Davis, Johnson, Jones, Smith, and Williams (The World Almanac, 2006). Assume that a sample of 50 individuals with one of these last names provided the following data.
$$\begin{array}{llll}
\text { Brown } & \text { Williams } & \text { Williams } & \text { Williams } & \text { Brown } \\
\text { Smith } & \text { Jones } & \text { Smith } & \text { Johnson } & \text { Smith } \\
\text { Davis } & \text { Smith } & \text { Brown } & \text { Williams } & \text { Johnson } \\
\text { Johnson } & \text { Smith } & \text { Smith } & \text { Johnson } & \text { Brown } \\
\text { Williams } & \text { Davis } & \text { Johnson } & \text { Williams } & \text { Johnson } \\
\text { Williams } & \text { Johnson } & \text { Jones } & \text { Smith } & \text { Brown } \\
\text { Johnson } & \text { Smith } & \text { Smith } & \text { Brown } & \text { Jones } \\
\text { Jones } & \text { Jones } & \text { Smith } & \text { Smith } & \text { Davis } \\
\text { Davis } & \text { Jones } & \text { Williams } & \text { Davis } & \text { Smith } \\
\text { Jones } & \text { Johnson } & \text { Brown } & \text { Johnson } & \text { Davis }
\end{array}$$
Summarize the data by constructing the following:
a. Relative and percent frequency distributions
b. A bar chart
c. A pic chart
d. Based on these data, what are the three most common last names?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
04:20

Problem 6

The Nielsen Media Research television rating measures the percentage of television owners who are watching a particular television program. The highest-rated television program in television history was the $M^{*} A^{*} S^{*} H$ Last Episode Special shown on February 28,1983 A 60.2 rating indicated that $60.2 \%$ of all television owners were watching this program. Nielsen Media Research provided the list of the 50 top-rated single shows in television history (The New York Times Almanac, 2006). The following data show the television network that produced each of these 50 top-rated shows.
$$\begin{array}{lllll}
\mathrm{ABC} & \text { ABC } & \text { ABC } & \text { NBC } & \text { CBS } \\
\text { ABC } & \text { CBS } & \text { ABC } & \text { ABC } & \text { NBC } \\
\text { NBC } & \text { NBC } & \text { CBS } & \text { ABC } & \text { NBC } \\
\text { CBS } & \text { ABC } & \text { CBS } & \text { NBC } & \text { ABC } \\
\text { CBS } & \text { NBC } & \text { NBC } & \text { CBS } & \text { NBC } \\
\text { CBS } & \text { CBS } & \text { CBS } & \text { NBC } & \text { NBC } \\
\text { FOX } & \text { CBS } & \text { CBS } & \text { ABC } & \text { NBC } \\
\text { ABC } & \text { ABC } & \text { CBS } & \text { NBC } & \text { NBC } \\
\text { NBC } & \text { CBS } & \text { NBC } & \text { CBS } & \text { CBS } \\
\text { ABC } & \text { CBS } & \text { ABC } & \text { NBC } & \text { ABC }
\end{array}$$
a. Construct a frequency distribution, percent frequency distribution, and bar chart for the data.
b. Which network or networks have done the best in terms of presenting top-rated television shows? Compare the performance of ABC, CBS, and NBC.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
02:51

Problem 7

Leverock's Waterfront Steakhouse in Maderia Beach, Florida, uses a questionnaire to ask customers how they rate the server, food quality, cocktails, prices, and atmosphere at the restaurant. Each characteristic is rated on a scale of outstanding (O), very good (V), good (G), average (A), and poor (P). Use descriptive statistics to summarize the following data collected on food quality. What is your feeling about the food quality ratings at the restaurant?
$$\left.\begin{array}{lllllllllllll}
G & O & V & G & A & O & V & O & V & G & O & V & A \\
V & O & P & V & O & G & A & O & O & O & G & O & V \\
V & A & G & O & V & P & V & O & O & G & O & O & V \\
O & G & A & O & V & O & O & G & V & A & G & &
\end{array}\right]$$

Pratyush Raitan
Pratyush Raitan
Numerade Educator
08:19

Problem 8

Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R).
$$\begin{array}{ccccccccccccccc}
\mathrm{L} & \mathrm{P} & \mathrm{C} & \mathrm{H} & 2 & \mathrm{P} & \mathrm{R} & 1 & \mathrm{S} & \mathrm{S} & 1 & \mathrm{L} & \mathrm{P} & \mathrm{R} & \mathrm{P} \\
\mathrm{P} & \mathrm{P} & \mathrm{P} & \mathrm{R} & \mathrm{C} & \mathrm{S} & \mathrm{L} & \mathrm{R} & \mathrm{P} & \mathrm{C} & \mathrm{C} & \mathrm{P} & \mathrm{P} & \mathrm{R} & \mathrm{P} \\
2 & 3 & \mathrm{P} & \mathrm{H} & \mathrm{L} & \mathrm{P} & 1 & \mathrm{C} & \mathrm{P} & \mathrm{P} & \mathrm{P} & \mathrm{S} & 1 & \mathrm{L} & \mathrm{R} \\
\mathrm{R} & 1 & 2 & \mathrm{H} & \mathrm{S} & 3 & \mathrm{H} & 2 & \mathrm{L} & \mathrm{P} & & & & &
\end{array}$$
a. Use frequency and relative frequency distributions to summarize the data.
b. What position provides the most Hall of Famers?
c. What position provides the fewest Hall of Famers?
d. What outfield position (L, C, or R) provides the most Hall of Famers?
e. Compare infielders $(1,2,3, \text { and } S)$ to outfielders (L, $C,$ and $R$ ).

Pratyush Raitan
Pratyush Raitan
Numerade Educator
08:07

Problem 9

The Pew Research Center's Social \& Demographic Trends project found that $46 \%$ of U.S. adults would rather live in a different type of community than the one where they are living now (Pew Research Center, January 29,2009 ). The national survey of 2260 adults asked: "Where do you live now?" and "What do you consider to be the ideal community?" Response options were City (C), Suburb (S), Small Town (T), or Rural (R). A representative portion of this survey for a sample of 100 respondents is as follows.
Where do you live now?
$$\begin{array}{lllllllllllllll}
\mathrm{S} & \mathrm{T} & \mathrm{R} & \mathrm{C} & \mathrm{R} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{T} \\
\mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{C} \\
\mathrm{T} & \mathrm{R} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{R} \\
\mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{S} & \mathrm{C} \\
\mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{R} \\
\mathrm{C} & \mathrm{T} & \mathrm{R} & \mathrm{R} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{S} & \mathrm{R} & \mathrm{T} \\
\mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & & & & &
\end{array}$$
What do you consider to be the ideal community?
$$\begin{array}{lllllllllllllll}
\mathrm{S} & \mathrm{C} & \mathrm{R} & \mathrm{R} & \mathrm{R} & \mathrm{S} & \mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{T} \\
\mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{R} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{S} \\
\mathrm{S} & \mathrm{R} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{R} & \mathrm{C} & \mathrm{T} & \mathrm{S} & \mathrm{R} & \mathrm{R} & \mathrm{R} \\
\mathrm{C} & \mathrm{T} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{R} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{R} & \mathrm{S} & \mathrm{S} \\
\mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{R} \\
\mathrm{C} & \mathrm{S} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{C} & \mathrm{R} & \mathrm{T} \\
\mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{R} & & & & &
\end{array}$$
a. Provide a percent frequency distribution for each question.
b. Construct a bar chart for each question.
c. Where are most adults living now?
d. Where do most adults consider the ideal community?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
10:46

Problem 10

The Financial Times/Harris Poll is a monthly online poll of adults from six countries in Europe and the United States. The poll conducted in January 2008 included 1015 adults. One of the questions asked was, "How would you rate the Federal Bank in handling the credit problems in the financial markets?" Possible responses were Excellent, Good, Fair, Bad, and Terrible (Harris Interactive website, January 2008 ). The 1015 responses for this question can be found in the data file named FedBank.
a. $\quad$ Construct a frequency distribution.
b. Construct a percent frequency distribution.
c. Construct a bar chart for the percent frequency distribution.
d. Comment on how adults in the United States think the Federal Bank is handling the credit problems in the financial markets.
e. In Spain, 1114 adults were asked," How would you rate the European Central Bank in handling the credit problems in the financial markets?" The percent frequency distribution obtained follows:

Pratyush Raitan
Pratyush Raitan
Numerade Educator
01:48

Problem 11

Consider the following data.
$$\begin{array}{lllll}
14 & 21 & 23 & 21 & 16 \\
19 & 22 & 25 & 16 & 16 \\
24 & 24 & 25 & 19 & 16 \\
19 & 18 & 19 & 21 & 12 \\
16 & 17 & 18 & 23 & 25 \\
20 & 23 & 16 & 20 & 19 \\
24 & 26 & 15 & 22 & 24 \\
20 & 22 & 24 & 22 & 20
\end{array}$$
a. Develop a frequency distribution using classes of $12-14,15-17,18-20,21-23,$ and $24-26$
b. Develop a relative frequency distribution and a percent frequency distribution using the classes in part (a).

Nick Johnson
Nick Johnson
Numerade Educator
03:43

Problem 12

Consider the following frequency distribution.
Construct a cumulative frequency distribution and a cumulative relative frequency distribution.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
05:38

Problem 13

Construct a histogram and an ogive for the data in exercise 12

Pratyush Raitan
Pratyush Raitan
Numerade Educator
07:31

Problem 14

Consider the following data.
$$\begin{array}{rrrrrrrrr}
8.9 & 10.2 & 11.5 & 7.8 & 10.0 & 12.2 & 13.5 & 14.1 & 10.0 & 12.2 \\
6.8 & 9.5 & 11.5 & 11.2 & 14.9 & 7.5 & 10.0 & 6.0 & 15.8 & 11.5
\end{array}$$
a. Construct a dot plot.
b. Construct a frequency distribution.
c. Construct a percent frequency distribution.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
07:23

Problem 15

A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period.
$$2 \quad 5 \quad 10 \quad 12 \quad 4 \quad 4 \quad 5 \quad 17 \quad 11 \quad 8 \quad 9 \quad 8 \quad 12 \quad 21 \quad 6 \quad 8 \quad 7 \quad 13 \quad 18 \quad 3$$
Use classes of $0-4,5-9,$ and so on in the following:
a. Show the frequency distribution.
b. Show the relative frequency distribution.
c. Show the cumulative frequency distribution.
d. Show the cumulative relative frequency distribution.
e. What proportion of patients needing emergency service wait 9 minutes or less?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
07:01

Problem 16

A shortage of candidates has required school districts to pay higher salaries and offer extras to attract and retain school district superintendents. The following data show the annual base salary $(\$ 1000 \mathrm{s})$ for superintendents in 20 districts in the greater Rochester, New York, area (The Rochester Democrat and Chronicle, February 10,2008 ).
$$\begin{array}{llll}
187 & 184 & 174 & 185 \\
175 & 172 & 202 & 197 \\
165 & 208 & 215 & 164 \\
162 & 172 & 182 & 156 \\
172 & 175 & 170 & 183
\end{array}$$
Use classes of $150-159,160-169,$ and so on in the following.
a. Show the frequency distribution.
b. Show the percent frequency distribution.
c. Show the cumulative percent frequency distribution.
d. Develop a histogram for the annual base salary.
e. Do the data appear to be skewed? Explain.
f. What percentage of the superintendents make more than $\$ 200,000 ?$

Hira Hussain
Hira Hussain
Numerade Educator
07:23

Problem 17

The Dow Jones Industrial Average (DJIA) underwent one of its infrequent reshufflings of companies when General Motors and Citigroup were replaced by Cisco Systems and Travelers (The Wall Street Journal, June 8,2009 ). At the time, the prices per share for the 30 companies in the DJIA were as follows:
a. What is the highest price per share? What is the lowest price per share?
b. Using a class width of $10,$ develop a frequency distribution for the data.
c. Prepare a histogram. Interpret the histogram, including a discussion of the general shape of the histogram, the midprice range, and the most frequent price range.
d. Use the The Wall Street Journal or another newspaper to find the current price per share for these companies. Prepare a histogram of the data and discuss any changes since June $2009 .$ What company has had the largest increase in the price per share? What company has had the largest decrease in the price per share?

Rebecca Wickersham
Rebecca Wickersham
Numerade Educator
02:03

Problem 18

NRF/BIG research provided results of a consumer holiday spending survey (USA Today, December 20,2005 ). The following data provide the dollar amount of holiday spending for a sample of 25 consumers.
$$\begin{array}{rrrrr}
1200 & 850 & 740 & 590 & 340 \\
450 & 890 & 260 & 610 & 350 \\
1780 & 180 & 850 & 2050 & 770 \\
800 & 1090 & 510 & 520 & 220 \\
1450 & 280 & 1120 & 200 & 350
\end{array}$$
a. What is the lowest holiday spending? The highest?
b. Use a class width of $\$ 250$ to prepare a frequency distribution and a percent frequency distribution for the data.
c. Prepare a histogram and comment on the shape of the distribution.
d. What observations can you make about holiday spending?

Alexander Cheng
Alexander Cheng
Numerade Educator
03:11

Problem 19

Sorting through unsolicited e-mail and spam affects the productivity of office workers. An InsightExpress survey monitored office workers to determine the unproductive time per day devoted to unsolicited e-mail and spam (USA Today, November 13,2003 ). The following data show a sample of time in minutes devoted to this task.
$$\begin{array}{rrrr}
2 & 4 & 8 & 4 \\
8 & 1 & 2 & 32 \\
12 & 1 & 5 & 7 \\
5 & 5 & 3 & 4 \\
24 & 19 & 4 & 14
\end{array}$$
Summarize the data by constructing the following:
a. A frequency distribution (classes $1-5,6-10,11-15,16-20, \text { and so on })$
b. $\quad$ A relative frequency distribution
c. $\quad$ A cumulative frequency distribution
d. A cumulative relative frequency distribution
c. An ogive
f. What percentage of office workers spend 5 minutes or less on unsolicited e-mail and spam? What percentage of office workers spend more than 10 minutes a day on this task?

Jon Southam
Jon Southam
Numerade Educator
11:25

Problem 20

The Golf Digest 50 lists the 50 professional golfers with the highest total annual income. Total income is the sum of both on-course and off-course earnings. Tiger Woods ranked first with a total annual income of $\$ 122$ million. However, almost $\$ 100$ million of this total was from off-course activities such as product endorsements and personal appearances. The 10 professional golfers with the highest off-course income are shown in the following table (Golf Digest website, February 2008 ).
The off-course income of all 50 professional golfers in the Golf Digest 50 can be found on the website that accompanies the text. The income data are in $\$ 1000$ s. Use classes of $0-4999,5000-9999,10,000-14,999,$ and so on to answer the following questions. Include an open-ended class of 50,000 or more as the largest income class.
a. Construct a frequency distribution and percent frequency distribution of the annual off-course income of the 50 professional golfers.
b. Construct a histogram for these data.
c. Comment on the shape of the distribution of off-course income.
d. What is the most frequent off-course income class for the 50 professional golfers? Using your tabular and graphical summaries, what additional observations can you make about the off-course income of these 50 professional golfers?

Mihir Nayar
Mihir Nayar
Numerade Educator
13:39

Problem 21

The Nielsen Home Technology Report provided information about home technology and its usage. The following data are the hours of personal computer usage during one week for a sample of 50 persons.
$$\begin{array}{rrrrrrrrr}
4.1 & 1.5 & 10.4 & 5.9 & 3.4 & 5.7 & 1.6 & 6.1 & 3.0 & 3.7 \\
3.1 & 4.8 & 2.0 & 14.8 & 5.4 & 4.2 & 3.9 & 4.1 & 11.1 & 3.5 \\
4.1 & 4.1 & 8.8 & 5.6 & 4.3 & 3.3 & 7.1 & 10.3 & 6.2 & 7.6 \\
10.8 & 2.8 & 9.5 & 12.9 & 12.1 & 0.7 & 4.0 & 9.2 & 4.4 & 5.7 \\
7.2 & 6.1 & 5.7 & 5.9 & 4.7 & 3.9 & 3.7 & 3.1 & 6.1 & 3.1
\end{array}$$
Summarize the data by constructing the following:
a. A frequency distribution (use a class width of three hours)
b. $\quad$ A relative frequency distribution
c. A histogram
d. An ogive
e. Comment on what the data indicate about personal computer usage at home.

Danielle Ashley
Danielle Ashley
Numerade Educator
03:09

Problem 22

Construct a stem-and-leaf display for the following data.
$$\begin{array}{ccccccc}
70 & 72 & 75 & 64 & 58 & 83 & 80 & 82 \\
76 & 75 & 68 & 65 & 57 & 78 & 85 & 72
\end{array}$$

Pratyush Raitan
Pratyush Raitan
Numerade Educator
04:07

Problem 23

Construct a stem-and-leaf display for the following data.
$$\begin{array}{cccccc}
11.3 & 9.6 & 10.4 & 7.5 & 8.3 & 10.5 & 10.0 \\
9.3 & 8.1 & 7.7 & 7.5 & 8.4 & 6.3 & 8.8
\end{array}$$

Pratyush Raitan
Pratyush Raitan
Numerade Educator
03:22

Problem 24

Construct a stem-and-leaf display for the following data. Use a leaf unit of 10 .
$$\begin{array}{lllllll}
1161 & 1206 & 1478 & 1300 & 1604 & 1725 & 1361 & 1422 \\
1221 & 1378 & 1623 & 1426 & 1557 & 1730 & 1706 & 1689
\end{array}$$

Pratyush Raitan
Pratyush Raitan
Numerade Educator
05:46

Problem 25

A psychologist developed a new test of adult intelligence. The test was administered to
20 individuals, and the following data were obtained.
$$\begin{array}{ccccccccc}
114 & 99 & 131 & 124 & 117 & 102 & 106 & 127 & 119 & 115 \\
98 & 104 & 144 & 151 & 132 & 106 & 125 & 122 & 118 & 118
\end{array}$$
Construct a stem-and-leaf display for the data.

Evelyn Cunningham
Evelyn Cunningham
Numerade Educator
13:50

Problem 26

The American Association of Individual Investors conducts an annual survey of discount brokers. The following prices charged are from a sample of 24 discount brokers (AAII Journal, January 2003 ). The two types of trades are a broker-assisted trade of 100 shares at $\$ 50$ per share and an online trade of 500 shares at $\$ 50$ per share.
a. Round the trading prices to the nearest dollar and develop a stem-and-leaf display for 100 shares at $\$ 50$ per share. Comment on what you learned about broker-assisted trading prices.
b. Round the trading prices to the nearest dollar and develop a stretched stem-and-leaf display for 500 shares online at $\$ 50$ per share. Comment on what you learned about online trading prices.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
04:33

Problem 27

Most major ski resorts offer family programs that provide ski and snowboarding instruction for children. The typical classes provide four to six hours on the snow with a certified instructor. The daily rate for a group lesson at 15 ski resorts follows (The Wall Street Journal, January 20,2006 ).
a. Develop a stem-and-leaf display for the data.
b. Interpret the stem-and-leaf display in terms of what it tells you about the daily rate for these ski and snowboarding instruction programs.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
10:00

Problem 28

The 2004 Naples, Florida, minimarathon $(13.1 \text { miles) had } 1228$ registrants (Naples Daily News, January 17,2004 ). Competition was held in six age groups. The following data show the ages for a sample of 40 individuals who participated in the marathon.
$$\begin{aligned}
&4\\
&\text { A }\\
&\begin{array}{lllll}
49 & 33 & 40 & 37 & 56 \\
44 & 46 & 57 & 55 & 32 \\
50 & 52 & 43 & 64 & 40 \\
46 & 24 & 30 & 37 & 43 \\
31 & 43 & 50 & 36 & 61 \\
27 & 44 & 35 & 31 & 43 \\
52 & 43 & 66 & 31 & 50 \\
72 & 26 & 59 & 21 & 47
\end{array}
\end{aligned}$$
a. Show a stretched stem-and-leaf display.
b. What age group had the largest number of runners?
c. What age occurred most frequently?
d. A Naples Daily News feature article emphasized the number of runners who were "20something." What percentage of the runners were in the 20 -something age group? What do you suppose was the focus of the article?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
02:23

Problem 29

The following data are for 30 observations involving two qualitative variables, $x$ and $y$. The categories for $x$ are $\mathrm{A}, \mathrm{B},$ and $\mathrm{C} ;$ the categories for $y$ are 1 and 2
a. Develop a crosstabulation for the data, with $x$ as the row variable and $y$ as the column variable.
b. Compute the row percentages.
c. Compute the column percentages.
d. What is the relationship, if any, between $x$ and $y ?$

Jorge Villanueva
Jorge Villanueva
Numerade Educator
05:55

Problem 30

The following 20 observations are for two quantitative variables, $x$ and $y$
a. Develop a scatter diagram for the relationship between $x$ and $y$
b. What is the relationship, if any, between $x$ and $y ?$

Mihir Nayar
Mihir Nayar
Numerade Educator
04:36

Problem 31

The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States: 2008 ).
a. Compute the row percentages and identify the percent frequency distributions of income for households in which the head is a high school graduate and in which the head holds a bachelor's degree.
b. What percentage of households headed by high school graduates earn $\$ 75,000$ or more? What percentage of households headed by bachelor's degree recipients earn $\$ 75,000$ or more?
c. Construct percent frequency histograms of income for households headed by persons with a high school degree and for those headed by persons with a bachelor's degree. Is any relationship evident between household income and educational level?

Hira Hussain
Hira Hussain
Numerade Educator
03:06

Problem 32

Refer again to the crosstabulation of houschold income by educational level shown in exercise 31
a. Compute column percentages and identify the percent frequency distributions displayed. What percentage of the heads of households did not graduate from high school?
b. What percentage of the households earning $\$ 100,000$ or more were headed by a person having schooling beyond a bachelor's degree? What percentage of the households headed by a person with schooling beyond a bachelor's degree earned over $\$ 100,000 ?$ Why are these two percentages different?
c. Compare the percent frequency distributions for those households earning "Under $25, " * 100$ or more," and for "Total." Comment on the relationship between household income and educational level of the head of household.

Hira Hussain
Hira Hussain
Numerade Educator
04:33

Problem 33

Recently, management at Oak Tree Golf Course received a few complaints about the condition of the greens. Several players complained that the greens are too fast. Rather than react to the comments of just a few, the Golf Association conducted a survey of 100 male and 100 female golfers. The survey results are summarized here.
a. Combine these two crosstabulations into one with Male and Female as the row labels and Too Fast and Fine as the column labels. Which group shows the highest percentage saying that the greens are too fast?
b. Refer to the initial crosstabulations. For those players with low handicaps (better players), which group (male or female) shows the highest percentage saying the greens are too fast?
c. Refer to the initial crosstabulations. For those players with higher handicaps, which group (male or female) shows the highest percentage saying the greens are too fast?
d. What conclusions can you draw about the preferences of men and women concerning the speed of the greens? Are the conclusions you draw from part (a) as compared with parts (b) and
(c) consistent? Explain any apparent inconsistencies.

Jorge Villanueva
Jorge Villanueva
Numerade Educator
02:00

Problem 34

Table 2.13 shows a data set containing information for 45 mutual funds that are part of the Morningstar Funds500 for 2008. The data set includes the following five variables:

Fund Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income)
Net Asset Value (\$): The closing price per share
5-Year Average Return (\%): The average annual return for the fund over the past 5 years
Expense Ratio (\%): The percentage of assets deducted each fiscal year for fund expenses
Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of $1-$ Star to a high of 5 -Stars
a. Prepare a crosstabulation of the data on Fund Type (rows) and the average annual return over the past 5 years (columns). Use classes of $0-9.99,10-19.99,20-29.99$ $30-39.99,40-49.99,$ and $50-59.99$ for the 5 -Year Average Return ( $\%$ ).
b. Prepare a frequency distribution for the data on Fund Type.
c. Prepare a frequency distribution for the data on 5-Year Average Return (\%).
d. How has the crosstabulation helped in preparing the frequency distributions in parts
(b) and (c)?
e. What conclusions can you draw about the fund type and the average return over the past 5 years?

Dominador Tan
Dominador Tan
Numerade Educator
04:37

Problem 35

Refer to the data in Table 2.13
a. Prepare a crosstabulation of the data on Fund Type (rows) and the expense ratio (columns). Use classes of $.25-.49, .50-.74, .75-.99,1.00-1.24,$ and $1.25-1.49$ for Expense Ratio (\%).
b. Prepare a percent frequency distribution for Expense Ratio (\%).
c. What conclusions can you draw about fund type and the expense ratio?

Tim Schmuhl
Tim Schmuhl
Numerade Educator
11:32

Problem 36

Refer to the data in Table 2.13
a. Prepare a scatter diagram with 5 -Year Average Return (\%) on the horizontal axis and Net Asset Value (\$) on the vertical axis.
b. Comment on the relationship, if any, between the variables.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
07:46

Problem 37

The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (Fuel Economy website, February 22,2008 ). A portion of the data for 311 compact, midsize, and large cars is shown in Table 2.14 . The data set contains the following variables:
Size: $\quad$ Compact, Midsize, and Large
Displacement: Engine size in liters
Cylinders: Number of cylinders in the engine
Drive: Front wheel (F), rear wheel (R), and four wheel (4)
Fuel Type: Premium (P) or regular (R) fuel
City MPG: Fuel efficiency rating for city driving in terms of miles per gallon
Hwy MPG: Fuel efficiency rating for highway driving in terms of miles per gallon
The complete data set is contained in the file named FuelData08.
a. Prepare a crosstabulation of the data on Size (rows) and Hwy MPG (columns). Use classes of $15-19,20-24,25-29,30-34,$ and $35-39$ for Hwy MPG.
b. Comment on the relationship beween Size and Hwy MPG.
c. Prepare a crosstabulation of the data on Drive (rows) and City MPG (columns). Use classes of $5-9,10-14,15-19,20-24,25-29,30-34,$ and $35-39$ for City MPG.
d. Comment on the relationship between Drive and City MPG.
e. Prepare a crosstabulation of the data on Fuel Type (rows) and City MPG (columns). Use classes of $5-9,10-14,15-19,20-24,25-29,30-34,$ and $35-39$ for City MPG.
f. Comment on the relationship between Fuel Type and City MPG.

Tim Schmuhl
Tim Schmuhl
Numerade Educator
04:07

Problem 38

Refer to exercise 37 and the data in the file named FuelData08.
a. Prepare a crosstabulation of the data on Displacement (rows) and Hwy MPG (columns). Use classes of $1.0-2.9,3.0-4.9,$ and $5.0-6.9$ for Displacement. Use classes of $15-19,20-24,25-29,30-34,$ and $35-39$ for Hwy MPG.
b. Comment on the relationship, if any, between Displacement and Hwy MPG.
c. Develop a scatter diagram of the data on Displacement and Hwy MPG. Use the vertical axis for Hwy MPG.
d. What does the scatter diagram developed in part (c) indicate about the relationship, if any, between Displacement and Hwy MPG?
e. In investigating the relationship between Displacement and Hwy MPG you developed a tabular summary of the data (crosstabulation) and a graphical summary (scatter diagram). In this case which approach do you prefer? Explain.

Tim Schmuhl
Tim Schmuhl
Numerade Educator
04:07

Problem 38

Refer to exercise 37 and the data in the file named FuelData08.
a. Prepare a crosstabulation of the data on Displacement (rows) and Hwy MPG (columns). Use classes of $1.0-2.9,3.0-4.9,$ and $5.0-6.9$ for Displacement. Use classes of $15-19,20-24,25-29,30-34,$ and $35-39$ for Hwy MPG.
b. Comment on the relationship, if any, between Displacement and Hwy MPG.
c. Develop a scatter diagram of the data on Displacement and Hwy MPG. Use the vertical axis for Hwy MPG.
d. What does the scatter diagram developed in part (c) indicate about the relationship, if any, between Displacement and Hwy MPG?
e. In investigating the relationship between Displacement and Hwy MPG you developed a tabular summary of the data (crosstabulation) and a graphical summary (scatter diagram). In this case which approach do you prefer? Explain.

Tim Schmuhl
Tim Schmuhl
Numerade Educator
07:39

Problem 39

The Higher Education Research Institute at UCLA provides statistics on the most popular majors among incoming college freshmen. The five most popular majors are Arts and Humanities (A), Business Administration
(B), Engineering (E), Professional (P), and Social Science
(S) (The New York Times Almanac, 2006). A broad range of other (O) majors, including biological science, physical science, computer science, and education, are grouped together. The majors selected for a sample of 64 college freshmen follow.
$$\begin{array}{llllllllllllllll}
\mathrm{S} & \mathrm{P} & \mathrm{P} & \mathrm{O} & \mathrm{B} & \mathrm{E} & \mathrm{O} & \mathrm{E} & \mathrm{P} & \mathrm{O} & \mathrm{O} & \mathrm{B} & \mathrm{O} & \mathrm{O} & \mathrm{O} & \mathrm{A} \\
\mathrm{O} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{S} & \mathrm{O} & \mathrm{B} & \mathrm{O} & \mathrm{A} & \mathrm{O} & \mathrm{E} & \mathrm{O} & \mathrm{E} & \mathrm{O} & \mathrm{B} & \mathrm{P} \\
\mathrm{B} & \mathrm{A} & \mathrm{S} & \mathrm{O} & \mathrm{E} & \mathrm{A} & \mathrm{B} & \mathrm{O} & \mathrm{S} & \mathrm{S} & \mathrm{O} & \mathrm{O} & \mathrm{E} & \mathrm{B} & \mathrm{O} & \mathrm{B} \\
\mathrm{A} & \mathrm{E} & \mathrm{B} & \mathrm{E} & \mathrm{A} & \mathrm{A} & \mathrm{P} & \mathrm{O} & \mathrm{O} & \mathrm{E} & \mathrm{O} & \mathrm{B} & \mathrm{B} & \mathrm{O} & \mathrm{P} & \mathrm{B}
\end{array}$$
a. Show a frequency distribution and percent frequency distribution.
b. Show a bar chart.
c. What percentage of freshmen select one of the five most popular majors?
d. What is the most popular major for incoming freshmen? What percentage of freshmen select this major?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
16:29

Problem 40

General Motors had a $23 \%$ share of the automobile industry with sales coming from eight divisions: Buick, Cadillac, Chevrolet, GMC, Hummer, Pontiac, Saab, and Saturn (Forbes, December 22,2008 . The data set GMSales shows the sales for a sample of 200 General Motors vehicles. The division for the vehicle is provided for each sale.
a. Show the frequency distribution and the percent frequency distribution of sales by division for General Motors.
b. Show a bar chart of the percent frequency distribution.
c. Which General Motors division was the company leader in sales? What was the percentage of sales for this division? Was this General Motors' most important division? Explain.
d. Due to the ongoing recession, high gasoline prices, and the decline in automobile sales, General Motors was facing bankruptcy in $2009 .$ A government "bail-out" loan and a restructuring of the company were anticipated. Expectations were that General Motors could not continue to operate all eight divisions. Based on the percentage of sales, which of the eight divisions looked to be the best candidates for General Motors to discontinue? Which divisions looked to be the least likely candidates for General Motors to discontinue?

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:16

Problem 41

Dividend yield is the annual dividend paid by a company expressed as a percentage of the price of the stock (Dividend/Stock Price $\times 100$ ). The dividend yield for the Dow Jones Industrial Average companies is shown in Table 2.15 (The Wall Street Journal, June 8,2009 ).
a. Construct a frequency distribution and percent frequency distribution.
b. Construct a histogram.
c. Comment on the shape of the distribution.
d. What do the tabular and graphical summaries tell about the dividend yields among the Dow Jones Industrial Average companies?
e. What company has the highest dividend yield? If the stock for this company currently sells for $\$ 20$ per share and you purchase 500 shares, how much dividend income will this investment generate in one year?

Hira Hussain
Hira Hussain
Numerade Educator
01:09

Problem 42

Approximately 1.5 million high school students take the Scholastic Aptitude Test (SAT) each year and nearly $80 \%$ of the college and universities without open admissions policies use SAT scores in making admission decisions (College Board, March 2009 ). The current version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is $2400 .$ A sample of SAT scores for the combined three-part SAT are as follows: version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is $2400 .$ A sample of SAT scores for the combined three-part SAT are as follows:

Maxime Rossetti
Maxime Rossetti
Numerade Educator
04:47

Problem 43

The Pittsburgh Steelers defeated the Arizona Cardinals 27 to 23 in professional football's 43rd Super Bowl. With this win, its sixth championship, the Pittsburgh Steelers became the team with the most wins in the 43 -year history of the event (Tampa Tribune, February 2
2009 ). The Super Bowl has been played in eight different states: Arizona (AZ), California
(CA), Florida (FL), Georgia (GA), Louisiana (LA), Michigan (MI), Minnesota (MN), and Texas (TX). Data in the following table show the state where the Super Bowls were played and the point margin of victory for the winning team.
a. Show a frequency distribution and bar chart for the state where the Super Bowl was played.
b. What conclusions can you draw from your summary in part (a)? What percentage of Super Bowls were played in the states of Florida or California? What percentage of Super Bowls were played in northern or cold-weather states?
c. Show a stretched stem-and-leaf display for the point margin of victory for the winning team. Show a histogram.
d. What conclusions can you draw from your summary in part (c)? What percentage of Super Bowls have been close games with the margin of victory less than 5 points? What percentage of Super Bowls have been won by 20 or more points?
e. The closest Super Bowl occurred when the New York Giants beat the Buffalo Bills. Where was this game played and what was the winning margin of victory? The biggest point margin in Super Bowl history occurred when the San Francisco 49 ers beat the Denver Broncos. Where was this game played and what was the winning margin of victory?

Bryan Meares
Bryan Meares
Numerade Educator
10:22

Problem 44

Data from the U.S. Census Bureau provides the population by state in millions of people (The World Almanac, 2006).
a. Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million.
b. Discuss the skewness in the distribution.
c. What observations can you make about the population of the 50 states?

Mihir Nayar
Mihir Nayar
Numerade Educator
03:31

Problem 45

Drug Store News (September 2002) provided data on annual pharmacy sales for the leading pharmacy retailers in the United States. The following data are annual sales in millions.
a. Show a stem-and-leaf display.
b. Identify the annual sales levels for the smallest, medium, and largest drug retailers.
c. What are the two largest drug retailers?

Sarah Wallace
Sarah Wallace
Numerade Educator
08:12

Problem 46

The daily high and low temperatures for 20 cities follow (USA Today, March 3, 2006).
a. Prepare a stem-and-leaf display of the high temperatures.
b. Prepare a stem-and-leaf display of the low temperatures.
c. Compare the two stem-and-leaf displays and make comments about the difference between the high and low temperatures.
d. Provide a frequency distribution for both high and low temperatures.

Mihir Nayar
Mihir Nayar
Numerade Educator
03:18

Problem 47

Refer to the data set for high and low temperatures for 20 cities in exercise 46
a. Develop a scatter diagram to show the relationship between the two variables, high temperature and low temperature.
b. Comment on the relationship between high and low temperatures.

Hira Hussain
Hira Hussain
Numerade Educator
09:28

Problem 48

One of the questions in a Financial Times/Harris Poll was, "How much do you favor or oppose a higher tax on higher carbon emission cars?" Possible responses were strongly favor, favor more than oppose, oppose more than favor, and strongly oppose. The following crosstabulation shows the responses obtained for 5372 adults surveyed in four countries in Europe and the United States (Harris Interactive website, February 27,2008 ).
a. Construct a percent frequency distribution for the level of support variable. Do you think the results show support for a higher tax on higher carbon emission cars?
b. Construct a percent frequency distribution for the country variable.
c. Does the level of support among adults in the European countries appear to be different than the level of support among adults in the United States? Explain.

Mihir Nayar
Mihir Nayar
Numerade Educator
02:43

Problem 49

Western University has only one women's softball scholarship remaining for the coming year. The final two players that Western is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each player's batting performance in their junior and senior years of high school are as follows:
A player's batting average is computed by dividing the number of hits a player has by the total number of at-bats. Batting averages are represented as a decimal number with three places after the decimal.
a. Calculate the batting average for each player in her junior year. Then calculate the batting average of each player in her senior year. Using this analysis, which player should be awarded the scholarship? Explain.
b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows:
Calculate each player's batting average for the combined two years. Using this analysis, which player should be awarded the scholarship? Explain.
c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.

Jorge Villanueva
Jorge Villanueva
Numerade Educator
01:45

Problem 50

A survey of commercial buildings served by the Cincinnati Gas \& Electric Company asked what main heating fuel was used and what year the building was constructed. A partial crosstabulation of the findings follows.
a. Complete the crosstabulation by showing the row totals and column totals.
b. Show the frequency distributions for year constructed and for fuel type.
c. Prepare a crosstabulation showing column percentages.
d. Prepare a crosstabulation showing row percentages.
e. Comment on the relationship between year constructed and fuel type.

Hira Hussain
Hira Hussain
Numerade Educator
01:23

Problem 51

Table 2.16 contains a portion of the data in the file named Fortune. Data on stockholders' equity, market value, and profits for a sample of 50 Fortune 500 companies are shown.
a. Prepare a crosstabulation for the variables Stockholders' Equity and Profit. Use classes of $0-200,200-400, \ldots, 1000-1200$ for Profit, and classes of $0-1200,1200-2400, \ldots$ $4800-6000$ for Stockholders' Equity.
b. Compute the row percentages for your crosstabulation in part (a).
c. What relationship, if any, do you notice between Profit and Stockholders' Equity?

Dominador Tan
Dominador Tan
Numerade Educator
01:23

Problem 52

Refer to the data set in Table 2.16
a. Prepare a crosstabulation for the variables Market Value and Profit.
b. Compute the row percentages for your crosstabulation in part (a).
c. Comment on any relationship between the variables.

Dominador Tan
Dominador Tan
Numerade Educator
11:12

Problem 53

Refer to the data set in Table 2.16
a. Prepare a scatter diagram to show the relationship between the variables Profit and Stockholders' Equity.
b. Comment on any relationship between the variables.

Paul A.
Paul A.
California State Polytechnic University, Pomona
11:12

Problem 54

Refer to the data set in Table 2.16
a. Prepare a scatter diagram to show the relationship between the variables Market Value and Stockholders' Equity.
b. Comment on any relationship between the variables.

Paul A.
Paul A.
California State Polytechnic University, Pomona