Essential of Statistics for Business and Economics

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

Chapter 2

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

Educators

Chapter Questions

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

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

Numerade Educator

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 graph.

Sarah Wallace

Numerade Educator

Problem 4

The top four primetime 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.
a. Are these data qualitative or quantitative?
b. Provide frequency and percent frequency distributions.
c. Construct a bar graph 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

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 graph
c. A pie chart
d. Based on these data, what are the three most common last names?

Pratyush Raitan

Pratyush Raitan

Numerade Educator

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 net- work that produced each of these 50 top-rated shows. $\begin{array}{lllll}\mathrm{ABC} & \mathrm{ABC} & \mathrm{ABC} & \mathrm{NBC} & \mathrm{CBS} \\ \mathrm{ABC} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{ABC} & \mathrm{NBC} \\ \mathrm{NBC} & \mathrm{NBC} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{NBC} \\ \mathrm{CBS} & \mathrm{ABC} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{ABC} \\ \mathrm{CBS} & \mathrm{NBC} & \mathrm{NBC} & \mathrm{CBS} & \mathrm{NBC} \\ \mathrm{CBS} & \mathrm{CBS} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{NBC} \\ \mathrm{FOX} & \mathrm{CBS} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{NBC} \\ \mathrm{ABC} & \mathrm{ABC} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{NBC} \\ \mathrm{NBC} & \mathrm{CBS} & \mathrm{NBC} & \mathrm{CBS} & \mathrm{CBS} \\ \mathrm{ABC} & \mathrm{CBS} & \mathrm{ABC} & \mathrm{NBC} & \mathrm{ABC}\end{array}$
a. Construct a frequency distribution, percent frequency distribution, and bar graph for the data.
b. Which network or networks have done the best in terms of presenting top-rated television shows? Compare the performance of $\mathrm{ABC}, \mathrm{CBS},$ and $\mathrm{NBC}$

Pratyush Raitan

Pratyush Raitan

Numerade Educator

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 $(\mathrm{A}),$ and poor $(\mathrm{P}) .$ Use descriptive statistics to summarize the following data collected on food quality. What is your feeling about the food quality ratings at the restaurant?

Pratyush Raitan

Pratyush Raitan

Numerade Educator

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). $\begin{array}{cccccccccccccc}\mathrm{L} & \mathrm{P} & \mathrm{C} & \mathrm{H} & 2 & \mathrm{P} & \mathrm{R} & 1 & \mathrm{S} & \mathrm{S} & 1 & \mathrm{L} & \mathrm{P} & \mathrm{R} \\ \mathrm{P} & \mathrm{P} & \mathrm{P} & \mathrm{R} & \mathrm{C} & \mathrm{S} & \mathrm{L} & \mathrm{R} & \mathrm{P} & \mathrm{C} & \mathrm{C} & \mathrm{P} & \mathrm{P} & \mathrm{R}\end{array}$
$2 \quad 3 \quad \mathrm{P} \quad \mathrm{H} \quad \mathrm{L} \quad \mathrm{P} \quad 1 \quad \mathrm{C} \quad \mathrm{P} \quad \mathrm{P} \quad \mathrm{P} \quad \mathrm{S} \quad 1$
$\mathrm{L}$
$\begin{array}{llllllllll}\mathrm{R} & 1 & 2 & \mathrm{H} & \mathrm{S} & 3 & \mathrm{H} & 2 & \mathrm{L} & \mathrm{P}\end{array}$
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 outficlders (L, C, and R).

Pratyush Raitan

Pratyush Raitan

Numerade Educator

Problem 9

About $60 \%$ of small and medium-sized businesses are family-owned. A TEC International Inc. survey asked the chief executive officers (CEOs) of family-owned businesses how they became the CEO (The Wall Street Journal, December 16,2003 ). Responses were that the CEO inherited the business, the CEO built the business, or the CEO was hired by the family-owned firm. A sample of $26 \mathrm{CEOs}$ of family-owned businesses provided the following data on how each became the CEO. $\begin{array}{llll}\text { Built } & \text { Built } & \text { Built } & \text { Inherited } \\ \text { Inherited } & \text { Built } & \text { Inherited } & \text { Built } \\ \text { Inherited } & \text { Built } & \text { Built } & \text { Built } \\ \text { Built } & \text { Hired } & \text { Hired } & \text { Hired } \\ \text { Inherited } & \text { Inherited } & \text { Inherited } & \text { Built } \\ \text { Built } & \text { Built } & \text { Built } & \text { Hired } \\ \text { Built } & \text { Inherited } & & \end{array}$
a. Provide a frequency distribution.
b. Provide a percent frequency distribution.
c. Construct a bar graph.
d. What percentage of CEOs of family-owned businesses became the CEO because they inherited the business? What is the primary reason a person becomes the CEO of a family-owned business?

Jerelyn Nevil

Numerade Educator

Problem 10

Netflix, Inc., of San Jose, California, provides DVD rentals of more than 50,000 titles by mail. Customers go online to create an order list of DVDs they would like to view. Before ordering a particular DVD, the customer may view a description of the DVD and, if desired, a summary of critics' ratings. Netflix uses a five-star rating system with the following descriptions:
Eighteen critics, including Roger Ebert of the Chicago Sun Times and Ty Burr of the Boston Globe, provided ratings for the movie Batman Begins (Netflix.com, March 1, 2006). The
ratings for Batman Begins were as follows:
4, 2, 5, 2, 4, 3, 3, 4, 4, 3, 4, 4, 4, 2, 4, 4, 5, 4
a. Comment on why these data are qualitative.
b. Provide a frequency distribution and relative frequency distribution for the data.
c. Provide a bar graph.
d. Comment on the critics' evaluation of Batman Begins.

James Kiss

Numerade Educator

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. Developa 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).

Jerelyn Nevil

Numerade Educator

Problem 12

Consider the following frequency distribution.
Class Frequency
$$\begin{array}{lr}10-19 & 10 \\20-29 & 14 \\30-39 & 17 \\40-49 & 7 \\50-59 & 2\end{array}$$
Construct a cumulative frequency distribution and a cumulative relative frequency distribution.

Pratyush Raitan

Pratyush Raitan

Numerade Educator

Problem 13

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

Pratyush Raitan

Pratyush Raitan

Numerade Educator

Problem 14

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

Pratyush Raitan

Pratyush Raitan

Numerade Educator

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?

Jerelyn Nevil

Numerade Educator

Problem 16

Consider the following two frequency distributions. The first frequency distribution provides an approximation of the annual adjusted gross income in the United States (Internal Revenue Service, March 2003 ). The second frequency distribution shows exam scores for students in a college statistics course.
a. Develop a histogram for the annual income data. What evidence of skewness does it show? Does this skewness make sense? Explain.
b. Develop a histogram for the exam score data. What evidence of skewness does it show? Explain.
c. Develop a histogram for the data in exercise $11 .$ What evidence of skewness does it show? What is the general shape of the distribution?

Harsh Gadhiya

Numerade Educator

Problem 17

What is the typical price for a share of stock for the 30 Dow Jones Industrial Average companies? The following data show the price for a share of stock to the nearest dollar in January 2006 (The Wall Street Journal, January 16,2006 ).
a. Prepare a frequency distribution of the data.
b. Prepare a histogram of the data. Interpret the histogram, including a discussion of the general shape of the histogram, the mid-price per share range, the most frequent price per share range, and the high and low extreme prices per share.
c. What are the highest-priced and the lowest-priced stocks?
d. Use The Wall Street Journal to find the current price per share for these companies. Prepare a histogram of the data and discuss any changes since January 2006

Rebecca Wickersham

Rebecca Wickersham

Numerade Educator

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.
\[
\begin{array}{rrrr}
1200 & 850 & 740 & 590 & 340 \\
450 & 890 & 260 & 610 & 350 \\
1780 & 180 & 850 & 2050 & 770 \\
800 & 1090 & 510 & 520 & 220 \\
1450 & 280 & 1120 & 200 & 350
\end{array}
\]
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

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. A relative frequency distribution
c. A cumulative frequency distribution
d. A cumulative relative frequency distribution
e. 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

Numerade Educator

Problem 20

The top 20 concert tours and their average ticket price for shows in North America are shown here. The list is based on data provided to the trade publication Pollstar by concert promoters and venue managers (Associated Press, November 21,2003 ).
Summarize the data by constructing the following:
a. $\quad$ A frequency distribution and a percent frequency distribution
b. A histogram
c. What concert had the most expensive average ticket price? What concert had the least expensive average ticket price?
d. Comment on what the data indicate about the average ticket prices of the top concert
tours.

Nick Johnson

Numerade Educator

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.
\[
\begin{array}{rrrrrrrr}
4.1 & 1.5 & 10.4 & 5.9 & 3.4 & 5.7 & 1.6 & 6.1 & 3.0 & 3.7 \\
3.1 & 4.8 & 2.0 & 14.8 & 5.4 & 4.2 & 3.9 & 4.1 & 11.1 & 3.5 \\
4.1 & 4.1 & 8.8 & 5.6 & 4.3 & 3.3 & 7.1 & 10.3 & 6.2 & 7.6 \\
10.8 & 2.8 & 9.5 & 12.9 & 12.1 & 0.7 & 4.0 & 9.2 & 4.4 & 5.7 \\
7.2 & 6.1 & 5.7 & 5.9 & 4.7 & 3.9 & 3.7 & 3.1 & 6.1 & 3.1
\end{array}
\]
Summarize the data by constructing the following:
a. $\quad$ A frequency distribution (use a class width of three hours)
b. 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

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

Problem 23

Construct a stem-and-leaf display for the following data.

Sarah Wallace

Numerade Educator

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

Problem 25

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

Evelyn Cunningham

Evelyn Cunningham

Numerade Educator

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

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

Problem 28

The 2004 Naples, Florida, mini marathon $(13.1 \text { miles) had } 1228$ 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.
\[
\begin{array}{lcccc}
49 & 33 & 40 & 37 & 56 \\
44 & 46 & 57 & 55 & 32 \\
50 & 52 & 43 & 64 & 40 \\
46 & 24 & 30 & 37 & 43 \\
31 & 43 & 50 & 36 & 61 \\
27 & 44 & 35 & 31 & 43 \\
52 & 43 & 66 & 31 & 50 \\
72 & 26 & 59 & 21 & 47
\end{array}
\]
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

Problem 29

The following data are for 30 observations involving two qualitative variables, $x$ and $y$. The categories for $x$ are $A, B,$ and $C ;$ 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

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

Numerade Educator

Problem 31

The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States: 2002 ).
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

Numerade Educator

Problem 32

Refer again to the crosstabulation of household 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 $25, " \cdot 100$ or more " and for "Total." Comment on the relationship between household income and educational level of the head of household.

Hira Hussain

Numerade Educator

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 Fernale 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.

Dominador Tan

Numerade Educator

Problem 34

Table 2.13 provides financial data for a sample of 36 companies whose stocks trade on the New York Stock Exchange (Investor's Business Daily, April 7, 2000). The data on Sales/Margins/ROE are a composite rating based on a company's sales growth rate, its profit margins, and its return on equity (ROE). EPS Rating is a measure of growth in earnings per share for the company.
a. Prepare a crosstabulation of the data on Sales/Margins/ROE (rows) and EPS Rating (columns). Use classes of $0-19,20-39,40-59,60-79,$ and $80-99$ for EPS Rating.
b. Compute row percentages and comment on any relationship between the variables.

Jerelyn Nevil

Numerade Educator

Problem 35

Refer to the data in Table 2.13
a. Prepare a crosstabulation of the data on Sales/Margins/ROE and Industry Group Relative Strength.
b. Prepare a frequency distribution for the data on Sales/Margins/ROE.
c. Prepare a frequency distribution for the data on Industry Group Relative Strength.
d. How has the crosstabulation helped in preparing the frequency distributions in parts
(b) and (c)?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 36

Refer to the data in Table 2.13
a. Prepare a scatter diagram of the data on EPS Rating and Relative Price Strength.
b. Comment on the relationship, if any, between the variables. (The meaning of the EPS Rating is described in exercise 34 . Relative Price Strength is a measure of the change in the stock's price over the past 12 months. Higher values indicate greater strength.)

Paul A.

California State Polytechnic University, Pomona

Problem 37

The National Football League rates prospects position by position on a scale that ranges from 5 to $9 .$ The ratings are interpreted as follows: $8-9$ should start the first year; $7.0-7.9$ should start; $6.0-6.9$ will make the team as a backup; and $5.0-5.9$ can make the club and contribute. Table 2.14 shows the position, weight, time (seconds to run 40 yards), and rating for 40 NFL prospects (USA Today, April 14, 2000).
a. Prepare a crosstabulation of the data on Position (rows) and Time (columns). Use classes of $4.00-4.49,4.50-4.99,5.00-5.49,$ and $5.50-5.99$ for Time.
b. Comment on the relationship between Position and Time based upon the crosstabulation developed in part (a).
c. Develop a scatter diagram of the data on Time and Rating. Use the vertical axis for Rating.
d. Comment on the relationship, if any, between Time and Rating.

Shu Naito

Numerade Educator

Problem 38

Five of the top-selling vehicles during 2006 were the Chevrolet Silverado/C/K pickup, Dodge Ram pickup, Ford F-Series pickup, Honda Accord, and Toyota Camry (WardsAuto.com, January 12,2007 ). Data from a sample of 50 vehicle purchases are presented in Table 2.15
a. Develop a frequency and percent frequency distribution.
b. What is the best-selling pickup truck, and what is the best-selling passenger car?
c. Show a pie chart.

Brandon Cleary

Numerade Educator

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.
$\begin{array}{llllllllllllllll}\mathrm{S} & \mathrm{P} & \mathrm{P} & \mathrm{O} & \mathrm{B} & \mathrm{E} & \mathrm{O} & \mathrm{E} & \mathrm{P} & \mathrm{O} & \mathrm{O} & \mathrm{B} & \mathrm{O} & \mathrm{O} & \mathrm{O} & \mathrm{A} \\ \mathrm{O} & \mathrm{E} & \mathrm{E} & \mathrm{B} & \mathrm{S} & \mathrm{O} & \mathrm{B} & \mathrm{O} & \mathrm{A} & \mathrm{O} & \mathrm{E} & \mathrm{O} & \mathrm{E} & \mathrm{O} & \mathrm{B} & \mathrm{P}\end{array}$
$\begin{array}{llllllllllllllll}\mathrm{B} & \mathrm{A} & \mathrm{S} & \mathrm{O} & \mathrm{E} & \mathrm{A} & \mathrm{B} & \mathrm{O} & \mathrm{S} & \mathrm{S} & \mathrm{O} & \mathrm{O} & \mathrm{E} & \mathrm{B} & \mathrm{O} & \mathrm{B} \\ \mathrm{A} & \mathrm{E} & \mathrm{B} & \mathrm{E} & \mathrm{A} & \mathrm{A} & \mathrm{P} & \mathrm{O} & \mathrm{O} & \mathrm{E} & \mathrm{O} & \mathrm{B} & \mathrm{B} & \mathrm{O} & \mathrm{P} & \mathrm{B}\end{array}$
a. Show a frequency distribution and percent frequency distribution.
b. Show a bar graph.
c. What percentage of freshmen selects 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

Problem 40

Golf Magazine's Top 100 Teachers were asked the question, "What is the most critical area that prevents golfers from reaching their potential?" The possible responses were lack of accuracy, poor approach shots, poor mental approach, lack of power, limited practice, poor putting, poor short game, and poor strategic decisions. The data obtained follow (Golf Magazine, February 2002 ):
a. Develop a frequency and percent frequency distribution.
b. Which four critical areas most often prevent golfers from reaching their potential?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

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 2.16 (The Wall Street Journal, March 3,2006 ).
a. $\quad$ 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

Numerade Educator

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 2006). A sample of SAT scores for the combined math and verbal portions of the test are as follows:
\[
\begin{array}{rrrrr}
1025 & 1042 & 1195 & 880 & 945 \\
1102 & 845 & 1095 & 936 & 790 \\
1097 & 913 & 1245 & 1040 & 998 \\
998 & 940 & 1043 & 1048 & 1130 \\
1017 & 1140 & 1030 & 1171 & 1035
\end{array}
\]
a. Show a frequency distribution and histogram for the SAT scores. Begin the first class with an SAT score of 750 and use a class width of 100 .
b. Comment on the shape of the distribution.
c. What other observations can be made about SAT scores based on the tabular and graphical summaries?

Mihir Nayar

Numerade Educator

Problem 43

Ninety-four shadow stocks were reported by the American Association of Individual Investors. The term shadow indicates stocks for small to medium-sized firms not followed closely by the major brokerage houses. Information on where the stock was traded -New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and over-the-counter (OTC) - the earnings per share, and the price/earnings ratio was provided for the following sample of 20 shadow stocks.
a. Provide frequency and relative frequency distributions for the exchange data. Where are most shadow stocks listed?
b. Provide frequency and relative frequency distributions for the earnings per share and price/earnings ratio data. Use classes of $0.00-0.19,0.20-0.39,$ and so on for the earnings per share data and classes of $0.0-9.9,10.0-19.9,$ and so on for the price/earnings ratio data. What observations and comments can you make about the shadow stocks?

Jerelyn Nevil

Numerade Educator

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

Numerade Educator

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

Numerade Educator

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

Numerade Educator

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

Numerade Educator

Problem 48

A study of job satisfaction was conducted for four occupations. Job satisfaction was measured using an 18 -item questionnaire with each question receiving a response score of 1 to 5 with higher scores indicating greater satisfaction. The sum of the 18 scores provides the job satisfaction score for each individual in the sample. The data are as follow.
a. Provide a crosstabulation of occupation and job satisfaction score.
b. Compute the row percentages for your crosstabulation in part (a).
c. What observations can you make concerning the level of job satisfaction for these occupations?

Michael Nartey

Numerade Educator

Problem 49

Do larger companies generate more revenue? The following data show the number of employees and annual revenue for a sample of 20 Fortune 1000 companies (Fortune, April 17,2000 )
a. Prepare a scatter diagram to show the relationship between the variables Revenue and Employees.
b. Comment on any relationship between the variables.

Nick Johnson

Numerade Educator

Problem 50

A survey of commercial buildings served by the Cinergy-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

Numerade Educator

Problem 51

Table 2.17 contains a portion of the data on the file named Fortune on the $\mathrm{CD}$ that accompanies the text. It provides data on stockholders' equity, market value, and profits for a sample of 50 Fortune 500 companies.
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

Numerade Educator

Problem 52

Refer to the data set in Table 2,17
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

Numerade Educator

Problem 53

Refer to the data set in Table 2.17
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.

California State Polytechnic University, Pomona

Problem 54

Refer to the data set in Table 2.17
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.

California State Polytechnic University, Pomona