Chapter 2, Descriptive Statistics Tabular and Graphical Displays Video Solutions, Statistics For Business & Economics | Numerade (2024)

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

A partial relative frequency distribution is given.
$$
\begin{array}{cc}
\text { Class } & \text { Relative Frequency } \\
\text { A } & .22 \\
\text { B } & .18 \\
\text { C } & .40 \\
\text { D } &
\end{array}
$$
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.

A questionnaire provides $58 \mathrm{Yes}, 42 \mathrm{No}$, 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.

For the 2010-2011 viewing season, the top five syndicated programs were Wheel of Fortune (WoF), Two and Half Men (THM), Jeopardy (Jep), Judge Judy (JJ), and the Oprah Winfrey Show (OWS) (Nielsen Media Research website, April 16, 2012). Data indicating the preferred shows for a sample of 50 viewers follow.
$$
\begin{array}{lllll}
\text { WoF } & \text { Jep } & \text { JJ } & \text { Jep } & \text { THM } \\
\text { THM } & \text { WoF } & \text { OWS } & \text { Jep } & \text { THM } \\
\text { Jep } & \text { OWS } & \text { WoF } & \text { WoF } & \text { WoF } \\
\text { WoF } & \text { THM } & \text { OWS } & \text { THM } & \text { WoF } \\
\text { THM } & \text { J } & \text { JJ } & \text { Jep } & \text { THM } \\
\text { OWS } & \text { OWS } & \text { JJ } & \text { JJ } & \text { Jep } \\
\text { JJ } & \text { WoF } & \text { THM } & \text { WoF } & \text { WoF } \\
\text { THM } & \text { THM } & \text { WoF } & \text { J } & \text { JJ } \\
\text { Jep } & \text { THM } & \text { WoF } & \text { Jep } & \text { Jep } \\
\text { WoF } & \text { THM } & \text { OWS } & \text { OWS } & \text { Jep }
\end{array}
$$
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?

In alphabetical order, the six most common last names in the United States are Brown, Johnson, Jones, Miller, Smith, and Williams (The World Almanac, 2012). Assume that a sample of 50 individuals with one of these last names provided the following data.
$$
\begin{array}{lllll}
\text { Brown } & \text { Williams } & \text { Williams } & \text { Williams } & \text { Brown } \\
\text { Smith } & \text { Jones } & \text { Smith } & \text { Johnson } & \text { Smith } \\
\text { Miller } & \text { Smith } & \text { Brown } & \text { Williams } & \text { Johnson } \\
\text { Johnson } & \text { Smith } & \text { Smith } & \text { Johnson } & \text { Brown } \\
\text { Williams } & \text { Miller } & \text { Johnson } & \text { Williams } & \text { Johnson } \\
\text { Williams } & \text { Johnson } & \text { Jones } & \text { Smith } & \text { Brown } \\
\text { Johnson } & \text { Smith } & \text { Smith } & \text { Brown } & \text { Jones } \\
\text { Jones } & \text { Jones } & \text { Smith } & \text { Smith } & \text { Miller } \\
\text { Miller } & \text { Jones } & \text { Williams } & \text { Miller } & \text { Smith } \\
\text { Jones } & \text { Johnson } & \text { Brown } & \text { Johnson } & \text { Miller }
\end{array}
$$
Summarize the data by constructing the following:
a. Relative and percent frequency distributions
b. A bar chart
c. A pie chart
d. Based on these data, what are the three most common last names?

Nielsen Media Research provided the list of the 25 top-rated single shows in television history (The World Almanac, 2012). The following data show the television network that produced each of these 25 top-rated shows.
$$
\begin{array}{lllll}
\text { CBS } & \text { CBS } & \text { NBC } & \text { FOX } & \text { CBS } \\
\text { CBS } & \text { NBC } & \text { NBC } & \text { NBC } & \text { ABC } \\
\text { ABC } & \text { NBC } & \text { ABC } & \text { ABC } & \text { NBC } \\
\text { CBS } & \text { NBC } & \text { CBS } & \text { ABC } & \text { NBC } \\
\text { NBC } & \text { CBS } & \text { CBS } & \text { ABC } & \text { CBS }
\end{array}
$$
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.

The Canmark Research Center Airport Customer Satisfaction Survey uses an online questionnaire to provide airlines and airports with customer satisfaction ratings for all aspects of the customers' flight experience (airportsurvey website, July 2012). After completing a flight, customers receive an e-mail asking them to go to the website and rate a variety of factors, including the reservation process, the check-in process, luggage policy, cleanliness of gate area, service by flight attendants, food/beverage selection, on-time arrival, and so on. A five-point scale, with Excellent (E), Very Good (V), Good (G), Fair (F), and Poor ( P ), is used to record customer ratings. Assume that passengers on a Delta Airlines flight from Myrtle Beach, South Carolina, to Atlanta, Georgia, provided the following ratings for the question, "Please rate the airline based on your overall experience with this flight." The sample ratings are shown below.
$$
\begin{array}{llllllllll}
\text { E } & \text { E } & \text { G } & \text { V } & \text { V } & \text { E } & \text { V } & \text { V } & \text { V } & \text { E } \\
\text { E } & \text { G } & \text { V } & \text { E } & \text { E } & \text { V } & \text { E } & \text { E } & \text { E } & \text { V } \\
\text { V } & \text { V } & \text { V } & \text { F } & \text { V } & \text { E } & \text { V } & \text { E } & \text { G } & \text { E } \\
\text { G } & \text { E } & \text { V } & \text { E } & \text { V } & \text { E } & \text { V } & \text { V } & \text { V } & \text { V } \\
\text { E } & \text { E } & \text { V } & \text { V } & \text { E } & \text { P } & \text { E } & \text { V } & \text { P } & \text { V }
\end{array}
$$
a. Use a percent frequency distribution and a bar chart to summarize these data. What do these summaries indicate about the overall customer satisfaction with the Delta flight?
b. The online survey questionnaire enabled respondents to explain any aspect of the flight that failed to meet expectations. Would this be helpful information to a manager looking for ways to improve the overall customer satisfaction on Delta flights? Explain.

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).
$$
\begin{array}{lllllllllllllll}
\mathrm{L} & \mathrm{P} & \mathrm{C} & \mathrm{H} & 2 & \mathrm{P} & \mathrm{R} & 1 & \mathrm{~S} & \mathrm{~S} & 1 & \mathrm{~L} & \mathrm{P} & \mathrm{R} & \mathrm{P} \\
\mathrm{P} & \mathrm{P} & \mathrm{P} & \mathrm{R} & \mathrm{C} & \mathrm{S} & \mathrm{L} & \mathrm{R} & \mathrm{P} & \mathrm{C} & \mathrm{C} & \mathrm{P} & \mathrm{P} & \mathrm{R} & \mathrm{P} \\
2 & 3 & \mathrm{P} & \mathrm{H} & \mathrm{L} & \mathrm{P} & 1 & \mathrm{C} & \mathrm{P} & \mathrm{P} & \mathrm{P} & \mathrm{S} & 1 & \mathrm{~L} & \mathrm{R} \\
\mathrm{R} & 1 & 2 & \mathrm{H} & \mathrm{S} & 3 & \mathrm{H} & 2 & \mathrm{~L} & \mathrm{P} & & & & &
\end{array}
$$
a. Construct 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 ( $1,2,3$, and S) to outfielders (L, C, and R).

Nearly 1.8 million bachelor's degrees and over 750,000 master's degrees are awarded annually by U.S. postsecondary institutions (National Center for Education Statistics website, November, 2014). The Department of Education tracks the field of study for these graduates in the following categories: Business (B), Computer Sciences and Engineering (CSE), Education (E), Humanities (H), Natural Sciences and Mathematics (NSM), Social and Behavioral Sciences (SBS), and Other (O). Consider the following samples of 100 graduates:
Bachelor's Degree Field of Study
$$
\begin{array}{llllllllll}
\text { SBS } & \text { H } & \text { H } & \text { H } & \text { E } & \text { B } & \text { O } & \text { SBS } & \text { NSM } & \text { CSE } \\
\text { O } & \text { B } & \text { B } & \text { O } & \text { O } & \text { H } & \text { B } & \text { O } & \text { SBS } & \text { O } \\
\text { H } & \text { CSE } & \text { CSE } & \text { O } & \text { CSE } & \text { B } & \text { H } & \text { O } & \text { O } & \text { SBS } \\
\text { SBS } & \text { SBS } & \text { B } & \text { H } & \text { NSM } & \text { B } & \text { B } & \text { O } & \text { SBS } & \text { SBS } \\
\text { B } & \text { H } & \text { SBS } & \text { O } & \text { B } & \text { B } & \text { O } & \text { O } & \text { B } & \text { O } \\
\text { O } & \text { H } & \text { SBS } & \text { H } & \text { CSE } & \text { CSE } & \text { B } & \text { E } & \text { CSE } & \text { SBS } \\
\text { SBS } & \text { NSM } & \text { NSM } & \text { CSE } & \text { H } & \text { H } & \text { E } & \text { E } & \text { SBS } & \text { CSE } \\
\text { NSM } & \text { NSM } & \text { SBS } & \text { O } & \text { H } & \text { H } & \text { B } & \text { SBS } & \text { SBS } & \text { NSM } \\
\text { H } & \text { B } & \text { B } & \text { O } & \text { O } & \text { O } & \text { NSM } & \text { H } & \text { E } & \text { B } \\
\text { E } & \text { B } & \text { O } & \text { B } & \text { B } & \text { B } & \text { O } & \text { O } & \text { O } & \text { O }
\end{array}
$$
Master’s degree field of Study
$$
\begin{array}{llllllllll}
\text { O } & \text { O } & \text { B } & \text { O } & \text { B } & \text { E } & \text { B } & \text { H } & \text { E } & \text { B } \\
\text { O } & \text { E } & \text { SBS } & \text { B } & \text { CSE } & \text { H } & \text { B } & \text { E } & \text { E } & \text { O } \\
\text { O } & \text { B } & \text { B } & \text { O } & \text { E } & \text { CSE } & \text { NSM } & \text { O } & \text { B } & \text { E } \\
\text { H } & \text { H } & \text { B } & \text { E } & \text { SBS } & \text { E } & \text { E } & \text { B } & \text { O } & \text { E } \\
\text { SBS } & \text { B } & \text { B } & \text { CSE } & \text { H } & \text { B } & \text { B } & \text { CSE } & \text { SBS } & \text { B } \\
\text { CSE } & \text { B } & \text { E } & \text { CSE } & \text { B } & \text { E } & \text { CSE } & \text { O } & \text { E } & \text { O } \\
\text { B } & \text { O } & \text { E } & \text { O } & \text { B } & \text { NSM } & \text { H } & \text { E } & \text { B } & \text { E } \\
\text { B } & \text { E } & \text { B } & \text { O } & \text { E } & \text { E } & \text { H } & \text { O } & \text { O } & \text { O } \\
\text { CSE } & \text { O } & \text { O } & \text { H } & \text { B } & \text { O } & \text { B } & \text { E } & \text { CSE } & \text { O } \\
\text { E } & \text { O } & \text { SBS } & \text { E } & \text { E } & \text { O } & \text { SBS } & \text { B } & \text { B } & \text { O }
\end{array}
$$
a. Provide a percent frequency distribution of field of study for each degree.
b. Construct a bar chart for field of study for each degree.
c. What is the lowest percentage field of study for each degree?
d. What is the highest percentage field of study for each degree?
e. Which field of study has the largest increase in percentage from bachelor's to masters'?

VirtualTourist provides ratings for hotels throughout the world. Ratings provided by 649 guests at the Sheraton Anaheim Hotel, located near the Disneyland Resort in Anaheim,
California, can be found in the DATAfile named HotelRatings (VirtualTourist website, February 25, 2013). Possible responses were Excellent, Very Good, Average, Poor, and Terrible.
a. Construct a frequency distribution.
b. Construct a percent frequency distribution.
c. Construct a bar chart for the percent frequency distribution.
d. Comment on how guests rate their stay at the Sheraton Anaheim Hotel.
e. Results for $\mathbf{1 6 7 9}$ guests who stayed at Disney's Grand Californian provided the following frequency distribution.
$$
\begin{array}{lc}
\text { Rating } & \text { Frequency } \\
\text { Excellent } & 807 \\
\text { Very Good } & 521 \\
\text { Average } & 200 \\
\text { Poor } & 107 \\
\text { Terrible } & 44
\end{array}
$$
Compare the ratings for disney’s Grand Californian with the results obtained for the
Sheraton Anaheim Hotel.

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).

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

Construct a histogram for the data in exercise 12.

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

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

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

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.
$\begin{array}{llllllllllllllllllll}2 & 5 & 10 & 12 & 4 & 4 & 5 & 17 & 11 & 8 & 9 & 8 & 12 & 21 & 6 & 8 & 7 & 13 & 18 & 3\end{array}$
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?

CBSSports.com developed the Total Player Ratings system to rate players in the National Basketball Association (NBA) based upon various offensive and defensive statistics. The following data show the average number of points scored per game (PPG) for 50 players with the highest ratings for a portion of the 2012-2013 NBA season (CBSSports.com website, February 25, 2013).
$$
\begin{array}{llllllllll}
27.0 & 28.8 & 26.4 & 27.1 & 22.9 & 28.4 & 19.2 & 21.0 & 20.8 & 17.6 \\
21.1 & 19.2 & 21.2 & 15.5 & 17.2 & 16.7 & 17.6 & 18.5 & 18.3 & 18.3 \\
23.3 & 16.4 & 18.9 & 16.5 & 17.0 & 11.7 & 15.7 & 18.0 & 17.7 & 14.6 \\
15.7 & 17.2 & 18.2 & 17.5 & 13.6 & 16.3 & 16.2 & 13.6 & 17.1 & 16.7 \\
17.0 & 17.3 & 17.5 & 14.0 & 16.9 & 16.3 & 15.1 & 12.3 & 18.7 & 14.6
\end{array}
$$
Use classes starting at 10 and ending at 30 in increments of 2 for PPG in the following.
a. Show the frequency distribution.
b. Show the relative frequency distribution.
c. Show the cumulative percent frequency distribution.
d. Develop a histogram for the average number of points scored per game.
e. Do the data appear to be skewed? Explain.
f. What percentage of the players averaged at least 20 points per game?

Based on the tons handled in a year, the ports listed below are the 25 busiest ports in the United States (The 2013 World Almanac).
$$
\begin{array}{lclc}
\text { Port } & \begin{array}{c}
\text { Tons Handled } \\
\text { (Millions) }
\end{array} & \text { Port } & \begin{array}{c}
\text { Tons Handled } \\
\text { (Millions) }
\end{array} \\
\text { Baltimore } & 39.6 & \text { Norfolk Harbor } & 41.6 \\
\text { Baton Rouge } & 55.5 & \text { Pascagoula } & 37.3 \\
\text { Beaumont } & 77.0 & \text { Philadelphia } & 34.0 \\
\text { Corpus Christi } & 73.7 & \text { Pittsburgh } & 33.8 \\
\text { Duluth-Superior } & 36.6 & \text { Plaquemines } & 55.8 \\
\text { Houston } & 227.1 & \text { Port Arthur } & 30.2 \\
\text { Huntington } & 61.5 & \text { Savannah } & 34.7 \\
\text { Lake Charles } & 54.6 & \text { South Louisiana } & 236.3 \\
\text { Long Beach } & 75.4 & \text { St. Louis } & 30.8 \\
\text { Los Angeles } & 62.4 & \text { Tampa } & 34.2 \\
\text { Mobile } & 55.7 & \text { Texas City } & 56.6 \\
\text { New Orleans } & 72.4 & \text { Valdez } & 31.9 \\
\text { New York } & 139.2 & & \\
& & &
\end{array}
$$
a. What is the largest number of tons handled? What is the smallest number of tons handled?
b. Using a class width of 25 , develop a frequency distribution of the data starting with $25-49.9,50-74.9,75-99.9$, and so on.
c. Prepare a histogram. Interpret the histogram.

The London School of Economics and the Harvard Business School conducted a study of how chief executive officers (CEOs) spend their day. The study found that CEOs spend on average about 18 hours per week in meetings, not including conference calls, business meals, and public events (The Wall Street Journal, February 14, 2012). Shown below is the time spent per week in meetings (hours) for a sample of 25 CEOs .
$$
\begin{array}{lllll}
14 & 15 & 18 & 23 & 15 \\
19 & 20 & 13 & 15 & 23 \\
23 & 21 & 15 & 20 & 21 \\
16 & 15 & 18 & 18 & 19 \\
19 & 22 & 23 & 21 & 12
\end{array}
$$
a. What is the least amount of time spent per week on meetings? The highest?
b. Use a class width of two hours 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.

Fortune provides a list of America's largest corporations based on annual revenue. Shown below are the 50 largest corporations, with annual revenue expressed in billions of dollars (CNN Money website, January 15, 2010).
$$
\begin{array}{lclc}
& & & \\
\text { Corporation } & \text { Revenue } & \text { Corporation } & \text { Revenue } \\
\text { Amerisource Bergen } & 71 & \text { Lowe's } & 48 \\
\text { Archer Daniels Midland } & 70 & \text { Marathon Oil } & 74 \\
\text { AT\&T } & 124 & \text { McKesson } & 102 \\
\text { Bank of America } & 113 & \text { Medco Health } & 51 \\
\text { Berkshire Hathaway } & 108 & \text { MetLife } & 55 \\
\text { Boeing } & 61 & \text { Microsoft } & 60 \\
\text { Cardinal Health } & 91 & \text { Morgan Stanley } & 62 \\
\text { Caterpillar } & 51 & \text { Pepsico } & 43 \\
\text { Chevron } & 263 & \text { Pfizer } & 48 \\
\text { Citigroup } & 112 & \text { Procter \& Gamble } & 84 \\
\text { ConocoPhillips } & 231 & \text { Safeway } & 44 \\
\text { Costco Wholesale } & 72 & \text { Sears Holdings } & 47 \\
\text { CVS Caremark } & 87 & \text { State Farm Insurance } & 61 \\
\text { Dell } & 61 & \text { Sunoco } & 52 \\
\text { Dow Chemical } & 58 & \text { Target } & 65 \\
\text { ExxonMobil } & 443 & \text { Time Wamer } & 47 \\
\text { Ford Motors } & 146 & \text { United Parcel Service } & 51 \\
\text { General Electric } & 149 & \text { United Technologies } & 59 \\
\text { Goldman Sachs } & 54 & \text { UnitedHealth Group } & 81 \\
\text { Hewlett-Packard } & 118 & \text { Valero Energy } & 118 \\
\text { Home Depot } & 71 & \text { Verizon } & 97 \\
\text { IBM } & 104 & \text { Walgreen } & 59 \\
\text { JPMorgan Chase } & 101 & \text { Walmart } & 406 \\
\text { Johnson \& Johnson } & 64 & \text { WellPoint } & 61 \\
\text { Kroger } & 76 & \text { Wells Fargo } & 52 \\
\hline
\end{array}
$$
Summarize the data by constructing the following:
a. A frequency distribution (classes $0-49,50-99,100-149$, and so on).
b. A relative frequency distribution.
c. A cumulative frequency distribution.
d. A cumulative relative frequency distribution.
c. What do these distributions tell you about the annual revenue of the largest corporations in America?
f. Show a histogram. Comment on the shape of the distribution.
g. What is the largest corporation in America and what is its annual revenue?

The following data show the year to date percent change (YTd % Change) for 30 stock-
market indexes from around the word (The wall Street Journal, August 26, 2013).
$$
\begin{array}{llr}
\text { Country } & \text { Index } & \text { YTD \% Change } \\
\text { Australia } & \text { S\&P/ASX200 } & 10.2 \\
\text { Belgium } & \text { Bel-20 } & 12.6 \\
\text { Brazil } & \text { São Paulo Bovespa } & -14.4 \\
\text { Canada } & \text { S\&P/TSX Comp } & 2.6 \\
\text { Chile } & \text { Santiago IPSA } & -16.3 \\
\text { China } & \text { Shanghai Composite } & -9.3 \\
\text { Eurozone } & \text { EURO Stoxx } & 10.0 \\
\text { France } & \text { CAC 40 } & 11.8 \\
\text { Germany } & \text { DAX } & 10.6 \\
\text { Hong Kong } & \text { Hang Seng } & -3.5 \\
\text { India } & \text { S\&P BSE Sensex } & -4.7 \\
\text { Isracl } & \text { Tel Aviv } & 1.3 \\
\text { Italy } & \text { FTSE MIB } & 6.6 \\
\text { Japan } & \text { Nikkei } & 31.4 \\
\text { Mexico } & \text { IPC All-Share } & -6.4 \\
\text { Netherlands } & \text { AEX } & 9.3 \\
\text { Singapore } & \text { Straits Times } & -2.5 \\
\text { South Korea } & \text { Kospi } & -6.4 \\
\text { Spain } & \text { IBEX 35 } & 6.4 \\
\text { Sweden } & \text { SX All Share } & 13.8 \\
\hline
\end{array}
$$
$$
\begin{array}{llc}
\text { Country } & \text { Index } & \text { YTD \% Change } \\
\text { Switzerland } & \text { Swiss Market } & 17.4 \\
\text { Taiwan } & \text { Weighted } & 2.3 \\
\text { U.K. } & \text { FTSE } 100 & 10.1 \\
\text { U.S. } & \text { S\&P 500 } & 16.6 \\
\text { U.S. } & \text { DJIA } & 14.5 \\
\text { U.S. } & \text { Dow Jones Utility } & 6.6 \\
\text { U.S. } & \text { Nasdaq 100 } & 17.4 \\
\text { U.S. } & \text { Nasdaq Composite } & 21.1 \\
\text { World } & \text { DJ Global ex U.S. } & 4.2 \\
\text { World } & \text { DJ Global Index } & 9.9
\end{array}
$$
a. What index has the largest positive YTD \% Change?
b. Using a class width of 5 beginning with -20 and going to 40 , develop a frequency distribution for the data.
c. Prepare a histogram. Interpret the histogram, including a discussion of the general shape of the histogram.
d. Use The Wall Street Journal or another media source to find the current percent changes for these stock market indexes in the current year. What index has had the largest percent increase? What index has had the smallest percent decrease? Prepare a summary of the data.

The DATAfile EngineeringSalary contains the median starting salary and median midcareer salary (measured 10 years after graduation) for graduates from 19 engineering schools (The Wall Street Journal website, November 2014). Develop a stem-and-leaf display for both the median starting salary and the median mid-career salary. Comment on any differences you observe.

Each year America.EDU ranks the best paying college degrees in America. The following data show the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary (America.EDU website, August 29, 2013).
$$
\begin{array}{lccc}
\text { Degree } & \text { Starting Salary } & \text { Mid-Career Salary } & \text { \% Increase } \\
\text { Aerospace engineering } & 59,400 & 108,000 & 82 \\
\text { Applied mathematics } & 56,400 & 101,000 & 79 \\
\text { Biomedical engineering } & 54,800 & 10,000 & 84 \\
\text { Chemical engineering } & 64,800 & 10,000 & 67 \\
\text { Civil enginering } & 53,500 & 93,400 & 75 \\
\text { Computer engineering } & 61,200 & 87,700 & 43 \\
\text { Computer science } & 56,200 & 97,700 & 74 \\
\text { Construction management } & 50,400 & 87,000 & 73 \\
\text { Economics } & 48,800 & 97,800 & 100 \\
\text { Electrical engineering } & 60,800 & 10,000 & 71 \\
\text { Finance } & 47,500 & 91,500 & 93 \\
\text { Government } & 41,500 & 8,300 & 113 \\
\text { Information systems } & 49,300 & 87,100 & 77 \\
\text { Management info. systems } & 50,900 & 90,300 & 77 \\
\text { Mathematics } & 46,400 & 88,300 & 90 \\
\text { Nuclear enginecring } & 63,900 & 10,000 & 63 \\
\text { Petroleum engineering } & 93,000 & 157,000 & 69 \\
\text { Physics } & 50,700 & 99,600 & 96 \\
\text { Software engineering } & 56,700 & 91,300 & 61 \\
\text { Statistics } & 50,000 & 93,400 & 87
\end{array}
$$
a. Using a class width of 10, construct a histogram for the percentage increase in the
starting salary.
b. Comment on the shape of the distribution.
c. develop a stem-and-leaf display for the percentage increase in the starting salary.
d. what are the primary advantages of the stem-and-leaf display as compared to the
histogram?

The 2011 Cincinnati flying Pig Half-Marathon (13.1 miles) had 10,897 finishers (Cin-
cinnati flying Pig Marathon website). The following data show the ages for a sample of
40 half-marathoners.
$$
\begin{array}{lllll}
49 & 33 & 40 & 37 & 56 \\
44 & 46 & 57 & 55 & 32 \\
50 & 52 & 43 & 64 & 40 \\
46 & 24 & 30 & 37 & 43 \\
31 & 43 & 50 & 36 & 61 \\
27 & 44 & 35 & 31 & 43 \\
52 & 43 & 66 & 31 & 50 \\
72 & 26 & 59 & 21 & 47
\end{array}
$$
a. Construct a stretched stem-and-leaf display.
b. which age group had the largest number of runners?
c. which age occurred most frequently?

The following data are for 30 observations involving two categorical variables, x and y.
The categories for x are A, b, and C; the categories for y are 1 and 2.
$$
\begin{array}{cccccc}
\text { Observation } & \boldsymbol{x} & \boldsymbol{y} & \text { Observation } & \boldsymbol{x} & \boldsymbol{y} \\
1 & \mathrm{~A} & 1 & 16 & \text { B } & 2 \\
2 & \mathrm{~B} & 1 & 17 & \text { C } & 1 \\
3 & \mathrm{~B} & 1 & 18 & \text { B } & 1 \\
4 & \text { C } & 2 & 19 & \text { C } & 1 \\
5 & \mathrm{~B} & 1 & 20 & \text { B } & 1 \\
6 & \text { C } & 2 & 21 & \text { C } & 2 \\
7 & \text { B } & 1 & 22 & \text { B } & 1 \\
8 & \text { C } & 2 & 23 & \text { C } & 2 \\
9 & \text { A } & 1 & 24 & \text { A } & 1 \\
10 & \text { B } & 1 & 25 & \text { B } & 1 \\
11 & \text { A } & 1 & 26 & \text { C } & 2 \\
12 & \text { B } & 1 & 27 & \text { C } & 2 \\
13 & \text { C } & 2 & 28 & \text { A } & 1 \\
14 & \text { C } & 2 & 29 & \text { B } & 1 \\
15 & \text { C } & 2 & 30 & \text { B } & 2
\end{array}
$$
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?

The following observations are for two quantitative variables, x and y.
$$
\begin{array}{cccccc}
\text { Observation } & \boldsymbol{x} & \boldsymbol{y} & \text { Observation } & \boldsymbol{x} & \boldsymbol{y} \\
1 & 28 & 72 & 11 & 13 & 98 \\
2 & 17 & 99 & 12 & 84 & 21 \\
3 & 52 & 58 & 13 & 59 & 32 \\
4 & 79 & 34 & 14 & 17 & 81 \\
5 & 37 & 60 & 15 & 70 & 34 \\
6 & 71 & 22 & 16 & 47 & 64 \\
7 & 37 & 77 & 17 & 35 & 68 \\
8 & 27 & 85 & 18 & 62 & 67 \\
9 & 64 & 45 & 19 & 30 & 39 \\
10 & 53 & 47 & 20 & 43 & 28
\end{array}
$$
a. Develop a crosstabulation for the data, with $x$ as the row variable and $y$ as the column variable. For $x$ use classes of 10-29,30-49, and so on; for $y$ use classes of 40-59, $60-79$, and so on.
b. Compute the row percentages.
c. Compute the column percentages.
d. What is the relationship, if any, between $x$ and $y$ ?

The Daytona 500 is a 500 -mile automobile race held annually at the Daytona International Speedway in Daytona Beach, Florida. The following crosstabulation shows the automobile make by average speed of the 25 winners from 1988 to 2012 (The 2013 World Almanac).
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a. Compute the row percentages.
b. What percentage of winners driving a Chevrolet won with an average speed of at least 150 miles per hour?
c. Compute the column percentages.
d. What percentage of winning average speeds $160-169.9$ miles per hour were Chevrolets?

The following crosstabulation shows the average speed of the 25 winners by year of the Daytona 500 automobile race (The 2013 World Almanac).
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a. Calculate the row percentages.
b. What is the apparent relationship between average winning speed and year? What might be the cause of this apparent relationship?

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.
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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 higher 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 higher 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.

The following crosstabulation shows the number of households (1000s) in each of the four regions of the United States and the number of households at each income level (U.S. Census Bureau website, August 2013).
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a. Compute the row percentages and identify the percent frequency distributions of income for households in each region.
b. What percentage of households in the West region have an income level of $$\$ 50,000$$ or more? What percentage of houscholds in the South region have an income level of $$\$ 50,000$$ or more?
c. Construct percent frequency histograms for each region of houscholds. Do any relationships between regions and income level appear to be evident in your findings?
d. Compute the column percentages. What information do the column percentages provide?
c. What percent of households with a houschold income of $$\$ 100,000$$ and over are from the South region? What percentage of households from the South region have a household income of $$\$ 100,000$$ and over? Why are these two percentages different?

Each year Forbes ranks the world's most valuable brands. A portion of the data for 82 of the brands in the 2013 Forbes list is shown in Table 2.12 (Forbes website, February, 2014). The data set includes the following variables:
Brand: The name of the brand.
Industry: The type of industry associated with the brand, labeled Automotive \& Luxury, Consumer Packaged Goods, Financial Services, Other, Technology.
Brand Value ( $$\$ billions$$): A measure of the brand's value in billions of dollars developed by Forbes based on a variety of financial information about the brand.
1-Yr Value Change (\%): The percentage change in the value of the brand over the previous year.
Brand Revenue ( $$\$ billions$$): The total revenue in billions of dollars for the brand.
a. Prepare a crosstabulation of the data on Industry (rows) and Brand Value ( $$\$ billions$$). Use classes of $0-10,10-20,20-30,30-40,40-50$, and $50-60$ for Brand Value ( $$\$ billions$$).
b. Prepare a frequency distribution for the data on Industry.
c. Prepare a frequency distribution for the data on Brand Value ( $$\$ billions$$).
( TABLE CAN'T COPY )
d. How has the crosstabulation helped in preparing the frequency distributions in parts (b) and (c)?
e. What conclusions can you draw about the type of industry and the brand value?

Refer to Table 2.12.
a. Prepare a crosstabulation of the data on Industry (rows) and Brand Revenue ( $$\$ billions$$). Use class intervals of 25 starting at 0 for Brand Revenue ( $$\$ billions$$).
b. Prepare a frequency distribution for the data on Brand Revenue ( $$\$ billions$$).
c. What conclusions can you draw about the type of industry and the brand revenue?
d. Prepare a crosstabulation of the data on Industry (rows) and the 1-Yr Value Change (\%). Use class intervals of 20 starting at -60 for 1-Yr Value Change (\%).
e. Prepare a frequency distribution for the data on 1-Yr Value Change (\%).
f. What conclusions can you draw about the type of industry and the 1-year change in value?

The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (Fuel Economy website, September, 2012). A portion of the data for 149 compact, midsize, and large cars is shown in Table 2.13 . The data set contains the following variables:
Size: Compact, Midsize, and Large
Displacement: Engine size in liters
Cylinders: Number of cylinders in the engine
Drive: All wheel (A), front wheel ( F ), and rear wheel (R)
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 FueIData2012.
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, 35-39, and 40-44 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 $10-14,15-19,20-24,25-29,30-34$, and $35-39$, and $40-44$ 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 $10-14,15-19,20-24,25-29,30-34,35-39$, and $40-44$ for City MPG.
f. Comment on the relationship between Fuel Type and City MPG.
( TABLE CAN'T COPY )

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

Consider the following data on two categorical variables. The first variable, x, can take on
values A, b, C, or d. The second variable, y, can take on values I or II. The following table
gives the frequency with which each combination occurs.
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a. Construct a side-by-side bar chart with x on the horizontal axis.
b. Comment on the relationship between x and y.

The following crosstabulation summarizes the data for two categorical variables,
x and y. The variable x can take on values low, medium, or high and the variable y can
take on values yes or no.
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a. Compute the row percentages.
b. Construct a stacked percent frequency bar chart with x on the horizontal axis.

A study on driving speed (miles per hour) and fuel efficiency (miles per gallon) for midsize
automobiles resulted in the following data:
$$
\begin{array}{l|llllllllll}
\text { Driving Speed } & 30 & 50 & 40 & 55 & 30 & 25 & 60 & 25 & 50 & 55 \\
\hline \text { Fuel Efficiency } & 28 & 25 & 25 & 23 & 30 & 32 & 21 & 35 & 26 & 25
\end{array}
$$
a. Construct a scatter diagram with driving speed on the horizontal axis and fuel efficiency on the vertical axis.
b. Comment on any apparent relationship between these two variables.

The Current Results website lists the average annual high and low temperatures (degrees Fahrenheit) and average annual snowfall (inches) for fifty-one major U.S. cities, based on data from 1981 to 2010. The data are contained in the file Snow. For example, the average low temperature for Columbus, Ohio is 44 degrees and the average annual snowfall is 27.5 inches.
a. Construct a scatter diagram with the average annual low temperature on the horizontal axis and the average annual snowfall on the vertical axis.
b. Does there appear to be any relationship between these two variables?
c. Based on the scatter diagram, comment on any data points that seem to be unusual.

People often wait until middle age to worry about having a healthy heart. However, recent studies have shown that earlier monitoring of risk factors such as blood pressure can be very beneficial (The Wall Street Journal, January 10, 2012). Having higher than normal blood pressure, a condition known as hypertension, is a major risk factor for heart disease. Suppose a large sample of individuals of various ages and gender was
selected and that each individual’s blood pressure was measured to determine if they
have hypertension. for the sample data, the following table shows the percentage of
individuals with hypertension.
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a. Develop a side-by-side bar chart with age on the horizontal axis, the percentage of individuals with hypertension on the vertical axis, and side-by-side bars based on gender.
b. What does the display you developed in part (a), indicate about hypertension and age?
c. Comment on differences by gender.

Smartphones are advanced mobile phones with Internet, photo, and music and video capability (The Pew Research Center, Internet \& American Life Project, 2011). The following survey results show smartphone ownership by age.
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a. Construct a stacked bar chart to display the above survey data on type of mobile phone ownership. Use age category as the variable on the horizontal axis.
b. Comment on the relationship between age and smartphone ownership.
c. How would you expect the results of this survey to be different if conducted in 2021 ?

Approximately 1.5 million high school students take the 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:
$$
\begin{array}{rrrrr}
1665 & 1525 & 1355 & 1645 & 1780 \\
1275 & 2135 & 1280 & 1060 & 1585 \\
1650 & 1560 & 1150 & 1485 & 1990 \\
1590 & 1880 & 1420 & 1755 & 1375 \\
1475 & 1680 & 1440 & 1260 & 1730 \\
1490 & 1560 & 940 & 1390 & 1175
\end{array}
$$
a. Show a frequency distribution and histogram. Begin with the first class starting at 800 and use a class width of 200 .
b. Comment on the shape of the distribution.
c. What other observations can be made about the SAT scores based on the tabular and graphical summaries?

The DATAfile MedianHousehold contains the median household income for a family with two earners for each of the fifty states (American Community Survey, 2013).
a. Construct a frequency and a percent frequency distribution of median household income. Begin the first class at 65.0 and use a class width of 5 .
b. Construct a histogram.
c. Comment on the shape of the distribution.
d. Which state has the highest median income for two-earner households?
e. Which state has the lowest median income for two-earner households?

Data showing the population by state in millions of people follow (The World Almanac, 2012).
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a. Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million.
b. Does there appear to be any skewness in the distribution? Explain.
c. What observations can you make about the population of the 50 states?

A startup company's ability to gain funding is a key to success. The funds raised (in millions of dollars) by 50 startup companies appear below (The Wall Street Journal, March 10, 2011).
$$
\begin{array}{rrrrr}
81 & 61 & 103 & 166 & 168 \\
80 & 51 & 130 & 77 & 78 \\
69 & 119 & 81 & 60 & 20 \\
73 & 50 & 110 & 21 & 60 \\
192 & 18 & 54 & 49 & 63 \\
91 & 272 & 58 & 54 & 40 \\
47 & 24 & 57 & 78 & 78 \\
154 & 72 & 38 & 131 & 52 \\
48 & 118 & 40 & 49 & 55 \\
54 & 112 & 129 & 156 & 31
\end{array}
$$
a. Construct a stem-and-leaf display.
b. Comment on the display.

Consumer complaints are frequently reported to the Better Business Bureau. In 2011, the industries with the most complaints to the Better Business Bureau were banks; cable and satellite television companies; collection agencies; cellular phone providers; and new car dealerships (USA Today, April 16, 2012). The results for a sample of 200 complaints are contained in the file BBB.
a. Show the frequency and percent frequency of complaints by industry.
b. Construct a bar chart of the percent frequency distribution.
c. Which industry had the highest number of complaints?
d. Comment on the percentage frequency distribution for complaints.

The term Beta refers to a measure of a stock's price volatility relative to the stock market as a whole. A Beta of 1 means the stock's price moves exactly with the market. A Beta of 1.6 means the stock's price would increase by $1.6 \%$ for an increase of $1 \%$ in the stock
( TABLE CAN'T COPY )
market. A larger Beta means the stock price is more volatile. The Betas for the stocks of the companies that make up the Dow Jones Industrial Average are shown in Table 2.17 (Yahoo Finance, November 2014).
a. Construct a frequency distribution and percent frequency distribution.
b. Construct a histogram.
c. Comment on the shape of the distribution.
d. Which stock has the highest Beta? Which has the lowest Beta?

The U.S. Census Bureau serves as the leading source of quantitative data about the nation's people and economy. The following crosstabulation shows the number of households ( 1000 s) and the household income by the level of education for heads of household having received a high school degree or more education (U.S. Census Bureau website, 2013).
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a. Construct a percent frequency distribution for the level of education variable. What percentage of heads of households have a master's or doctoral degree?
b. Construct a percent frequency distribution for the household income variable. What percentage of households have an income of $$\$ 50,000$$ or more?
c. Convert the entries in the crosstabulation into column percentages. Compare the level of education of houscholds with a household income of under $$\$ 25,000$$ to the level of education of households with a household income of $$\$ 100,000$$ or more. Comment on any other items of interest when reviewing the crosstabulation showing column percentages.

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:
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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:
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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.

Fortune magazine publishes an annual survey of the 100 best companies to work for. The data in the DATAfile named FortuneBest 100 shows the rank, company name, the size of the company, and the percentage job growth for full-time employees for 98 of the Fortune 100 companies for which percentage job growth data were available (Fortune magazine website, February 25, 2013). The column labeled Rank shows the rank of the company in the Fortune 100 list; the column labeled Size indicates whether the company is a small company (less than 2500 employees), a midsized company ( 2500 to 10,000 employees), or a large company (more than $10,000 \mathrm{employees}$ ); and the column labeled Growth Rate $(\%)$ shows the percentage growth rate for full-time employees.
a. Construct a crosstabulation with Job Growth (\%) as the row variable and Size as the column variable. Use classes starting at -10 and ending at 70 in increments of 10 for Growth Rate (\%).
b. Show the frequency distribution for Job Growth ( $\%$ ) and the frequency distribution for Size.
c. Using the crosstabulation constructed in part (a), develop a crosstabulation showing column percentages.
d. Using the crosstabulation constructed in part (a), develop a crosstabulation showing row percentages.
e. Comment on the relationship between the percentage job growth for full-time employees and the size of the company.

Table 2.18 shows a portion of the data for a sample of 103 private colleges and universities. The complete data set is contained in the file named Colleges. The data include the name of the college or university, the year the institution was founded, the tuition and fees (not including room and board) for the most recent academic year, and the percentage of full time, first-time bachelor's degree-seeking undergraduate students who obtain their degree in six years or less (The World Almanac, 2012).
a. Construct a crosstabulation with Year Founded as the row variable and Tuition \& Fees as the column variable. Use classes starting with 1600 and ending with 2000 in increments of 50 for Year Founded. For Tuition \& Fees, use classes starting with I and ending 45000 in increments of 5000.
b. Compute the row percentages for the crosstabulation in part (a).
c. What relationship, if any, do you notice between Year Founded and Tuition \& Fees?

Refer to the data set in Table 2.18.
a. Construct a crosstabulation with Year Founded as the row variable and \% Graduate as the column variable. Use classes starting with 1600 and ending with 2000 in increments of 50 for Year Founded. For \% Graduate, use classes starting with $35 \%$ and ending with $100 \%$ in increments of $5 \%$.
b. Compute the row percentages for your crosstabulation in part (a).
c. Comment on any relationship between the variables.

Refer to the data set in Table 2.18.
a. Construct a scatter diagram to show the relationship between Year Founded and Tuition \& Fees.
b. Comment on any relationship between the variables.

Refer to the data set in Table 2.18.
a. Prepare a scatter diagram to show the relationship between Tuition \& Fees and \% Graduate.
b. Comment on any relationship between the variables.
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Google has changed its strategy with regard to how much and over which media it invests in advertising. The following table shows Google's marketing budget in millions of dollars for 2008 and 2011 (The Wall Street Journal, March 27, 2012).
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a. Construct a side-by-side bar chart with year as the variable on the horizontal axis. Comment on any trend in the display.
b. Convert the above table to percentage allocation for each year. Construct a stacked bar chart with year as the variable on the horizontal axis.
c. Is the display in part (a) or part (b) more insightful? Explain.

A zoo has categorized its visitors into three categories: member, school, and general. The member category refers to visitors who pay an annual fee to support the zoo. Members receive certain benefits such as discounts on merchandise and trips planned by the zoo. The school category includes faculty and students from day care and elementary and secondary schools; these visitors generally receive a discounted rate. The general category includes all other visitors. The zoo has been concerned about a recent drop in attendance. To help better understand attendance and membership, a zoo staff member has collected the following data:
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a. Construct a bar chart of total attendance over time. Comment on any trend in the data.
b. Construct a side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis.
c. Comment on what is happening to zoo attendance based on the charts from parts (a) and (b).