Pareto Diagrams
1.4 G RAPHS TO D ESCRIBE T IME -S ERIES D ATA
1.16 On what type of Internet activity do you spend the
most time? The responses from a random sample of 700 Internet users were banking online, 40; buying a product, 60; getting news, 150; sending or reading e-mail, 200; buying or making a reservation for travel, 75; checking sports scores or information, 50; and searching for an answer to a question, 125. Describe the data graphically.
1.17 A random sample of 100 business majors was asked a series of demographic questions includ-ing major, gender, age, year in school, and current grade point average (GPA). Other questions were also asked for their levels of satisfaction with campus park-ing, campus houspark-ing, and campus dining. Responses to these satisfaction questions were measured on a scale from 1 to 5, with 5 being the highest level of sat-isfaction. Finally, these students were asked if they planned to attend graduate school within 5 years of their college graduation (0: no; 1: yes). These data are contained in the data file Finstad and Lie Study.
a. Construct a cluster bar chart of the respondents’
major and gender.
b. Construct a pie chart of their majors.
1.18 The Healthy Eating Index–2005 measures how well the population follows the recommendations of the 2005 Dietary Guidelines for Americans. Table 1.2 is a frequency distribution of males and females in each of three activity level lifestyles: sendentary, active, and very
active. This activity level was taken at the first interview (daycode = 1).
a. Use the data in Table 1.2 or data (coded daycode = 1) contained in the data file HEI Cost Data Variable Subset to construct a pie chart of the percent of males in each of the activity level categories.
b. Use the data in Table 1.2 or data (coded daycode = 1) contained in the data file HEI Cost Data Variable Subset to construct a pie chart of the percent of females in each of the activity level categories.
1.19 Internet Explorer (IE) dropped below 50% of the worldwide market for the first time in Sep-tember 2010 (StatCounter Global Stats Microsoft 2010).
IE’s worldwide market share continued to decrease over the next several months. Worldwide market share data from January 2010 through February 2011 for IE, Firefox, Chrome, Safari, and Opera are con-tained in the data file Browser Wars.
a. Depict the worldwide market shares for February 2011 for the data contained in the data file Browser Wars using a pie chart.
b. Use a pie chart to depict the current market shares for these Internet browsers (Source: gs.statcounter.com).
c. Select a country or region from the list provided by StatCounter Global Stats and depict the market shares for the current time period with a pie chart (Source: gs.statcounter.com).
1.4 G
RAPHS TOD
ESCRIBET
IME-S
ERIESD
ATASuppose that we take a random sample of 100 boxes of a new variety of cereal. If we collect our sample at one point in time and weigh each box, then the measurements obtained are known as cross-sectional data. However, we could collect and measure a random sample of 5 boxes every 15 minutes or 10 boxes every 20 minutes. Data measured at successive points in time are called time-series data. A graph of time-series data is called a line chart or time-series plot.
Line Chart (Time-Series Plot)
A time series is a set of measurements, ordered over time, on a particular quan-tity of interest. In a time series the sequence of the observations is important. A line chart, also called a time-series plot, is a series of data plotted at various time intervals. Measuring time along the horizontal axis and the numerical quantity of interest along the vertical axis yields a point on the graph for each observation.
Joining points adjacent in time by straight lines produces a time-series plot.
Examples of time-series data include annual university enrollment, annual interest rates, the gross domestic product over a period of years (Example 1.5), daily closing prices for shares of common stock, daily exchange rates between various world currencies ( Example 1.6), gov-ernment receipts and expenditures over a period of years (Example 1.7), monthly product sales, quarterly corporate earnings, and social network weekly traffic (such as weekly num-ber of new visitors) to a company’s Web site (Example 1.8). In Chapter 16 we consider four components (trend, cyclical, seasonal, and irregular) that may affect the behavior of time-series data, and we present descriptive procedures for analyzing time-time-series data.
36 Chapter 1 Using Graphs to Describe Data
Example 1.5 Gross Domestic Product (Time-Series Plot)
One of the world’s most prominent providers of economic statistics is the Bureau of Economic Analysis (BEA), an agency of the U.S. Department of Commerce. The BEA provides economic data such as the annual (or quarterly or monthly) Gross Domestic Product (GDP), as well as many other regional, industrial, national, and international economic statistics. These data are valuable to government officials, business executives, and individuals in making decisions in the face of uncertainty. The annual GDP from 1929 through 2009 (in billions) is contained in the data file Macro 2009. GDP and other data provided by Bureau of Economic Analysis are available online at www.bea.gov. Graph GDP from 1929–2009 with a time-series plot.
Solution The time-series plot in Figure 1.7 shows the annual GDP data growing rather steadily over a long period of time from 1929 through 2009. This pattern clearly shows a strong upward trend component that is stronger in some periods than in others. This time plot reveals a major trend component that is important for initial analysis and is usually followed by more sophisticated analyses (Chapter 16).
Figure 1.7 Gross Domestic Product by Time: 1929–2009 (Time-Series Plot)
Example 1.6 Currency Exchange Rates (Time-Series Plot)
Investors, business travelers, tourists, and students studying abroad are all aware of the fluctuations in the exchange rates between various world currencies. Exchange rates between U.S. dollars (USD) and the euro (EUR) as well as the exchange rates between USD and the British pound (GBP) for the 6-month period from August 22, 2010, through February 17, 2011, are contained in the data file Currency Exchange Rates. Plot these data with time-series plots.
Solution Figure 1.8 shows the currency conversion from USD to 1 EUR. Figure 1.9 is a time series plot of the currency exchange rate from USD to 1 GBP.
6000 14000
Billions of Real 2005 Dollars
12000
4000
0
1929 1949 1969 1989 2009
2000 8000 10000
1.4 Graphs to Describe Time-Series Data 37
Example 1.7 Federal Government Receipts and Expenditures: 1929–2009 (Time-Series Plot)
The state of the economy is important to each of us. It is not just a topic for govern-ment officials. The data file Macro 2009 contains information such as the gross domes-tic product, personal consumption expenditure, gross private domesdomes-tic investment, imports, exports, personal savings in 2005 dollars, and many other variables from 1929 through 2009. Graph the annual U.S. federal government receipts and expenditures from 1929 to 2009.
1.35 1.45
Currency Exchange Rate
1.40
1.30
1.20
22-Aug 22-Sep 22-Oct 22-Nov 22-Dec
U.S. Dollars (USD) to 1 Euro (EUR) August 22, 2010 to February 17, 2011
1.25
22-Jan
Figure 1.8 Currency Exchange Rates: USD to EUR (Time-Series Plot)
Figure 1.9 Currency Exchange Rates: USD to GBP (Time-Series Plot)
1.58 1.64
Currency Exchange Rate
1.62 1.60
1.56 1.54
1.50
22-Aug 22-Sep 22-Oct 22-Nov 22-Dec
U.S. Dollars (USD) to 1 British Pound (GBP) August 22, 2010 to February 17, 2011
1.52
22-Jan
Example 1.7 and Example 1.8 illustrate that sometimes a time-series plot is used to compare more than one variable over time
38 Chapter 1 Using Graphs to Describe Data
Solution From the data in the data file Macro 2009 we construct two time-series plots. Figure 1.10 is a time plot that shows the annual U.S. federal government receipts and expenditures in billions of real 2005 dollars from 1929 through 2009. In Figure 1.11 the annual U.S. federal government receipts and expenditures are plotted as a percent of the GDP.
Figure 1.10 U.S. Federal Government Receipts and Expenditures: 1929–2009 (Time-Series Plot)
Figure 1.11 U.S. Federal Government Receipts and Expenditures as Percent of GDP: 1929–2009 (Time-Series Plot)
Example 1.8 Social Network Traffic (Time-Series Plot)
RELEVANT Magazine keeps records of traffic (such as the number of weekly new visitors) to its Web site from various social networks such as Facebook and Twitter (Butcher 2011). This information may be helpful to Richard Butcher, Marketing As-sistant of RELEVANT Magazine. Plot the number of weekly new visitors for a recent
1500 3000
Billions of Real 2005 Dollars
1000
0
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
U.S. Federal Government Receipts and Expenditures Real 2005 Dollars
500 2000 2500
Variable
Real Fed Govt Receipts Real Fed Govt Expenditures
Year
30 50
Percent of GDP
20
0
1920 1930 1940 1950 1960 1970 Year
1980 1990 2000 2010 U.S. Federal Government Receipts and Expenditure as Percent of GDP
Real 2005 Dollars
10 40
Percent GDP Fed Exp Percent GDP Fed Receipts Variable
Exercises 39 9-week period from both Facebook and Twitter. Use a time-series plot. The data are stored in the data file RELEVANT Magazine.
Solution From the data file RELEVANT Magazine we obtain the number of weekly new visitors for a recent 9-week period from both Facebook and Twitter. This information is given in Table 1.5. The time series plot in Figure 1.12 shows the trend over this same time period.
Table 1.5 Social Network Traffic: Weekly New Visitors to RELEVANT Magazine Web Site
WEEK TWITTER FACEBOOK
1 5,611 20,499
2 6,799 22,060
3 6,391 21,365
4 6,966 17,905
5 6,111 17,022
6 8,101 20,572
7 7,370 22,201
8 7,097 17,628
9 7,531 24,256
Figure 1.12 RELEVANT Magazine: Social Network Traffic of Weekly New Visitors (Time-Series Plot)
RELEVANT Magazine Social Network Traffic
Week
Number of New Visitors
1 30000 25000 20000 15000 10000 5000 0
2 3 4 5 6 7 8 9
Facebook Twitter
E
XERCISESVisit www.mymathlab.com/global or www.pearsonglobal editions.com/newbold to access the data files.
Basic Exercises
1.20 Construct a time-series plot for the following number of customers shopping at a new mall during a given week.
Day Number of Customers
Monday 525
Tuesday 540
Wednesday 469
Thursday 500
Friday 586
Saturday 640
40 Chapter 1 Using Graphs to Describe Data
1.21 The number of males and females enrolled in colleges (undergraduate and postbaccalaureate) in the United States from 2000 through 2008 is given here. Graphi-cally present these data with a time-series plot.
College Enrollment
(in thousands) Males Females
2000 6,721.8 8,590.5
2001 6,960.8 967.2
2002 7,202.1 9,409.6
2003 7,255.6 9,644.9
2004 7,387.3 9,884.4
2005 7,455.9 10,031.6
2006 7,574.8 10,184.1
2007 7,815.9 10,432.2
2008 8,188.9 10,913.9
source: Table 275. (2011). Statistical Abstract of the United States.
Application Exercises
1.22 From the data file Macro 2009 use a time plot to graph both gross domestic investment and gross private savings in billions of real 2005 dollars.
1.23 Information about the GDP in the area of manufactur-ing of durable and nondurable goods is important to business owners and economists.
a. Use a time-series plot to graph the GDP in manu-facturing in current and real (2005) dollars by in-dustry for durable goods (such as wood products, furniture and related products, motor vehicles, and equipment) from 2000 to 2009. Data are in billions of dollars (Source: Table 1002. 2011. Statistical Ab-stract of the United States).
b. Use a time-series plot to graph the GDP in manu-facturing in real dollars (2005) by industry for non-durable goods (such as food, apparel, and leather products) from 2000 to 2009. Data are in billions of dollars (Source: Table 1002 2011).
1.24 In Example 1.6 we plotted the USD to 1 EUR for a 6-month time period.
a. Use a time-series plot to graphically display the currency conversion from the EUR to 1 USD. The data are contained in the data file Currency Ex-change Rates.
b. Use a time-series plot to graphically display the currency conversion from the GBP to 1 USD. The data are contained in the data file Currency Ex-change Rates.
c. Compare your currency with an appropriate world currency for the last 30 days.
1.25 Market shares for a period of 14 months for var-ious Internet providers are contained in the data file Browser Wars.
a. Use a time-series plot to graphically display the worldwide market shares of IE, Firefox, Chrome, Safari, and Opera.
b. Use a time-series plot to graphically display the European market shares of IE, Firefox, Chrome, Safari, and Opera.
c. Use a time-series plot to graphically display the North American market shares of IE, Firefox, Chrome, Safari, and Opera.
1.26 Select annual returns on a stock market index over 14 years from the Internet. Graph the data with a time-series plot.
1.27 The data file Gold Price shows the year-end price of gold (in dollars) over 14 consecutive years. Graph the data with a time-series plot.
1.28 The data file Housing Starts shows private housing units started per thousand persons in the U.S. population over a period of 24 years. Describe the data with a graph.
1.29 Earnings per share of a corporation over a pe-riod of 28 years are stored in the data file Earn-ings per Share. Graph the series and comment on the plot.