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A survey of taxpayers who complete their own tax returns were asked the following questions. Determine the type of data each question produces.

a. Did you use software?

b. How long did it take you to complete this year’s return?

c. Rate the ease with which you completed this year’s return (very easy, quite easy, neither easy or difficult, quite difficult, very difficult)

A random sample of car owners was asked these questions. Identify the type of data.

a. Make of car

b. Age of your car in months

c. Amount of annual insurance

d. Number of miles on odometer

The total reserves of oil in the world are 1,689,078,618,100 barrels. The total reserves of the top 15 countries listed in Exercise 2.13 are 1,563,350,000,000 barrels. Use a graphical technique that emphasizes the percentage breakdown of the top 15 countries.

The following table lists the average oil consumption per day of the top 20 oil-consuming nations. Use a graphical technique to display this information.

 

The production of steel has often been used as a measure of the economic strength of a country. The next table lists the steel produced in the 20 largest steel-producing nations in 2014. The units are millions of metric tons. Use a graphical technique to display these figures. 

Last year the world generated almost 2.6 trillion pounds of garbage. Here is a breakdown of the amounts of garbage produced by different regions of the world. Use a graphical technique to present these statistics.

The table below is breakdown of types and amounts of garbage the world creates. Use an appropriate graphical technique to present these figures.
The following table lists the top 10 countries and the amounts of oil (in thousands of barrels per day) they exported to the United States in 2015. 

Each year Michigan State University’s Collegiate Employment Research Institute (CERI) conducts a broad-based survey that tracks starting salaries. This year CERI collected data from the employment offices at 200 universities, which gathered starting salaries from 3,300 employers. The table below lists the undergraduate degrees with the 25 highest average starting salaries. Use an appropriate graphical technique to display the results.
24 The following table lists the annual world production of 21 fruits (in millions of metric tons). Use a graphical technique to present these figures.
Governments in both Canada and the United States have considered passing legislation that increases the minimum hourly wage to $15. The current (as of October 2015) minimum hourly wage in each Canadian province and the percentage of employees earning the minimum wage was recorded and listed below. Use a graphical technique to present these figures. Province Minimum Wage Percent Earning Minimum Wage Alberta 10.20 2.20% British Columbia 10.45 5.60% Saskatchewan 10.20 3.30%



The following exercises require a computer and software. 

Pew Research Center Date: June 2015 Population: Americans who are most likely to vote, donate to campaigns, and participate directly in politics. (They comprise about 20% of all Americans.) Question: Views of their close friends. Responses:

1. Many close friends share my views on government and politics.

2. Some of my close friends share my views but many do not.

3. I don’t really know what my close friends think. Use a graphical method to describe the results of the survey.

Pew Research Center Date: December 2015 Population: American adults Question 1: “Which Social Class does the Republican Party favor?” Question 2: “Which Social Class does the Democratic Party favor?” (Each question was posed to a different sample.) 

Responses: 1. Rich 2. Middle class 3. Poor 

a. For each question draw a pie chart. 

b. What do the pie charts tell you about Americans’ perception of the Republican and Democratic parties?

The table below lists the electricity consumption (in Kilowatt-hours) in the top 20 electricity using countries. Graph the numbers to help describe the figures.


Gallup Organization Date: April 2016 Population: American adults Question: “As I read off some different groups, please tell me if you think they are paying their FAIR share in federal taxes, paying too MUCH or paying too LITTLE? First, how about upper income people? Responses: 1. Fair share 2. Too much 3. Too little 4. No opinion a. Determine the frequency and the relative frequency distributions. b. Draw a bar chart. c. Draw a pie chart. d. Briefly describe your findings.

Pew Research Center
Date: November 2015
Population: Married, two-parent households with at least one child under 18
Question: How do working parents share the work load at home?
Responses:
1. Mom: Full time; Dad: Full time
2. Mom: Part time; Dad: Full time
3. Mom: Not employed; Dad: Full time
4. Mom: Full time; Dad: Part time or not employed
5. Mom: Not employed; Dad: Not employed
6. Other
a. Create the frequency and the relative frequency distributions.
b. Draw a pie chart.
c. Draw a bar chart.
d. Describe your results.

Gallup Organization
Date: May 2016
Population: American adults
Question “Please tell me whether you strongly favor or strongly oppose keeping the Affordable Care Act in place.
Responses:
1. Favor
2. Oppose
3. No opinion
Use a graphical technique to summarize these data.
Describe what you discovered.

Gallup Organization
Date: May 2016
Population: American adults
Question: “Describe your views on social issues.”
Responses:
1. Liberal
2. Moderate
3. Conservative
a. Determine the frequency and the relative frequency distributions.
b. Draw a pie chart and describe the results.

Gallup Organization
Date: May 2016
Population: American adults
Question: “Describe your views on economic issues.”
Responses:
1. Liberal
2. Moderate
3. Conservative
a. Determine the frequency and the relative frequency distributions.
b. Draw a pie chart and describe the results.

Has the educational level of adults changed over the past 15 years? To help answer this question the Bureau of Labor Statistics compiled the following table, which lists the number (1,000) of adults 25 years of age and older who are employed. Use a graphical technique to present these figures. Briefly describe what the chart tells you.

The average loss from robbery in the United States in 2014 (last year available) was $1,227. Suppose that an insurance analyst wanted to know whether the type of robbery differs in the years 1995, 2000, 2005, 2009, and 2014. A random sample of robbery reports was taken from each of these years and the types recorded using the codes that follow. Determine whether there are differences in the types of robberies over the 19-year span. 

1. Street or highway
2. Commercial house
3. Gas station
4. Convenience store
5. Residence
6. Bank
7. Other

Exercise 2.34 presented the data from a Pew Research Center survey of American adults describing whether their friends share their political views. Also recorded were the political views of the respondents. The responses are as follows: 

1. Consistent conservative
2. Mostly conservative
3. Mixed
4. Mostly liberal
5. Consistent liberal
Use a graphical technique to determine whether the responses to the question differs between the five political views.

In Exercise 2.35 a Gallup survey asked American adults whether they believed that upper income people are paying their fair share in federal taxes. Each respondent was also classified as 1. Conservative 2. Moderate 3. Liberal Present a graphical method to determine whether there are differences between the three political groups in their responses to the issue of higher income people paying their fair share of federal taxes.

In addition to asking American adults whether they support keeping the Affordable Care Act the Gallup poll determined whether the respondents were 1. Democrats or 2. Republicans. Determine whether Democrats and Republicans differ in their support of the Affordable Care Act.

Exercise 2.39 featured a Gallup survey of American adults asking whether they are liberal, moderate or conservative on social issues. In addition, the survey asked respondents whether they considered themselves to be 1. Democrat 2. Independent 3. Republican Develop a graph that depicts the differences between the three political parties with respect to their responses about social issues.

The Gallup poll in Exercise 2.40 asked American adults about their views on economic issues. The survey also asked which political party they supported. 1. Democrat 2. Independent 3. Republican Use a graphical technique to gauge the differences between the three political parties concerning economic issues.

As of May 2016 the U.S. government owes $19,190,059,553,782. To whom does the U.S. government owe money? The list is shown below (in $billions). Use a graphical technique to depict these figures.

 

Refer to Exercise 2.55. Here is a list of the top 10 foreign governments that own the U.S. debt (in order of magnitude). Depict these figures with a graph.
June 7 is known as Tax Freedom day in Canada. The annual taxes paid by an average Canadian family earning $105,236 is $45,167. The breakdown of these taxes is shown in the table below. Use an appropriate graphical technique to present these figures.

The Consumer Expenditure Survey measures how consumers allocate their spending. A recent survey asked respondents to specify the amount of their budget spent on food, housing, transportation, healthcare, and insurance and pensions. Also recorded were the composition of the consumer unit. These are summarized in the table below. Use a pie chart to allow a comparison of the three consumer units.

The primary objective of the Affordable Care Act was to decrease the number of nonelderly without any health insurance. It is estimated that there are still approximately 40 million Americans without health insurance. Researchers asked a sample of them why they are not insured. The responses and the percentages are listed in the table below. Use a graphical method to depict these figures. (Numbers do not add to 100% because of rounding.)


The following exercises require a computer and software. 

Refer to Exercise 2.59. The percentage of uninsured in 2013 and 2014 in each of the 50 states plus District of Columbia was recorded. Use a graphical technique to show the decrease in the uninsured rate.

The population of the United States is approximately evenly divided between men and women. Draw a pie chart of the number of male and female respondents. Does it appear that the General Social Survey chose its respondents at random?

Graphically describe the racial makeup of the respondents.

a. Determine the relative frequency distribution of marital status.

b. Which graphical technique would you use to graphically describe marital status?

c. Use your choice of graph.

Graphically describe the respondents’ highest completed degree.

Are there differences between men and women in terms of the completion of their highest degree? Use a graphical method to answer the question.

Use a pie chart to depict the proportion of respondents who worked for the government or worked in the private sector.

Are there differences between the three categories of race with respect to working for the government or working in the private sector? Draw a graph to depict the differences.

Use a graphical method to determine whether men and women differ with respect to working for themselves or someone else. 


The following exercises are based on the General Social Survey in 2014 featuring the variables listed next.
SEX: 1. Male; 2. Female
RACE: 1. White; 2. Black; 3. Other
MARITAL: 1. Married; 2. Widowed; 3. Divorced; 4. Separated; 5. Never married
DEGREE: 0. Left high school; 1. Graduated high school; 2. Completed junior college; 3. Completed
Bachelor’s degree; 4. Completed graduate degree
WRKGOVT: 1. Government; 2. Private
WRKSLF: 1. Self-employed; 2. Work for someone else

Use a graphical technique to describe the respondents’ family structure. 

Are there differences between men and women heads of households in terms of education category (EDCL)? Use a graphical method to answer the question.

Graphically describe the racial makeup of the respondents.

Are there differences between the races in terms of family structure? Graphically answer the question.

Are there differences between the four categories of education in terms of home ownership. Use a graph to answer the question.

A data set consists of 300 observations that range between 147 and 241. 

a. What is an appropriate number of classes to have in the histogram? 

b. What class intervals would you suggest?

A statistics practitioner would like to draw a histogram of 40 observations that range from 5.2 to 6.1.
a. How many class intervals should the histogram use?
b. Define the upper limits of the classes.

An Uber driver kept track of the number of calls he received over a 28-day period. The data are listed here. Create a histogram.

There are a number of minor-league baseball players who never make it to the major leagues. A statistics practitioner kept track of the age at which 32 players realized their dream of playing in the majors would never be fulfilled and retired. Draw a histogram of these data

.

The 17th hole at the TPC (Tournament Players Club) is an island green that causes even professional players to put their tee shots into the surrounding pond. A statistics practitioner kept track of the number of golf balls put into the pond by amateurs for each of 30 days with the results listed here. Draw a histogram of these data.

A survey of 60 individuals leaving a mall asked how many stores they entered during this visit to the mall. The figures are listed here. 

a. Draw a histogram to summarize these data. 

b. Describe the shape of the histogram. The following exercises require a computer and statistical software. 

Among American adults with children draw a histogram of their ages when their first child was born (AGEKDBRN).

How much television were American adults watching in 2014 (TVHOURS)? Produce a histogram to help answer the question.

How well were Americans doing financially in 2014. Draw a histogram of respondents’ incomes (RINCOME). Describe the shape.

How educated were American adults in 2014? Draw a histogram to help provide a graphical answer (EDUC).

Draw a histogram of the ages (AGE) of the respondents. What information do you draw from the histogram?

Users of previous editions of this book could download an Excel add-in called Data Analysis Plus from our website. We recorded the number of daily downloads during a 78-day period.

a. Draw a histogram.

b. Describe its shape.

The number of customers entering a bank in the first hour of operation for each of the last 200 days was recorded. Draw a histogram and describe its shape.

Currently Ebay lists over 550,000 U.S. collector coins for sale or auction. An avid collector tracked the number of days it took for 500 coins to be sent to his home. Create a histogram of these figures. What information can you draw from the shape of the histogram?

The annual incomes for a sample of 200 first-year accountants were recorded. Draw a histogram and describe its shape.

A survey of 50 baseball fans to report the number of games they attended last year. Draw a histogram and describe its shape.

Draw a histogram of the ages of the respondents in the 2013 survey. What information can you extract from the histogram?

Create a histogram of the number of children. Despite the fact that the sample size is over 6,000, why should you not have 20 class intervals?

One of the questions asked respondents to report the total value of assets held by the household in 2013 dollars. Note that the range is very large. The minimum is $0 and the maximum is $1,312,587,840.

a. Draw a histogram using the number of class intervals suggested by the following table that is, between 13 and 17 class intervals. What problems did you encounter?

b. Try drawing a histogram with the following class intervals 10,000, 20,000, . . . 200,000 What problem do you encounter?

c. Draw a histogram with the following class intervals 100,000, 200,000, . . . 2,000,000 d. Briefly discuss which histogram drawn in (a), (b), and (c) is best.

Number of Observations Number of Classes                                         Less than 50 5–7
50–200.......................................................................................................................... 7–9
200–500....................................................................................................................... 9–10
500–1,000...................................................................................................................10–11
1,000–5,000 ...............................................................................................................11–13
5,000–50,000..............................................................................................................13–17
More than 50,000......................................................................................................17–20

Respondents were asked to report the total value of certificates of deposit (CDs) in 2013 dollars held by the household.

a. Try drawing histograms with different numbers of class intervals and different upper limits.

b. What problem do you encounter in drawing a histogram of CDs?

c. Suggest ways of solving the problem of drawing histograms when the range is very large.

How well have Canada and the United States performed at the Winter Olympics? In the table displayed here, we list the total number of medals won by the two countries in each year. Draw a chart to describe both time series.

Determine the number of classes of a histogram for 1500 observations.


It won’t come as a surprise to hockey fans that with each passing season the number of goals scored is decreasing. Many experts blame goalie equipment. The oversized pads and other protection for goalies now makes even relatively small goalies look like 250-pound athletes. To learn more about the problem a statistics practitioner recorded the save percentage (the percentage of shots that a goalie saves) and the goals against average (the average number of goals allowed) for each season between 1984 and 2016. These data are listed here. 

a. Draw a line chart of the save percentage 

b. Draw a line chart of the goals against average

The number of violent crimes and the number of property crimes (burglary, larceny theft, and car theft) (in thousands) for the years 1993 to 2012 (latest figures available) are listed here. 

a. Draw a line chart of the violent crimes. 

b. Draw a line chart of the property crimes 


The following exercises require a computer and statistical software. Exercises 3.35 to 3.45 deal with various parts of the U.S. federal budget. For each exercise, draw the following line charts and briefly describe what the chart tells you about each variable. a. Original data b. Per capita data c. Per capita in constant 1982–1984 dollars 

The United States spends more money on health care than any other country. To gauge how fast costs are rising we recorded the total health care costs since 1950.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

The U.S. government provides Medicare to Americans who are 65 years and older. Medicare Part A pays the costs of hospital and nursing care, but not physicians’ bills. The file lists Medicare Part A costs since 1966.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Medicare Part B pays for a portion of physicians’ visits, medical equipment, outpatient procedures, rehabilitative therapy, laboratory tests, X-rays, ambulance service, and blood. Costs were recorded for 1967 to 2015.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Medicaid is a program created by the federal government, but administered by the state, to provide payment for medical services for low-income citizens. The costs were recorded from 1962 to 2015.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Social Security Disability Insurance a program that pays monthly benefits to individuals who have become disabled before reaching retirement age and aren’t able to work. SSDI costs were recorded for the years 1958 to 2015.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Social Insurance Old Age Survivor Insurance provides a pension for Americans who are over 60 years of age and whose spouse has died. Costs for 1958 to 2015 were recorded.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

The defense budget for years 1935 to 2015 were recorded.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Total Federal government spending from 1935 to 2015 is stored.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Welfare payments for 1965 to 2015 were recorded.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Education spending from 1935 to 2015 was recorded.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Interest on Federal Debt from 1935 to 2015 was recorded.


Draw the following line charts and briefly describe what the chart tells you about each variable.
a. Original data
b. Per capita data
c. Per capita in constant 1982–1984 dollars

Refer to Exercise 3.34.

a. Draw a line chart of the violent crime rate per 100,000 of population.

b. Draw a line chart of the property crime rate per 100,000 of population.

c. Describe your findings.

The average daily U.S. oil consumption and production (thousands of barrels) was recorded for the years 1973 to 2015. Draw a line chart for both sets of figures. Describe what you have learned.

The gross domestic product (GDP) is the sum total of the economic output of a country. It is an important measure of the wealth of a country. The GDP of the United States from 1935 to 2015 is stored in the file. 

a. Draw a line chart of the GDP. 

b. Adjust the GDP for inflation and draw line chart of the adjusted GDP 

c. Briefly describe what the charts tell you.

The monthly value of U.S. exports to Canada (in $millions) and imports from Canada from 1985 to 2016 was recorded.

a. Draw a line chart of U.S. exports to Canada.

b. Draw a line chart of U.S. imports from Canada.

c. Calculate the trade balance and draw a line chart.

d. What do all the charts reveal?

The monthly value of U.S. exports to Japan (in $millions) and imports from Japan from 1985 to 2016 was recorded.

a. Draw a line chart of U.S. exports to Japan.

b. Draw a line chart of U.S. imports from Japan.

c. Calculate the trade balance and draw a line chart.

d. What do all the charts reveal?

The monthly value of U.S. exports to China (in $millions) and imports from China from 1985 to 2016 was recorded.

a. Draw a line chart of U.S. exports to China.

b. Draw a line chart of U.S. imports from China.

c. Calculate the trade balance and draw a line chart.

d. What do all the charts reveal?

The exchange rate of the Canadian dollar to one U.S. dollar was recorded monthly for the period 1971 to 2016. Draw a graph of these figures and interpret your findings.

The exchange rate of the Japanese Yen to one U.S. dollar was recorded monthly for the period 1971 to 2016. Draw a graph of these figures and interpret your findings.

The Jones Industrial Average was recorded monthly (close) from 1950 to 2016. Use a graph to describe these numbers.

Because inflation reduces the purchasing power of the dollar, investors seek investments that will provide higher returns when inflation is higher. It is frequently stated that common stocks provide just such a hedge against inflation. The annual percentage rates of return on common stock and annual inflation rates for a recent 10-year period are listed here.

 

Draw a scatter diagram and describe what it tells you about the relationship between returns and inflation. 

It is well known that mathematicians do their best work before the age of 30. But, what happens to them as they grow older? A statistician took a random sample of mathematics professors who were older than 40 and determined their age and the number of top-tier journal publication they produced in the previous 5 years. Draw a scatter diagram and report what it tells you about the research productivity as mathematicians grow older.

In attempt to determine the factors that affect the amount of energy used, 200 households were analyzed. The number of occupants and the amount of electricity used were measured for each household. Produce a scatter diagram. What does the graph tell you about the relationship between number of people in a household and electrical use?

Do chief executive officers (CEOs) of publicly traded companies earn their compensation? Every year the National Post’s Business magazine attempts to answer the question by reporting the CEO’s annual compensation ($1,000), the profit (or loss) ($1,000), and the three-year share return (%) for the top 50 Canadian companies. 

a. Draw a scatter diagram of the CEO’s annual compensation and the profit of the company. 

b. Draw a scatter diagram of the CEO’s annual compensation of the three-year share return. 

c. Based on the scatter diagrams in (a) and (b) report whether the CEO’s earn their compensation.

Are younger workers less likely to stay with their jobs? To help answer this question, a random sample of workers was selected. All were asked to report their ages and how many months they had been employed with their current employers. 

a. Produce a scatter diagram. 

b. Does your graph produce evidence to indicate that younger workers are less likely to stay with their jobs?

It is generally believed that higher interest rates result in less employment because companies are more reluctant to borrow to expand their business. To determine whether there is a relationship between bank prime rate and unemployment, an economist collected the monthly prime bank rate and the monthly unemployment rate for the years 1950 to 2012. 

a. Create a scatter diagram of the employment and interest rates.

b. Is there a negative relationship?

Do better golfers play faster than poorer ones? To determine whether a relationship exists, a sample of 125 foursomes was selected. Their total scores and the amount of time taken to complete the round were recorded. Graphically depict the data and describe what they tell you about the relationship between total score and time.

Is airline travel becoming safer? To help answer this question, a statistics professor recorded the number of fatal accidents involving airliners carrying at least 19 passengers that occurred in the years 1950 to 2014. Use a graphical method to answer the question.

The monthly values of one British pound measured in American dollars since 1971 were recorded. Produce a graph that shows how the exchange rate has varied over the past 45 years.

When the Dow-Jones Industrial Index increases it usually means that the economy is growing, which in turn usually means that the unemployment rate is low. A statistics professor pointed out that in numerous periods (including when this edition was being written) the stock market has been booming while the rest of the economy was performing poorly. To learn more about the issue, the monthly closing DJIA and the monthly unemployment rates were recorded for the years 1950 to 2016. Draw a graph of the data and report your results.

In Chapters 16, 17, and 18, we introduce regression analysis, which addresses the relationships among variables. One of the first applications of regression analysis was to analyze the relationship between the heights of fathers and sons. Suppose that in a sample of 80 father–son combinations their heights were recorded.

a. Draw a graph that displays the relationship.

b. What is the direction of the relationship?

c. Does it appear that there is a linear relationship between the two variables? Explain.

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