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mathematics
statistics

Questions and Answers of Statistics

The numbers of property crimes (burglary, larceny, theft, car theft) (in thousands) for the years 1992 to 2009 are listed next. Draw a line chart and interpret theresults.
Refer to Exercise. Another way of measuring the number of property crimes is to calculate the number of crimes per 100,000 of population. This allows us to remove the effect of the increasing
The gross national product (GNP) is the sum total of the economic output of the citizens (nationals) of a country. It is an important measure of the wealth of a country. The following table lists the
The average daily U.S. oil consumption and production (thousands of barrels) is shown for the years 1973 to 2011. Use a graphical technique to describe these figures. What does the graph tell you?
The table below lists the value ($millions) of new residential construction in the United States between 1981 and 2010. Graph these data and describe what you have learned.Value of New Residential
How has the size of government changed? To help answer this question we recorded the U.S. federal budget receipts and outlays (billions of current dollars) for the years 1980 to 2011.a. Use a
Refer to Exercise. Another way of judging the size of budget surplus/deficits is to calculate the deficit as a percentage of GNP. Use the dataÂ inÂ Exercises 3.35 and 3.38 to calculate
Repeat Exercise, using the CPI-Annual file to convert all amounts to constant 1982â€“1984 dollars. Draw a line chart to show thesedata.
Refer to Example. The following table lists the average gasoline consumption in miles per gallon (MPG) and the average distance (thousands of miles) driven by cars in each of the years 1980 to 2009.
The monthly value of U.S. exports to Canada (in $millions) and imports from Canada from 1985 to 2012 were recorded.a. Draw a line chart of U.S. exports to Canada.b. Draw a line chart of U.S. imports
The monthly value of U.S. exports to Japan (in $millions) and imports from Japan from 1985 to 2012 were recorded.a. Draw a line chart of U.S. exports to Japan.b. Draw a line chart of U.S. imports
The value of the Canadian dollar in U.S. dollars was recorded monthly for the period 1971 to 2012. Draw a graph of these figures and interpret your findings.
The value of the Japanese yen in U.S. dollars was recorded monthly for the period 1971 to 2012. Draw a graph of these figures and interpret your findings.
The Dow Jones Industrial Average was recorded monthly for the years 1950 to 2012. Use a graph to describe these numbers.
Refer to Exercise. Use the CPI-monthly file to measure the Dow Jones Industrial Average in 1982–1984 constant dollars. What have you learned?
Black Friday in the United States is the day after Thanksgiving. Many retailers offer door-crasher specials to induce customers to shop at their stores. The number of door-crasher specials is
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
In a university where calculus is a prerequisite for the statistics course, a sample of 15 students was drawn. The marks for calculus and statistics were recorded for each student. The data are as
The cost of repairing cars involved in accidents is one reason that insurance premiums are so high. In an experiment, 10 cars were driven into a wall. The speeds were varied between 2 and 20 mph. The
The growing interest in and use of the Internet have forced many companies into considering ways to sell their products on the Web. Therefore, it is of interest to these companies to determine who is
A statistics professor formed the opinion that students who handed in quiz and exams early outperformed students who handed in their papers later. To develop data to decide whether her opinion is
In an 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
Many downhill skiers eagerly look forward to the winter months and fresh snowfalls. However, winter also entails cold days. How does the temperature affect skiers’ desire? To answer this question,
One general belief held by observers of the business world is that taller men earn more money than shorter men. In a University of Pittsburgh study, 250 MBA graduates, all about 30 years old, were
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
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
A very large contribution to profits for a movie theater is the sales of popcorn, soft drinks, and candy. A movie theater manager speculated that the longer the time between showings of a movie, the
An analyst employed at a commodities trading firm wanted to explore the relationship between prices of grains and livestock. Theoretically, the prices should move in the same direction because, as
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
Do younger people have more education (EDUC) than older people (AGE)? Use the American National Election Survey from 2004 and a graphical technique to help answer the question. In the 2008 survey,
Use a graphical technique to determine whether people who spend more time reading news on the Internet also devote more time to watching news on television.
Analyze the relationship between the amount of time reading news on the Internet and reading news in a printed newspaper. Does it appear that they are linearly related?
Refer to Exercise. Study the scatter diagram. Does it appear that something is wrong with the data? If so, how do you correct the problem and determine whether a linear relationship exists?
Graphically describe the relationship between the amount of time watching news on television and listening to news on the radio. Are the two linearly related?
Do younger people spend more time reading news on the Internet than older people? Use a graphical technique to help answer the question.
Do more educated people tend to marry people with more education? Draw a scatter diagram of EDUC and SPEDUC to answer the question.
Do the children of more educated men (PAEDUC) have more education (EDUC)? Produce a graph that helps answer the question.
Is there a positive linear relationship between the amount of education of mothers (MAEDUC) and their children (EDUC)? Draw a scatter diagram to answer the question.
If one member of a married couple works more hours (HRS) does his or her spouse work less hours (SPHRS)? Draw a graph to produce the information you need.
A computer company has diversified its operations into financial services, construction, manufacturing, and hotels. In a recent annual report, the following tables were provided. Create charts to
The following table lists the number (in thousands) of violent crimes and property crimes committed annually in 1985 to 2006 (the last year data were available).a. Draw a chart that displays both
Refer to Exercise. We've added the United States population.a. Incorporate this variable into your charts to show crime rate trends.b. Summarize your findings.c. Can you think of another demographic
Refer to Exercises. Weâ€™ve included the number of Americans aged 15 to 24.a. What is the significance of adding the populations aged 15 to 24?b. Include these data in your analysis. What have
To determine premiums for automobile insurance, companies must have an understanding of the variables that affect whether a driver will have an accident. The age of the driver may top the list of
During 2002 in the state of Florida, a total of 365,474 drivers were involved in car accidents.The accompanying table breaks down this number by the age group of the driver and whether the driver was
The accompanying table lists the average test scores in the Scholastic Assessment Test (SAT) for the years 1967, 1970, 1975, 1980, 1985, 1990, 1995, and 1997 to 2007.Draw a chart for each of the
The monthly unemployment rate in one state for the past 12 months is listed here.a. Draw a bar chart of these data with 6.0% as the lowest point on the vertical axis.b. Draw a bar chart of these data
Gold and other precious metals have traditionally been considered a hedge against inflation. If this is true, we would expect that a fund made up of precious metals (gold, silver, platinum, and
The monthly values of one Australian dollar measured in American dollars since 1971 were recorded. Draw a graph that shows how the exchange rate has varied over the 41-year period.
Studies of twins may reveal more about the “nature or nurture” debate. The issue being debated is whether nature or the environment has more of an effect on individual traits such as
An economist wanted to determine whether a relationship existed between interest rates and currencies (measured in U.S. dollars). He recorded the monthly interest rate and the currency indexes for
One hundred students who had reported that they use their computers for at least 20 hours per week were asked to keep track of the number of crashes their computers incurred during a 12-week period.
In Chapters, 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
When the Dow Jones Industrial Average’s 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
The monthly values of one British pound measured in American dollars since 1987 were recorded. Produce a graph that shows how the exchange rate has varied over the past 25 years.
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 18
The value of monthly U.S. exports to Mexico and imports from Mexico (in $ millions) since 1985 were recorded.a. Draw a chart that depicts exports.b. Draw a chart that exhibits imports.c. Compute the
An increasing number of consumers prefer to use debit cards in place of cash or credit cards. To analyze the relationship between the amounts of purchases made with debit and credit cards, 240 people
Most publicly traded companies have boards of directors. The rate of pay varies considerably. A survey was undertaken by the Globe and Mail (February 19, 2001) wherein 100 companies were surveyed and
Refer to Exercise. In addition to reporting the annual payment per director, the survey recorded the number of meetings last year. Use a graphical technique to summarize and present these data.
Is airline travel becoming safer? To help answer this question, a student recorded the number of fatal accidents and the number of deaths that occurred in the years 1986 to 2008 for scheduled
Most car-rental companies keep their cars for about a year and then sell them to used car dealerships. Suppose one company decided to sell the used cars themselves. Because most used car buyers make
Several years ago, the Barnes Exhibit toured major cities all over the world, with millions of people flocking to see it. Because of the size and value of the collection, it was predicted (correctly)
Examples 3.3 and 3.4 listed the final marks in the business statistics course and the mathematical statistics course. The professor also provided the final marks in the first-year required calculus
In addition to the previously discussed data in Examples 3.3 and 3.4, the professor listed the midterm mark. Conduct an analysis of the relationship between final exam mark and midterm mark in each
Two other questions were asked in Exercise:Number of weeks job searching? Salary ($ thousands)? The placement office wants the following:a. Graphically describe salary.b. Is salary related to the
In the last part of the 20th century, scientists developed the theory that the planet was warming and the primary cause was the increasing amounts of carbon dioxide (Co2), which is the product of
Adam Smith published The Wealth of Nations in 1776. In it, he argued that when institutions protect the liberty of individuals, greater prosperity results for all. Since 1995, the Wall Street Journal
A sample of 12 people was asked how much change they had in their pockets and wallets. The responses (in cents) areDetermine the mean, median, and mode for thesedata.
The number of sick days due to colds and flu last year was recorded by a sample of 15 adults. The data areCompute the mean, median, andmode.
The midterm test for a statistics course has a time limit of 1 hour. However, like most statistics exams this one was quite easy. To assess how easy, the professor recorded the amount of time taken
Compute the geometric mean of the following rates of return..25 −.10 .50
What is the geometric mean of the following rates of return?.50.30 −.50 −.25
The following returns were realized on an investment over a 5-year period.a. Compute the mean and median of the returns.b. Compute the geometric mean.c. Which one of the three statistics computed in
The starting salaries of a sample of 125 recent MBA graduates are recorded.a. Determine the mean and median of these data.b. What do these two statistics tell you about the starting salaries of MBA
To determine whether changing the color of its invoices would improve the speed of payment, a company selected 200 customers at random and sent their invoices on blue paper. The number of days until
A survey undertaken by the U.S. Bureau of Labor Statistics, Annual Consumer Expenditure, asks American adults to report the amount of money spent on reading material in 2009.a. Compute the mean and
A survey of 350 workers in California and 300 workers in New York State asked each to report the average amount of time spent commuting to work.a. Compute the mean and median of the commuting times
In the United States, banks and financial institutions often require buyers of houses to pay fees in order to arrange mortgages. In a survey conducted by the U.S. Federal Housing Finance Board, 400
In an effort to slow drivers, traffic engineers painted a solid line 3 feet from the curb over the entire length of a road and filled the space with diagonal lines. The lines made the road look
How much do Americans spend on various food groups? Three hundred American families were surveyed and asked to report the amount of money spent annually on fruits and vegetables. Compute the mean and
Calculate the variance of the following data.9 3 7 4 1 7 5 4
Calculate the variance of the following data.4 5 3 6 5 6 5 6
Determine the variance and standard deviation of the following sample.12 6 22 31 23 13 15 1721
Find the variance and standard deviation of the following sample.0 −5 −3 6 4 −4 1 −5 0 3
Refer to Exercise. Calculate the variance for each part. Was your answer in Exercisecorrect?
A set of data whose histogram is bell shaped yields a mean and standard deviation of 50 and 4, respectively. Approximately what proportion of observationsa. Are between 46 and 54?b. Are between 42
Refer to Exercise. Approximately what proportion of observationsa. Are less than 46?b. Are less than 58?c. Are greater than 54?
A statistics practitioner determined that the mean and standard deviation of a data set were 120 and 30, respectively. What can you say about the proportions of observations that lie between each of
There has been much media coverage of the high cost of medicinal drugs in the United States. One concern is the large variation from pharmacy to pharmacy. To investigate, a consumer advocacy group
Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a
Three men were trying to make the football team as punters. The coach had each of them punted the ball 50 times, and the distances were recorded.a. Compute the variance and standard deviation for
Variance is often used to measure quality in production-line products. Suppose that a sample of steel rods that are supposed to be exactly 100 cm long is taken. The length of each is determined, and
To learn more about the size of withdrawals at a banking machine, the proprietor took a sample of 75 withdrawals and recorded the amounts. Determine the mean and standard deviation of these data, and
Everyone is familiar with waiting lines or queues. For example, people wait in line at a supermarket to go through the checkout counter. There are two factors that determine how long the queue
Calculate the first, second, and third quartiles of the following sample.5 8 2 9 5 3 7 4
Find the third and eighth deciles (30th and 80th percentiles) of the following dataset.
Find the first and second quintiles (20th and 40th percentiles) of the data shownhere.
Determine the first, second, and third quartiles of the followingdata.
Calculate the 3rd and 6th deciles of the accompanyingdata.

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