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mathematics
statistics

Questions and Answers of Statistics

A survey asked chief executives at leading U.S. firms the following question: €œWhere do you expect the U.S. economy to be 12 months from now?€ A representative sample of their
AccuWeather.com reported the following weather delays at these major U.S. airline hubs for July 21, 2010:a. Construct frequency and relative frequency distributions that summarize the delays at major
Fifty pro-football rookies were rated on a scale of 1 to 5, based on performance at a training camp as well as on past performance. A ranking of 1 indicated a poor prospect whereas a ranking of 5
A recent survey asked 5,324 individuals: “What’s most important to you when choosing where to live?” The responses are shown in the following relative frequency distribution.Response
What is the perfect summer trip? A National Geographic Kids survey (AAA Horizons, April 2007) asked this question to 316 children ages 8 to 14. Their responses are given in
The following table lists U.S. revenue (in $ billions) of the major car-rental companies.Car-Rental Company ...... Revenue in 2009Enterprise ........... $10.7Hertz ............. 4.7Avis Budget
A survey conducted by CBS News asked 829 respondents which of the following events will happen first. The responses are summarized in the following table:Cure for cancer found ..... 40%End of
A 2010 poll conducted by NBC asked respondents who would win Super Bowl XLV in 2011. The responses by 20,825 people are summarized in the following table.Team ......... Number of VotesAtlanta
Consider the following data set:a. Construct a frequency distribution using classes of 3 up to 5, 5 up to 7, etc.b. Construct relative frequency, cumulative frequency, and cumulative relative
Consider the following data set:a. Construct a frequency distribution using classes of 210 up to 0, 0 up to 10, etc. How many of the observations are at least 10 but less than 20?b. Construct a
Consider the following frequency distribution:Class ...... Frequency10 up to 20 ... 1220 up to 30 .... 1530 up to 40 ... 2540 up to 50 ... 4a. Construct a relative frequency
Consider the following frequency distribution:Class ....... Frequency1000 up to 1100 ..... 21100 up to 1200 ... 71200 up to 1300 ... 31300 up to 1400 .... 4a. Construct a
Consider the following cumulative frequency distribution:Class ..... Cumulative Frequency15 up to 25 .... 3025 up to 35 .... 5035 up to 45 .... 12045 up to 55 .... 130a. Construct a
Consider the following relative frequency distribution: Class ...... Relative Frequency220 up to 210 ... 0.04210 up to 0 .... 0.280 up to 10 .... 0.2610 up to 20 ..... 0.2220 up to 30
Consider the following cumulative relative frequency distribution.Class .......... Cumulative Relative Frequency150 up to 200 ...... 0.10200 up to 250 ...... 0.35250 up to 300 ...... 0.70300 up to
Kiplinger€™s (August 2007) lists the assets (in billions of $) for the 20 largest stock mutual funds (ranked by size) as follows:a. Construct a frequency distribution using classes of 40
The number of text messages sent by 25 13-year-olds over the past month was as follows:a. Construct a frequency distribution using classes of 500 up to 600, 600 up to 700, etc.b. Construct the
AccuWeather.com listed the following high temperatures (in degrees Fahrenheit) for 33 European cities on July 21, 2010.a. Construct a frequency distribution using classes of 60 up to 70, 70 up to 80,
Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution.Vacancy Rate (in percent) ....Frequency0 up to 3 ........... 53 up to
The following relative frequency distribution summarizes the ages of women who had a child in the last year.Ages ...... Relative Frequency15 up to 20 ... 0.1020 up to 25 ... 0.2525 up to 30
The manager of a nightclub near a local university recorded the ages of the last 100 guests in the following cumulative frequency distribution.Ages ....... Cumulative Frequency18 up to 22 .....
The following ogive summarizes the median household income for the 50 states in the United States (U.S. Census, 2010).a. Approximate the percentage of states with median household income less than
The following histogram summarizes the salaries (in $1,000,000s) for the 30 highest-paid players in the National Basketball Association (NBA) for the 2012 season (www.nba.com, data retrieved March
The following ogive summarizes the salary (in $1,000,000s) for the 30 highest-paid players in the National Basketball Association (NBA) for the 2012 season (www.nba.com, data retrieved March 2012).a.
The following table lists a portion of the average math SAT scores for each state for the year 2009. The entire data set, labeled Math_SAT, can be found on the text website.State ..........
The accompanying table shows a portion of median house values for the 50 states as reported by the U.S. Census Bureau in 2010. The entire data set, labeled Census, can be found on the text
The accompanying table shows a portion of the average price for a gallon of gas for the 50 states during April 2012. The entire data set, labeled Gas_Prices_2012, can be found on the text
For the first three months of 2012, the stock market put up its best first-quarter performance in over a decade (Money.cnn.com, April 9, 2012). The accompanying table shows a portion of the daily
Consider the following data set:Construct a stem-and-leaf diagram. Is the distribution symmetric? Explain.
Consider the following data set:Construct a stem-and-leaf diagram. Is the distribution symmetric?Explain.
A sample of patients arriving at Overbrook Hospital€™s emergency room recorded the following body temperature readings over the weekend:Construct and interpret a stem-and-leaf diagram.
Suppose the following high temperatures were recorded for major cities in the contiguous United States for a day in July.Construct and interpret a stem-and-leafdiagram.
A police officer is concerned with excessive speeds on a portion of Interstate 90 with a posted speed limit of 65 miles per hour. Using his radar gun, he records the following speeds for 25 cars and
Spain was the winner of the 2010 World Cup, beating the Netherlands by a score of 1€“0. The ages of the players from both teams were as follows:Construct a stem-and-leaf diagram for each
Construct a scatter plot with the following data. Categorize the relationship between x and y.
Construct a scatter plot with the following data. Does a linear relationship exist between x andy?
Construct a scatter plot with the following data. Categorize the relationship between x andy.
A statistics instructor wants to examine whether a relationship exists between the hours a student spends studying for the final exam (Hours) and a studentâ€™s grade on the final exam (Grade).
A recent study offers evidence that the more weight a woman gains during pregnancy, the higher the risk of having a high-birth-weight baby, defined as at least 8 pounds, 13 ounces, or 4 kilograms
In order to diversify risk, investors are often encouraged to invest in assets whose returns have either a negative relationship or no relationship. The annual return data on two assets is shown
In an attempt to determine whether a relationship exists between the price of a home and the number of days it takes to sell the home, a real estate agent collects data on the recent sales of eight
A 2003 survey by the Centers for Disease Control and Prevention concluded that smoking is forbidden in nearly 75% of U.S. households (Boston Globe, May 25, 2007). The survey gathered responses from
Patrons at a local restaurant were asked to rate their recent experience at the restaurant with respect to its advertised atmosphere of upbeat, comfortable, and clean. Possible responses included
A survey conducted by CBS News asked parents about the professions they would want their children to pursue. The results are summarized in the following table.Profession ..............Parents’
The one-year return (in %) for 24 mutual funds is as follows:a. Construct a frequency distribution using classes of 220 up to 210, 210 up to 0, etc.b. Construct the relative frequency, the
The Statistical Abstract of the United States, 2010 provided the following frequency distribution of the number of people who live below the poverty level by region.Region ...... Number of People (in
Money magazine (January 2007) reported that an average of 77 million adults in the United States make financial resolutions at the beginning of a new year. Consider the following frequency
A recent poll of 3,057 individuals asked: “What’s the longest vacation you plan to take this summer?” The following relative frequency distribution summarizes the results.Response
A survey conducted by CBS News asked 1,026 respondents:“What would you do with an unexpected tax refund?” The responses are summarized in the following table.Pay of debts ..... 47%Put it in the
The following table lists the U.S. sales (in $ millions) of prescription drugs used to treat seizure disorders.Drug ........ Sales in 2006Topamax ...... $1,825.4Lamictal ....... 1,684.3Depakote
The manager at a water park constructed the following frequency distribution to summarize attendance in July and August.Attendance ..... Frequency1,000 up to 1,250 .... 51,250 up to 1,500 ....
A researcher conducts a mileage economy test involving 80 cars. The frequency distribution describing average miles per gallon (mpg) appears in the following table.Average mpg ..... Frequency15 up
The Wall Street Journal (August 28, 2006) asked its readers:“Ideally, how many days a week, if any, would you work from home?” The following relative frequency distribution summarizes the
The accompanying table lists a portion of the ages and net worth of the wealthiest people in America; the complete data set can be found on the text website and is labeled Wealthiest_Americans.a.
The price-to-earnings growth ratio, or PEG ratio, is the market’s valuation of a company relative to its earnings prospects. A PEG ratio of 1 indicates that the stock’s price is in line with
The following table lists the sale price and type of 20 recently sold houses in New Jersey.a. Construct a frequency distribution on types of houses sold in New Jersey. Interpret your findings.b.
A manager of a local retail store analyzes the relationship between Advertising (in $100s) and Sales (in $1,000s) by reviewing the store’s data for the previous six months. Construct a scatter plot
The following table lists the National Basketball Association€™s (NBA€™s) leading scorers, their average minutes per game (MPG), and their average points per game (PPG) for
In a recent USA TODAY/Gallup Poll, respondents favored Barack Obama over Mitt Romney in terms of likeability, 60% to 30% (Los Angeles Times, July 28, 2012). The following bar chart summarizes the
A recent survey of 992 people asked: In which professional sport€”football, boxing, hockey, or martial arts€”is an athlete most likely to sustain an injury that will affect the athlete after
The accompanying figure plots the monthly stock price of Caterpillar, Inc., from July 2009 through March 2011. The stock has experienced tremendous growth over this time period, almost tripling in
The following relative frequency histogram summarizes the median household income for the 50 states in the United States (U.S. Census, 2010).a. Is the distribution symmetric? If not, is it positively
The following histogram summarizes Apple Inc.€™s monthly stock price for the years 2007 through 2011 (finance.yahoo.com, data retrieved April 20, 2012).a. Is the distribution symmetric? If
In its 2000 and 2009 Annual Reports, Nike, Inc. reported the following net revenues, in millions of dollars, in four distinct regions of the world:In a report, use the sample information to:1.
When reviewing the overall strength of a particular firm, financial analysts typically examine the net profit margin. This statistic is generally calculated as the ratio of a firm’s net profit
The following table lists a portion of U.S. life expectancy (in years) for the 50 states; the entire data set, labeled Life_Expectancy, can be found on the text website.In a report, use the sample
Given the following observations from a sample, calculate the mean, the median, and the mode.
Given the following observations from a sample, calculate the mean, the median, and themode.
Given the following observations from a population, calculate the mean, the median, and themode.
At a small arm in Boston, seven employees were asked to report their one-way commute time (in minutes) into the city. Their responses were.a. How long was the shortest commute? The longest commute?b.
In order to get an idea on current buying trends, a real estate agent collects data on 10 recent house sales in the area. Specifically, she notes the number of bedrooms in each house as follows:a.
The following table shows the 10 highest-paid chief executive officers of the last decade.a. Calculate the mean compensation for the 10 highest-paid chief executive officers.b. Does the mean
An investor bought common stock of Dell Inc. on three occasions at the following prices. Date ...... Price Per ShareJanuary 2009 ... $10.34July 2009 .... $13.98December 2009 ... $14.02a. What is the
The following table shows Fortune 500€™s rankings of America€™s 10 largest corporations for 2010. Next to each corporation is its market capitalization (in billions of dollars as
One important statistic in baseball is a pitcher€™s earned run average, or ERA. This number represents the average number of earned runs given up by the pitcher per nine innings. The
Calculate the 20th, 50th, and 80th percentiles for the following dataset:
Calculate the 20th, 40th, and 70th percentiles for the following dataset:
Consider the following data set:a. Calculate and interpret the 25th, 50th, and 75th percentiles. b. Construct a box plot. Are there any outliers?
Consider the following data set:a. Calculate and interpret the 25th, 50th, and 75th percentiles. b. Construct a box plot. Are there anyoutliers?
Scores on the final in a statistics class are as follows.a. Calculate and interpret the 25th, 50th, and 75th percentiles.b. Construct a box plot. Are there any outliers? Is the distribution
Consider the return data (in percent) for the Income fund in Table.a. Calculate and interpret the 25th, 50th, and 75th percentiles.b. Construct a box plot. Are there any outliers?c. Is the
A price-earnings ratio or P/E ratio is calculated as a firm’s share price compared to the income or profit earned by the firm per share. Generally, a high P/E ratio suggests that investors are
The accompanying table shows a portion of median household income (Income) and median house value (House Value) for the 50 states in 2010. The entire data set, labeled Census, can be found on the
Consider the following population data:a. Calculate the range.b. Calculate MAD.c. Calculate the population variance.d. Calculate the population standarddeviation.
Consider the following population data:a. Calculate the range.b. Calculate MAD.c. Calculate the population variance.d. Calculate the population standarddeviation.
Consider the following sample data:a. Calculate the range.b. Calculate MAD.c. Calculate the sample variance.d. Calculate the sample standarddeviation.
Consider the following sample data:a. Calculate the range.b. Calculate MAD.c. Calculate the sample variance and the sample standard deviation.
The Department of Transportation (DOT) fields thousands of complaints about airlines each year. The DOT categorizes and tallies complaints, and then periodically publishes rankings of airline
The monthly closing stock prices (rounded to the nearest dollar) for Starbucks Corp. and Panera Bread Co. for the first six months of 2010 are reported in the following table.a. Calculate the sample
While the housing market is in recession and is not likely to emerge anytime soon, real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24,
Go to the text website and access the data labeled Largest_Corporations. It shows the Fortune 500 rankings of America’s largest corporations for 2010. Next to each corporation are its market
Go to the text website and access the data labeled Census. It shows, among other variables, median household income and median house value for the 50 states.a. Compute and discuss the range of
Consider the following data for two investments, A and B:a. Which investment provides the higher return? Which investment provides less risk? Explain.b. Given a risk-free rate of 2%, calculate the
Consider the following data for two investments, A and B:a. Which investment provides the higher return? Which investment provides less risk? Explain.b. Given a risk-free rate of 1.4%, calculate the
Consider the following returns for two investments, A and B, over the past four years:a. Which investment provides the higher return?b. Which investment provides less risk?c. Given a risk-free rate
The following table shows the annual returns (in percent) and summary measures for the Vanguard Energy Fund and the Vanguard Health Care Fund from 2005 through 2009.a. Which fund had the higher
The following table shows the annual returns (in percent) for the Fidelity Latin America Fund and the Fidelity Canada Fund from 2005 through 2009.a. Which fund had the higher average return?b. Which
The accompanying table shows a portion of the annual return (in percent) for the Fidelity Select Technology Fund and Fidelity Select Energy Fund from 2000 through 2011. The entire data set, labeled
A data set has a mean of 80 and a standard deviation of 5.a. Using Chebyshev’s theorem, what percentage of the observations fall between 70 and 90?b. Using Chebyshev’s theorem, what percentage of
A data set has a mean of 1500 and a standard deviation of 100.a. Using Chebyshev’s theorem, what percentage of the observations fall between 1300 and 1700?b. Using Chebyshev’s theorem, what

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