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3.2 Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median.
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3.3 Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
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3.4 Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.
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3.5 The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows:...
a. What is the mean hotel room rate?
b. What is the median hotel room rate?
c. What is the mode?
d. What is the first quartile?
e. What is the third quartile?
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3.6
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3.7
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3.8
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3.9
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3.10
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3.11
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3.12 Walt Disney Company bought Pixar Animation Studios, Inc., in a deal worth $7.4 billion (http://CNNMoney.com, January 24, 2006). The animated movies produced by Disney and Pixar during the previous 10 years are listed below. The box office revenues are in millions of dollars. Compute the total revenue, the mean, the median, and the quartiles to compare the box office success of the movies produced by both companies. Do the statistics suggest at least one of the reasons Disney was interested in buying Pixar? Discuss....
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3.13 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and inter quartile range.
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3.14 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the variance and standard deviation.
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3.15 Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, inter quartile range, variance, and standard deviation.
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3.16 A bowler’s scores for six games were 182, 168, 184, 190, 170, and 174. Using these data as a sample, compute the following descriptive statistics.
a. Range
b. Variance
c. Standard deviation
d. Coefficient of variation
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3.17 A home theater in a box is the easiest and cheapest way to provide surround sound for a home entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide, 2004). The prices are for models with a DVD player and for models without a DVD player....
a. Compute the mean price for models with a DVD player and the mean price for models without a DVD player. What is the additional price paid to have a DVD player included in a home theater unit?
b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for models with and without a DVD player?
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3.18 Car rental rates per day for a sample of seven Eastern U.S. cities are as follows (The Wall Street Journal, January 16, 2004)....
a. Compute the mean, variance, and standard deviation for the car rental rates.
b. A similar sample of seven Western U.S. cities showed a sample mean car rental rate of $38 per day. The variance and standard deviation were 12.3 and 3.5, respectively. Discuss any difference between the car rental rates in Eastern and Western U.S. cities.
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3.19 The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5, a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?
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3.20 The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, Inc., and J.C. Clark Distributors (see Figure 3.2)....Use the range and standard deviation to support the previous observation that Dawson Supply provides the more consistent and reliable delivery times.
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3.21 How do grocery costs compare across the country? Using a market basket of 10 items including meat, milk, bread, eggs, coffee, potatoes, cereal, and orange juice, Where to Retire magazine calculated the cost of the market basket in six cities and in six retirement areas across the country (Where to Retire, November/December 2003). The data with market basket cost to the nearest dollar are as follows:...
a. Compute the mean, variance, and standard deviation for the sample of cities and the sample of retirement areas.
b. What observations can be made based on the two samples?
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3.22
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3.23 Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:2005 Season 74 78 79 77 75 73 75 772006 Season 71 70 75 77 85 80 71 79
a. Use the mean and standard deviation to evaluate the golfer’s performance over the two-year period.
b. What is the primary difference in performance between 2005 and 2006? What improvement, if any, can be seen in the 2006 scores?
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3.24 The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes)....After viewing this sample of running times, one of the coaches commented that the quarter milers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data. Does the use of the coefficient of variation indicate that the coach’s statement should be qualified?
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3.25 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations.
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3.26 Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?
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3.27 Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges:
a. 20 to 40b. 15 to 45c. 22 to 38d. 18 to 42e. 12 to 48
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3.28 Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:
a. 20 to 40b. 15 to 45c. 25 to 35
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3.29 The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours.
a. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.
b. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.
c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. How does this result compare to the value that you obtained using Chebyshev’s theorem in part (a)?
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3.30
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3.31
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3.32
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3.33 Florida Power & Light (FPL)Company has enjoyed a reputation for quickly fixing its electric system after storms. However, during the hurricane seasons of 2004 and 2005, a new reality was that the company’s historical approach to emergency electric system repairs was no longer good enough (The Wall Street Journal, January 16, 2006). Data showing the days required to restore electric service after seven hurricanes during 2004 and 2005 follow....Based on this sample of seven, compute the following descriptive statistics:
a. Mean, median, and mode
b. Range and standard deviation
c. Should Wilma be considered an outlier in terms of the days required to restore electric service?
d. The seven hurricanes resulted in 10 million service interruptions to customers. Do the statistics show that FP&L should consider updating its approach to emergency electric system repairs? Discuss.
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3.34 A sample of 10 NCAA college basketball game scores provided the following data (USA Today, January 26, 2004).......
a. Compute the mean and standard deviation for the points scored by the winning team.
b. Assume that the points scored by the winning teams for all NCAA games follow a bell-shaped distribution. Using the mean and standard deviation found in part (a), estimate the percentage of all NCAA games in which the winning team scores 84 or more points. Estimate the percentage of NCAA games in which the winning team scores more than 90 points.
c. Compute the mean and standard deviation for the winning margin. Do the data contain outliers? Explain.
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3.35 Consumer Review posts reviews and ratings of a variety of products on the Internet. The following is a sample of 20 speaker systems and their ratings (http://www.audioreview.com). The ratings are on a scale of 1 to 5, with 5 being best....
a. Compute the mean and the median.
b. Compute the first and third quartiles.
c. Compute the standard deviation.
d. The skewness of this data is –1.67. Comment on the shape of the distribution.
e. What are the z-scores associated with Allison One and Omni Audio?
f. Do the data contain any outliers? Explain.
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3.36 Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five number summary for the data.
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3.37 Show the box plot for the data in exercise 36.
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3.38 Show the five-number summary and the box plot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.
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3.39 A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding box plot. Should a data value of 65 be considered an outlier?
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3.40
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3.41 Annual sales, in millions of dollars, for 21 pharmaceutical companies follow....
a. Provide a five-number summary.
b. Compute the lower and upper limits.
c. Do the data contain any outliers?
d. Johnson & Johnson’s sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?
e. Show a box plot.
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3.42
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3.43
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3.44 A listing of 46 mutual funds and their 12-month total return percentage is shown in Table 3.6 (Smart Money, February 2004).
a. What are the mean and median return percentages for these mutual funds?d. Do the data contain any outliers? Show a box plot.TABLE 3.6 TWELVE-MONTH RETURN FOR MUTUAL FUNDS...
b. What are the first and third quartiles?
c. Provide a five-number summary.
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3.45 Five observations taken for two variables follow....
a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.
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3.46 Five observations taken for two variables follow....
a. Develop a scatter diagram for these data.
b. What does the scatter diagram indicate about a relationship between x and y?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.
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3.47 Nielsen Media Research provides two measures of the television viewing audience: a television program rating, which is the percentage of households with televisions watching a program, and a television program share, which is the percentage of households watching a program among those with televisions in use. The following data show the Nielsen television ratings and share data for the Major League Baseball World Series over a nine-year period (Associated Press, October 27, 2003)....
a. Develop a scatter diagram with rating on the horizontal axis.
b. What is the relationship between rating and share? Explain.
c. Compute and interpret the sample covariance.
d. Compute the sample correlation coefficient. What does this value tell us about the relationship between rating and share?
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3.48 A department of transportation’s study on driving speed and miles per gallon for midsize automobiles resulted in the following data:...Compute and interpret the sample correlation coefficient.
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3.49
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3.50 The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 Index (S&P 500) are both used to measure the performance of the stock market. The DJIA is based on the price of stocks for 30 large companies; the S&P 500 is based on the price of stocks for 500 companies. If both the DJIA and S&P 500 measure the performance of the stock market, how are they correlated? The following data show the daily percent increase or daily percent decrease in the DJIA and S&P 500 for a sample of nine days over a three-month period (The Wall Street Journal, January 15 to March 10, 2006)....
a. Show a scatter diagram.
b. Compute the sample correlation coefficient for these data.
c. Discuss the association between the DJIA and SP 500. Do you need to check both before having a general idea about the daily stock market performance?
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3.51
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3.52 Consider the following data and corresponding weights....
a. Compute the weighted mean.
b. Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.
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3.53 Consider the sample data in the following frequency distribution....
a. Compute the sample mean.
b. Compute the sample variance and sample standard deviation.
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3.54 The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 33 credit hours of C, and 3 credit hours of D.
a. Compute the student’s grade point average.
b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?
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3.55
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3.56
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3.57
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3.58 According to the 2003 Annual Consumer Spending Survey, the average monthly Bank of America Visa credit card charge was $1838 (U.S. Airways Attaché Magazine, December 2003). A sample of monthly credit card charges provides the following data....
a. Compute the mean and median.
b. Compute the first and third quartiles.
c. Compute the range and interquartile range.
d. Compute the variance and standard deviation.
e. The skewness measure for these data is 2.12. Comment on the shape of this distribution. Is it the shape you would expect? Why or why not?
f. Do the data contain outliers?
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3.59 The U.S. Census Bureau provides statistics on family life in the United States, including the age at the time of first marriage, current marital status, and size of household (U.S. Census Bureau website, March 20, 2006). The following data show the age at the time of first marriage for a sample of men and a sample of women....
a. Determine the median age at the time of first marriage for men and women.
b. Compute the first and third quartiles for both men and women.
c. Twenty-five years ago the median age at the time of first marriage was 25 for men and 22 for women. What insight does this information provide about the decision of when to marry among young people today?
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3.60 Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. A sample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16, 2004)....
a. What are the mean and median dividend yields?
b. What are the variance and standard deviation?
c. Which company provides the highest dividend yield?
d. What is the z-score for McDonald’s? Interpret this z-score.
e. What is the z-score for General Motors? Interpret this z-score.
f. Based on z-scores, do the data contain any outliers?
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3.61 The U.S. Department of Education reports that about 50% of all college students use a student loan to help cover college expenses (National Center for Educational Studies, January 2006). A sample of students who graduated with student loan debt is shown here. The data, in thousands of dollars, show typical amounts of debt upon graduation....
a. For those students who use a student loan, what is the mean loan debt upon graduation?
b. What is the variance? Standard deviation?
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3.62 Small business owners often look to payroll service companies to handle their employee payroll. Reasons are that small business owners face complicated tax regulations and penalties for employment tax errors are costly. According to the Internal Revenue Service, 26% of all small business employment tax returns contained errors that resulted in a tax penalty to the owner (The Wall Street Journal, January 30, 2006). The tax penalty for a sample of 20 small business owners follows:...
a. What is the mean tax penalty for improperly filed employment tax returns?b. What is the standard deviation?company to handle employee payroll services, including the employment tax returns?
c. Is the highest penalty, $2040, an outlier?
d. What are some of the advantages of a small business owner hiring a payroll service
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3.63 Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of times recorded for each method are shown. Times are in minutes....
a. Compute the sample mean time to get to work for each method.
b. Compute the sample standard deviation for each method.
c. On the basis of your results from parts (a) and (b), which method of transportation should be preferred? Explain.
d. Develop a box plot for each method. Does a comparison of the box plots support your conclusion in part (c)?
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3.64 The National Association of Realtors reported the median home price in the United States and the increase in median home price over a five-year period (The Wall Street Journal, January 16, 2006). Use the sample home prices shown here to answer the following questions....
a. What is the sample median home price?
b. In January 2001, the National Association of Realtors reported a median home price of $139,300 in the United States. What was the percentage increase in the median home price over the five-year period?
c. What are the first quartile and the third quartile for the sample data?
d. Provide a five-number summary for the home prices.
e. Do the data contain any outliers?
f. What is the mean home price for the sample? Why does the National Association of Realtors prefer to use the median home price in its reports?
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3.65
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3.66
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3.67
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3.68
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3.69 The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds....
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3.70 Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds....
a. What is the mean speed of the automobiles traveling on this road?
b. Compute the variance and the standard deviation.
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