# Descriptive Statistics

Descriptive Statistics Question 1: 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 Atlanta | \$163| Minneapolis| \$125| Boston | 177| New Orleans| 169| Chicago| 166| New York| 245| Cleveland| 126| Orlando| 146| Dallas| 123| Phoenix| 139| Denver| 120| Pittsburgh| 134| Detroit| 144| San Francisco| 167| Houston| 173| Seattle| 162| Los Angeles| 160| St. Louis| 145| Miami| 192| Washington D. C. | 207| 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? Question 2: The National Association of Collage and Employers compiled information about annual starting salaries for college graduates by major. The mean starting salary for business administration graduates was \$39,850 (CNNM Money. com, February 15, 2006). Samples with annual starting data for marketing majors and accounting majors follow (data are in thousands): Marketing Majors| 34. 2| 45| 39. 5| 28. | 37. 7| 35. 8| 30. 6| 35. 2| 34. 2| 42. 4| Accounting Majors| 33. 5| 57. 1| 49. 7| 40. 2| 44. 2| 45. 2| 47. 8| 38| 53. 9| 41. 1| 41. 7| 40. 8| 55. 5| 43. 5| 49. 1| 49. 9| a. Compute the mean, median, and mode of the annual starting salary for both majors. b. Compute the first and third quartiles for both majors. c. Business administration students with accounting majors generally obtain the highest annual salary after graduation. What do the sample data indicate about the difference between the annual starting salaries for marketing and accounting majors?

Question 3: The American Association of Individual Investors conducted an annual survey of discount brokers (AAII Journal, January 2003). The commissions charged by 24 discount brokers for two types of trades, a broker-assisted trade of 100 shares at \$50 per share and an online trade of 500 shares at \$50 per share. a. Compute the mean, median, and mode for the commission charged on a broker-assisted trade of 100 shares at \$50 per share. b. Compute the mean, media, and mode for the commission charged on an online trade of 500 shares at \$50 per share. c.

Which costs more, a broker-assisted trade of 100 shares at \$50 per share or an online trade of 500 shares at \$50 per share? d. Is the cost of a transaction related to the amount of the transaction? TABLE: COMMISSIONS CHARGED BY DISCOUNT BROKERS Question 4: A sample of 10 NCAA college basketball game scores provided the following data (USA Today, January 26, 2004) Winning Team| Points| Losing Team | Points | Winning Margin| Arizona | 90| Oregon | 66| 24| Duke| 85| Georgetown| 66| 19| Florida State| 75| Wake Forest| 70| 5| Kansas| 78| Colorado| 57| 21|

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Kentucky| 71| Notre Dame| 63| 8| Louisville| 65| Tennessee| 62| 3| Oklahoma State| 72| Texas| 66| 6| Purdue| 76| Michigan State| 70| 6| Stanford | 77| Southern Cal| 67| 10| Wisconsin | 76| Illinois | 56| 20| a. Compute the mean and standard deviation for the points scored by the winning team. b. Assume that the points 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. Question 5: Consumer Review posts reviews and rating of a variety of products on the Internet. The following is a sample of 20 speaker systems and their ratings (www. audioreview. com). The ratings are on a scale of 1 to 5, with 5 being best. Speaker| Rating| Speaker| Rating | Infinity Kappa | 4. 00| ACI Sapphire III| 4. 67| Allison One| 4. 12| Bose 501 Series | 2. 14| Cambridge Ensemble II| 3. 82| DCM KX-212| 4. 09|

Dynaudio Contour 1. 3| 4. 00| Eosone RSR1000| 4. 17| Hsu Rsch. HRSW12V| 4. 56| Joseph Audio RM7si| 4. 88| Legacy Audio Focus| 4. 32| Martin Logan Aerius| 4. 26| Mission 73li| 4. 33| Omni Audio SA 12. 3| 2. 32| PSB 400i| 4. 50| Polk Audio RT12| 4. 50| Snell Acoustics DIV| 4. 64| Sunfire True Subwoofer| 4. 17| Thiel CS 1. 5| 4. 20| Yamaha NS-A636| 2. 17| 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. Question 6:

According to the 2003 Annual Consumer Spending Survey, the average monthly Bank of America Visa credit card charge was \$1838 (U. S. Airways Attache Magazine, December 2003). A sample of monthly credit card charges provides the following data. 236| 1710| 1351| 825| 7450| 316| 4135| 1333| 1584| 387| 991| 3396| 170| 1428| 1688| 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. Question 7: 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 tax penalty to the owner (The Wall Street Journal, January 30, 2006). The tax penalty for a sample of 20 small business owners follows: 820| 270| 450| 1010| 890| 700| 1350| 350| 300| 1200| 390| 730| 2040| 230| 640| 350| 420| 270| 370| 620| a. What is the mean tax penalty for improperly filed employment tax returns? b.

What is the standard deviation? c. Is the highest penalty, \$2040, an outlier? d. What are some of the advantages of a small business owner hiring a payroll service company to handle employee payroll services, including the employment tax returns? Question 8: 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. 995. 9| 48. 8| 175. 0| 263. 50| 298. 0| 218. 9| 209. | 628. 3| 111. 0| 212. 9| 92. 6| 2325. 0| 958. 0| 212. 5| 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. 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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