Descriptive Statistics

Descriptive Statistics caput 1 The Dow Jones Travel Index reported what air travelers pay for hotel live per night in major U. S. cities (The environ Street Journal, January 16,2004). The average hotel direction 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 capital of Colorado 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 hatch hotel room rate? b. What is the average hotel room rate? c. What is the expressive style? d. What is the first quartile? e. What is the third quartile? Question 2 The National Association of Collage and Employers compiled learning about one-year starting salaries for college graduates by major. The believe starting salary for business administration graduates was $39,850 (CNNM Money. com, February 15, 2006). Samples with annua l starting entropy for marketing majors and accounting majors follow (data are in thousands) plow 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. fancy the mean, median, and mode of the annual starting salary for both majors. b. see 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 pattern 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 one hundred shares at $50 per share and an online trade of d 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 operation related to the amount of the transaction? TABLE COMMISSIONS CHARGED BY DISCOUNT BROKERS Question 4 A sample of 10 NCAA college basketball game game scores provided the following data (USA Today, January 26, 2004) Winning Team Points Losing Team Points Winning Margin azimuth 90 Oregon 66 24 Duke 85 Georgetown 66 19 Florida State 75 commove Forest 70 5 Kansas 78 Colorado 57 21Kentucky 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 amiable 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 ofNCAA 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 strain 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 crustal plate 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. 09Dynaudio 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 A erius 4. 26 agency 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 6According to the 2003 one-year 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 trading 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 groin 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 foundation price in the United States and the increase in median topographic point price everyplace a five-year period (The Wall Street, Journa l, 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?