Class Question Describing data 1. StatsCom is studying the number of minutes used monthly by clients in a particular cellphone rate plan, A random sample of 12 clients showed the following number of minutes used last month. 90 77 94 89 119 112 91 110 92 100 113 83 What is the arithmetic number of minutes used? 2. You received the following marks in your marketing course.. What is the mean grade in the course? Tests Quiz-1 Quiz-2 Miterm-1 Miterm-2 Assignemt-1 Assignemt-2 Final Exam Scores % 60 80 75 70 95 90 55 Assigned marks 5 5 15 15 5 5 50 3. According to Statistics Canada, the average weekly employment insurance benefits for 2007, by category, are: $316, $295, $330, $379, $103, and $379. a. What is the median monthly benefit? b. How many observations are below the median? Above it? 4. Average earnings of Canadians 15 years and older with university degrees in selected cities are shown below. What is the Mode ? City Salary($) City Salary($) Calgary 58000 Regina 46000 Edmonton 45000 Saint John 50000 Halifax 43000 Greater Sudbury 56000 Hamilton 52000 Toronto 43000 London 48000 Winnipeg 46000 Montreal 47000 Vancouver 42000 Ottawa-Gatineau 55000 Victoria10. 11. 12. The numbers of work stoppages in the automobile industry for six months are 6, 0, 10, 14, 8. and 0. a. What is the median number of stoppages? b. How many observations are below the median? Above it? c. What is the modal number of work stoppages? The return on investment earned by Atkins construction Company for four successive years was: 30 percent, 20 percent, -40 percent, and 200 percent. What is the geometric mean rate of return on investment? The population of Alberta grew from 2974807 in 2001 to 3290350 in 2006. What was the average annual rate of percentage increase during the period? The percent increase in sales. for the last four years at Combs Cosmetics are: 4.91. 5.75, 8.12, and 21.60. a) Find the geometric percent increase. b) Find the arithmetic percent increase. o) Is the arithmetic mean equal to or greater than the geometric mean? Production of Cables trucks increased from 23 000 units in 1988 to 120 520 units in 2009. a) Find the geometric mean annual percent increase. Listed are the commissions earned, in dollars. last month by a sample of 15 brokers at Salomon Smith Barney's ofce. $2038 1?58 1721 1637 2097 2047 2205 1787 2287 1940 2311 2054 2406 1471 1460 a. Locate the median, the first quartile, and the third quartile for the commissions earned. The quality control department of the Elajnsyille Peanut Company is responsible for checking the mass of the 500g jar of peanut butter. The masses of a sample of nine jars produced last hour are: 490 495 496 498 500 500 501 504 505 a. What is the median mass? b. Determine the masses corresponding to the rst and third quartiles. Alexander's Pizza offers free delivery of its pizza within 15 km. Alex, the owner, wants some information on the time it takes for delivery. How long does a typical delivery take? Within what range of times will most deliveries be completed? For a sample of 20 deliveries, he determined the following information: Minimum value = 13 minutes 1st Quartile = 15 minutes 13. 14. 15. 16. 17. Median = 18 minutes Maximum value = 30 minutes 3rd Quartile = 22 minutes Develop a box plot for the delivery times. The Henson Trucking Company is a small company in the business of moving people from one home to another within the Dallas Texas. area. Historically the owners have charged the customers on an hourly basis, regardless of the distance of the move within Dallas area. However they are considering adding a surcharge for moves over a certain distance. They have decided to base their charge on the 30m percentile. They have a sample of travel- distance data for 30 moves. The data is as follows: 13.5 16.2 21.4 21 23.7 4.1 13.8 20.5 9.6 11.5 5.8 10.1 11.1 4.4 12.2 13 15.7 13.2 13.4 21.7 14.6 14.1 12.4 24.9 19.3 26.9 11.7 Also draw a box and whisker plot lst Step for solution is to sort the data W): 4.1 4.4 5.8 9.6 10.1 11.1 11.5 11.7 12.2 12.4 13 13.2 13.4 13.5 13.8 14.1 14.6 15.7 16.2 19.3 20.5 21 21.4 21.7 23.7 24.9 26.9 The numbers of cappuccinos sold at the coffee shop in the Kings County Municipal Airport between 4 and 7 pm. for a sample of 5 days last year were 20, 40, 50, 60, and 80. Determine the mean absolute deviation. The masses of a group of crates being shipped to Ireland are (in kilograms): 95 103 105 110 104 105 112 90 a. What is the range of the masses? b. Compute the arithmetic mean mass. 0. Compute the mean deviation of the masses. The ages of all the patients in the isolation ward of Mountainview Hospital are 38, 26, 13, 41, and 22 years. Determine the population variance. An office of Price Waterhouse Coopers LLP hired ve accounting trainees this year. Their monthly starting salaries were: $3536; $3173; $3448; $3121; and $3622. a) Compute the population mean. b) Compute the population variance. c) Compute the population standard deviation. 18. 19. 20. 21. 22. 23. 24. 25. d) Another location hired six trainees. 11.1.91! mean monthly salary was $3550. and the standard deviation was $250. Compare the two groups. The hourly wages for a sample of part-time employees at Fruit Packers Inc. are: $12. $20, $16. $18. and $19. What is the sample variance? The years of service for a sample of seven employees at an insurance claims ofce are: 4, 2. 5. 4. 5. 2. and 6. a) What is the sample variance? b) Compute the sample standard deviation. The average biweekly amount contributed by the Dupree Paint employees to the company's prot-sharing plan is $51.54. and the standard deviation is $7.51 . At least what percent of the contributions lie within plus and minus 3.5 standard deviations of the mean? Asample of the rental rates at the College Park apartments approximates a symmetrical, bell- shaped distribution. The sample mean is $500; the standard deviation is $20. Using the Empirical Rule. answer these questions: a) About 66 percent of the rental rates are between what two amounts? b) About 95 percent of the rental rates are between what two amounts? c) Almost all of the rental rates are between what two amounts? Astudy of the amount of bonus paid and the years of service of employees at Sea Pro Marine Inc. resulted in these statistics: The mean bonus paid was $200; the standard deviation was $40; the mean number of years of service was 20 years; the standard deviation was 2 years. Compare the relative dispersion in the two distributions using the coefcient of variation. A large group of Air Force inductees was given two experimental testsa mechanical aptitude test and a nger dexterity test. The arithmetic mean score on the mechanical aptitude test was 200, with a standard deviation of 10. The mean was 30 and the standard deviation for the nger dexterity test was 6. Compare the relative dispersion in the two groups. Following are the earnings per share, in dollars, for a sample of 15 software companies for the year 2009. $0.09 0.13 0.41 0.51 1.12 1.20 1.49 3.18 3.50 6.36 7.83 8.92 10.13 12.99 16.40 The mean is $4.95. The standard deviation is $5.22. The median is $3.18. Find the coefcient of skewness using Pearson's estimate. A sample of ve data entry clerks employed in the customer service department of a large pharmaceutical distribution company revised the following number of records last hour: 73, 98. 60. 92. and 84. a. Find the mean, median, and the standard deviation. b. Compute the coefficient of skewness using Pearson's method. c. What is your conclusion regarding the skewness of the data? 26. The P/E data set contains several large data values. Would we classify them as unusual or as outliers? 7 8 8 10 10 10 10 12 13 13 13 13 13 13 13 14 14 14 15 15 15 15 15 16 16 16 17 18 18 18 18 19 19 19 19 19 20 20 20 21 21 21 22 22 23 23 23 24 25 26 26 26 26 27 29 29 30 31 34 36 37 40 41 45 48 55 68 91 For the P/E data,x = 22.72 and s = 14.08. From these sample statistics, the Empirical Rule says that if the sample came from a normal distribution: x +Is: 68.26% of the P/E ratios would be within the interval 8.6 to 36.8. x + 2s: 95.44% of the P/E ratios would be within the interval -5.4 to 50.9. x + 3s: 99.73% of the P/E ratios would be within the interval -19.5 to 65.0. Calculate the standardized value of the last four values and interpret them? 27. A Copier Sales Inc. sales manager gathered information on the number of sales calls made and the number of copiers sold for a random sample of 10 sales representatives. As a part of her presentation at the upcoming sales meeting, Ms. Rakhi, the sales manager, would like to offer specific information about the relationship between the number of sales calls and the number of copiers sold. Calculate the relation between the two variables (correlation) Sales Representative Number of Sales Calls Number of Copiers Sold Carlos Ramirez 20 30 Mike Van Holst 40 60 Mohammad Arif 20 40 Joe Kalashnikov 30 60 Saira Banu 10 30 Soni Takahara 10 40 Shanti Prakash 20 40 Mike Marakadis 20 50 Jeff Bell 20 30 Susan Pelletier 30 70 28. For the south-east area of Edmonton a frequency distribution for the list prices is constructed.. Determine the group arithmetic mean, group standard deviation of the list price .List Price Frequen (S thousands) cy (f) $250 to under $375 33 375 to under 500 41 500 to under 625 11 625 to under 750 5 750 to under 875 4 875 to under 1000 1 1000 to under 1125 1 Total 96