Descriptive Statistics Numerical Ch5 (127-153)

127. A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. 40 25 35 30 20 Using this data set, compute the a. median b. mean c. mode d. 40th percentile e. range f. sample variance g. standard deviation ANSWER: a. b. c. d. e. f. g. 40 30 20 40 10 30 20 10 5 20 25 25 20 20 35 128.571 11.339 128. A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. Their responses are given below. 2 1 0 2 0 Using this data set, compute the a. mode b. median c. mean d. range e. interquartile range f. variance g. standard deviation h. coefficient of variation ANSWER: a. 2 b. 1.5 c. 1.25 d. 2 2 1 2 0 2 1 2 e. f. g. h. 1.75 0.75 0.866 69.28% 129. The following is a frequency distribution of grades of a sample of statistics examinations. Grade Frequency 50 - 59 7 60 - 69 10 70 - 79 22 80 - 89 15 90 - 99 6 Compute the following measures: a. The mean b. The variance c. The standard deviation d. The coefficient of variation ANSWER: a. 75 b. 130.25 c. 11.41 d. 15.22% 130. The following shows the number of job losses and gains (in thousands) between 2008 and 2009 for a sample of seven cities. City Memphis Nashville Atlanta Chattanooga Birmingham Huntsville Knoxville Job Change (in thousands) -11 -7 -6 -5 -5 0 6 a. Compute the mean. b. Determine the mode. c. Determine the median. d. Determine the standard deviation. ANSWER: a. -4000 b. -5000 c. -5000 d. 5,477 (rounded) 131. For the following frequency distribution, Class 45 - 47 48 - 50 51 - 53 54 - 56 57 - 59 Frequency 3 6 8 2 1 a. Compute the mean. b. Compute the standard deviation. (Assume the data represent a population.) ANSWER: a. 50.8 b. 3.14 132. Below you are given the ages of a sample of 10 college students who are enrolled in statistics. 20 a. b. c. d. e. f. g. h. 18 20 22 18 20 Compute the mean. Compute the variance. Compute the standard deviation. Compute the coefficient of variation. Determine the 25th percentile. Determine the median Determine the 75th percentile. Determine the range. 22 17 19 24 ANSWER: a. b. c. d. e. f. g. h. 20 4.667 2.16 10.8% 18 20 22 7 133. A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below. 3 12 4 7 14 6 2 9 11 a. Compute the mean. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation. e. Determine the 25th percentile. f. Determine the median g. Determine the 75th percentile. h. Determine the range. ANSWER: a. 7.56 b. 17.78 c. 4.22 d. 55.8 e. 3.5 f. 7.0 g. 11.5 h. 12 134. For the following frequency distribution (assume the data represent a population), Class 70 - 79 Frequency 5 80 - 89 90 - 99 100 - 109 110 - 119 9 11 9 6 a. Compute the mean. b. Compute the standard deviation. ANSWER: a. 95 b. 12.6 (rounded) 135. The starting salaries of a sample of college students are given below. Starting Salary (In $1,000) 20-24 25-29 30-34 35-39 40-44 45-49 Frequency 1 3 7 6 2 1 a. Compute the mean. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation. ANSWER: a. 34 b. 35.26 c. 5.94 d. 17.46% 136. The following frequency distribution shows the time (in minutes) that a sample of students uses the computer terminals per day. Time 20 - 39 Frequency 2 40 - 59 60 - 79 80 - 99 100 - 119 4 6 4 2 a. Compute the mean. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation. ANSWER: a. 69.5 b. 564.71 c. 23.76 d. 34.19% 137. The growth rate in thepopulation of Atlanta for the past five years are shown below. Growth Year Factors 1 1.0298 2 1.0270 3 1.0319 4 1.0258 5 1.0304 a. Compute the Geometric mean b. What has been the percentage growth in the population of Atlanta? ANSWER: a. 1.028977546 b. 2.8977% 138. The growth rates in the population of Dalton for the past three years are shown below. Growth Year Factors 1 1.0313 2 1.0429 3 1.0343 a. Compute the Geometric mean b. What has been the percentage growth in the population of Dalton? ANSWER: a. 1.036161368 b. 3.616% 139. A sample of charge accounts at a local drug store revealed the following frequency distribution of unpaid balances. Unpaid Balance 10 - 29 30 - 49 50 - 69 70 - 89 90 - 109 Frequency 1 6 9 11 13 a. Determine the mean unpaid balance. b. Determine the variance. c. Determine the standard deviation. d. Compute the coefficient of variation. ANSWER: a. 74 b. 533.08 (rounded) c. 23.09 d. 31.20% 140. The amount of time that a sample of students spends watching television per day is given below. Student 1 2 3 4 5 6 7 8 Time (In Minutes) 40 28 71 48 49 35 40 57 a. Compute the mean. b. Compute the median. c. Compute the standard deviation. d. Compute the 75th percentile. ANSWER: a. 46 b. 44 c. 13.5 d. 55 141. In 2012, the average donation to the Community Kitchen was $900 with a standard deviation of $180. In 2013, the average donation was $1,600 with a standard deviation of $240. In which year do the donations show a more dispersed distribution? The coefficient of variation in 2012 was 20% (more dispersed). The coefficient of variation ANSWER: in 2013 was 15%. 142. The following data represent the daily demand (y in thousands of units) and the unit price (x in dollars) for a product. Daily Demand (y) 47 39 35 44 34 20 15 30 Unit Price (x) 1 3 5 3 6 8 16 6 a. Compute and interpret the sample covariance for the above data. b. Compute and interpret the sample correlation coefficient. ANSWER: -47. Since the covariance is negative, it indicates a negative relationship between x and a. y. b. -0.922. There is a strong negative relationship between x and y. 143. The following observations are given for two variables. y 5 8 18 20 22 30 10 7 x 2 12 3 6 11 19 18 9 a. Compute and interpret the sample covariance for the above data. b. Compute the standard deviation for x. c. Compute the standard deviation for y. d. Compute and interpret the sample correlation coefficient. ANSWER: 19.286 (rounded). Since the covariance is positive, it indicates a positive relationship a. between x and y. b. 6.32 c. 8.83 0.345. There is a positive relationship between x and y. The relationship is not very d. strong. 144. Compute the weighted mean for the following data. xi Weight (wi) 9 10 8 12 5 4 3 5 2 3 ANSWER: 6.676 CH 03 - Descriptive Statistics: Numerical 145. Compute the weighted mean for the following data. xi Weight (wi) 19 12 17 30 14 28 13 10 18 10 ANSWER: 16 146. Jason, a freshman at a local college, just completed 15 credit hours. His grade report is presented below. Credit Course Grades Hours Calculus 5 C Biology 4 A English 3 D Music 2 B P.E. 1 A The local university uses a 4 point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. Compute Jason's semester grade point average. 2.6 ANSWER: 147. The following data show the yearly salaries of a random sample of Chattanooga residents. Salary Resident (In $1,000) A 97 B 48 C 69 D 85 E 92 F 48 G 79 H 74 For the above sample, determine the following measures (Give your answer in dollars): a. b. The mean yearly salary. The standard deviation. c. The mode. d. The median. e. The 70th percentile ANSWER: a. b. c. d. e. $74,000 $18,423.59 $48,000 $76,500 $87,100 148. The following frequency distribution shows the yearly tuition (in $1,000s) of a sample of private colleges. Yearly Frequency Tuition 12 - 16 5 17 - 21 4 22 - 26 3 27 - 31 2 For the above data, compute the mean yearly tuition. (Give your answer in dollars.) $19,714.29 ANSWER: 149. The following data represent the daily supply (y in thousands of units) and the unit price (x in dollars) for a product. Daily Supply (y) Unit Price (x) 5 2 7 4 9 8 12 5 10 7 13 8 16 16 16 6 a. Compute and interpret the sample covariance for the above data. b. Compute the standard deviation for the daily supply. c. Compute the standard deviation for the unit price. d. Compute and interpret the sample correlation coefficient. ANSWER: 11.43 (rounded). The covariance is positive. Therefore, there is a positive relationship between x and y. b. 4 c. 4.175 d. 0.6844. There is a fairly strong positive relationship between x and y. a. 150. The yearly incomes of the top highest paying professions in the United States are shown below. Yearly Income Profession (in $1,000) Surgeons 136 Obstetricians 132 Anesthesiologists 130 Internists 126 Pediatricians 116 Psychiatrists 114 Dentists 110 General Practitioners 110 Chief Executives 107 Airline Pilots 99 For the above sample, determine the following measures (Give your answer in dollars). a. The mean yearly salary b. The standard deviation c. The median d. The mode ANSWER: a. b. c. d. $118,000 $12,283.68 $115,000 $110,000 151. The population change between 2000 and 2010 for several small cities are shown below. City Chattanooga Collegedale Population Change (number of residents) 3083 1466 East Ridge -461 Lakeside 1113 Ridgeside -11 Signal Mountain 395 Soddy-Daisy 3290 Walden 437 For the above sample, determine the following measures. a. The mean b. The standard deviation c. The median ANSWER: a. b. c. 1,164 1,385.51 775 152. The Michael Painting Company has purchased paint from several suppliers. The purchase price per gallon and the number of gallons purchased are shown below. Supplier Price Per Gallon ($) A 23 B 25 C 29 D 27 Compute the weighted average price per gallon. $24.50 ANSWER: Number of Gallons 700 200 100 200 153. In the fall semester of 2009, the average Graduate Management Admission Test (GMAT) of the students at UTC was 500 with a standard deviation of 80. In the fall of 2010, the average GMAT was 560 with a standard deviation of 84. Which year's GMAT scores show a more dispersed distribution? The coefficient of variation in 2009 = 16%. ANSWER: The coefficient of variation in 2010= 15%. Therefore, 2009 had a more dispersed distribution.