Descriptive Statistics Numerical Ch6 (154-176)

154. The following frequency distribution shows the starting salaries (in $1,000s) of a sample of business students: Starting Salary Frequency 22 - 26 3 27 - 31 5 32 - 36 8 37 - 41 4 For the above data, compute the mean starting salary: (Give your answer in dollars.) $32,250 ANSWER: 155. In the last month, Nancy purchased gasoline from four different gas stations. The following table shows the price per gallon and the gallons of gasoline that she purchased. Gallons Price per Gas Station Purchased Gallon ($) Texaco 20 3.95 Mobil 8 3.10 BP 18 4.80 Shell 12 3.99 Determine the average price per gallon that Nancy paid for the gasoline. $4.10 (rounded) ANSWER: 156. The price of a selected stock over a five day period is shown below. 17, 11, 13, 17, 16 Using the above data, compute the mean, the median, and the mode. Mean = 14.8 ANSWER: Median = 16 Mode = 17 157. Global Engineers hired the following number of Class 1 engineers during the first six months of the past year. (Assume the data represents a sample.) Month January February March April May June No. of Class 1 Engineers Hired 3 2 4 2 6 0 a. Determine the mean, the median, the mode, and the range for the above data. b. Compute the variance and the standard deviation. c. Compute the first and the third quartiles. d. Compute the z-scores for the months of May and June. a. Mean = 2.833 Median = 2.5 Mode = 2.0 Range = 6 ANSWER: b. S2 = 4.166 S = 2.041 c. First quartile = 1.5 Third quartile = 4.5 d. Z-score for May = 1.55 (rounded) Z-score for June = -1.39 (rounded) 158. In a statistics class, the average grade on the final examination was 75 with a standard deviation of 5. Use Chebyshev’s theorem to answer the following questions. a. At least what percentage of the students received grades between 50 and 100? Determine an interval for the grades that will be true for at least 70% of the students. (Hint: b. First, compute the Z-score.) a. 96% ANSWER: b. 75 ± (1.826)(5) = 65.87 to 84.13 159. The flashlight batteries produced by one of the northern manufacturers are known to have an average life of 60 hours with a standard deviation of 4 hours. Use Chebyshev’s theorem to answer the following questions. a. b. At least what percentage of flashlights will have a life of 54 to 66 hours? At least what percentage of the batteries will have a life of 52 to 68 hours? Determine an interval for the lives of the batteries that will be true for at least 80% of the c. batteries. (Hint: First compute the Z-score.) a. 56% ANSWER: b. 75% 60 + (2.236)(4). This indicates that at least 80% of the batteries will have lives of 51.056 c. to 68.944 hours. 160. Consider a sample with the following data values. 462 490 350 294 574 Compute the Z scores for the above five observations. Mean = 434 ANSWER: Standard Deviation = 112 X Z-Score 462 0.25 490 0.5 350 -0.75 294 -1.25 574 1.25 161. The standard deviation of a sample was reported to be 7. The report indicated that sample size? = 980. What is the ANSWER: 21 162. The variance of a sample was reported to be 81. The report indicated that size? ANSWER: = 972. What is the sample 13 163. The following data show the yearly salaries of a sample of EMBA graduates. EMBA Student A B C D E F G H Salary (in $1,000) 88 97 90 110 114 98 92 95 a. b. Compute the mean yearly salary and give your answer in dollars. Compute the standard deviation and give your answer in dollars. Compute the 75th percentile and give your answer in dollars. Fully explain what the value c. that you have determined indicates. a. $98,000 ANSWER: b. $9,355.03 c. $107,000; Approx. 75 percent of the observations are less than $107,000. 164. Descriptive statistics for the closing stock prices of two companies for several trading periods are shown below. Baba, Inc. Maman, Inc. Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 4.04 0.11 4.07 3.59 1.13 1.28 -1.10 0.04 3.98 2.00 5.98 416.05 103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 16.41 0.22 16.83 16.59 2.34 5.48 9.10 -2.85 12.57 6.29 18.86 1919.63 117 Which company’s stock price has a more dispersed distribution? Explain. Show your complete work and support your answer. b. Compare the Skewness of the two and explain what is indicated. Coefficient of variation for Baba, Inc = 27.97% ANSWER: a. Coefficient of variation for Maman, Inc. = 14.25% Therefore, Baba, Inc. shows a more dispersed stock price distribution. Baba, Inc.’s price is skewed to the right (+ 0.04) and Maman, Inc.’s price is skewed to b. the left (-2.85). a. 165. The following frequency distribution shows the GMAT scores of a sample of MBA students. GMAT Score Frequency 300 up to 400 1 400 up to 500 5 500 up to 600 9 600 up to 700 3 700 up to 800 2 For the above data, compute the mean GMAT score. 550 ANSWER: 166. The last semester grades of Nancy, a freshman at a local college are shown below. Course Physics Calculus Biology Music P.E. Credit Hours 4 6 3 2 1 Grades C A B F A The local university uses a 4 point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. Compute Nancy’s semester grade point average. 167. The following data shows the yearly salaries of a sample of MBA graduates. MBA Student Salary (in $1,000) A 78 B 87 C 80 D 100 E 104 F 88 G 82 H 85 a. b. Compute the mean yearly salary and give your answer in dollars. Compute the standard deviation and give your answer in dollars. Compute the 75th percentile and give your answer in dollars. Fully explain what the value that c. you have determined indicates. a. $88,000 ANSWER: b. $9,355.03 c. $97,000; Approx. 75 percent of the observations are less than $97,000. 168. Descriptive statistics for the closing stock prices of two companies for several trading periods are shown below. Baba, Inc Mean Standard Error Median 4.00 0.11 3.92 Maman, Inc. Mean Standard Error Median 15.91 0.29 16.59 Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 4.19 1.12 1.25 -1.15 0.08 3.95 2.03 5.98 436.32 109 Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 15.58 3.21 10.31 3.52 -2.09 13.45 5.55 18.99 1972.61 124 Which company’s stock price has a more dispersed distribution? Explain. Show your complete work and support your answer. b. Compare the Skewness' of the two and explain what is indicated. ANSWER: Coefficient of variation for Baba, Inc = 28% a. Coefficient of variation for Maman, Inc. = 20.18% Therefore, Baba, Inc. shows a more dispersed stock price distribution. a. b. Baba, Inc’s price is skewed to the right (+ 0.08) and Maman, Inc’s price is skewed to the left (-2.09). 169. The following frequency distribution shows the GMAT scores of a sample of MBA students: GMAT Score 300 up to 400 400 up to 500 500 up to 600 600 up to 700 700 up to 800 Frequency 2 6 10 5 2 For the above data, compute the mean GMAT score. 546 ANSWER: 170. Last semester grades of Michael, a freshman at a local college are shown below. Course Credit Hours Grades Chemistry Calculus English Music P.E. 5 5 4 3 1 C A C F A The local university uses a 4 point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. Compute Michael’s semester grade point average. 2.33 ANSWER: 171. A recent survey of a local neighborhood measured the number of children per household. The results are given below. Household Children 1 2 2 0 3 1 4 6 5 2 6 2 7 3 8 1 9 2 For the above data compute the following measures. (Round to the nearest tenth, as needed.) a. The mean b. Then median c. The mode ANSWER: a. 2.1 b. 2 c. 2 172. The following data shows the number of students enrolled in various professors’ statistics classes. Professor Enrollment A 256 B 167 C 159 D 164 E 170 F 156 For the above sample, compute the following measures. a. The variance b. The standard deviation If we consider professor A’s enrollment as an outlier, compute the variance and the standard c. deviations, excluding Professor A’s class. (Round to two decimal places.) a. 1461.47 ANSWER: b. 38.23 c. Variance =32.7; Standard deviation = -5.72 173. Below you are given a sample of ACT scores of 12 college applicants. 19 23 27 21 32 17 20 29 a. Determine the first quartile. b. Determine the 75th percentile. c. Determine the interquartile range. a. 19.25 ANSWER: b. 28.5 c. 9.25 174. Below is a sample of scores from a professor’s most recent exam. Student 1 2 3 4 5 6 7 Calculate the following. a. The mean b. The standard deviation c. The 65th percentile a. ANSWER: 88 Score 83 91 79 99 88 81 95 22 30 25 15 b. 7.46 c. 91.8 175. Aubree, a college freshman, took 15 hours her first semester. Below is her grade report. Class Credit Hours Grade Physics 4 D Biology 4 B Statistics 3 B Seminar 1 A Macroeconomics 3 A Aubree’s university uses a 4-point grading system, i.e., A=4, B=3, C=2, D=1, F=0. a. Compute Aubree’s grade point average at the end of the semester. The next semester, Aubree retakes physics and makes a B. If this B replaces her old grade (D), what would her revised GPA be? (Assume the only class she took her second semester was physics.) (Round to the nearest hundred.) a. 2.73 ANSWER: b. 3.27 b. 176. The table below shows the population growth rate of a city for the years 2008 through 2012. Population Year Growth Rate 2008 0.8923 2009 1.0587 2010 1.1934 2011 1.2345 2012 1.0995 a. Compute the geometric mean. b. What has been the percentage growth in the population of the city between 2008 to 2012? a.. Geometric Mean = 1.088808 ANSWER: b. 8.88%