CHAPTER 3—DESCRIPTIVE STATISTICS: NUMERICAL MEASURES MULTIPLE CHOICE 1. Geometric mean is a measure of a. location b. dispersion c. variability d. weight of items, when arranged in descending order ANS: A PTS: 1 TOP: Descriptive Statistics 2. Growth factors for the population of Chattanoonga in the past two years has been 8 and 12. The geometric mean has a value of a. 20 b. square root of 20 c. square root of 96 d. 96 ANS: C PTS: 1 TOP: Descriptive Statistics 3. Growth factors for the population of Atlanta in the past five years have been 1, 2, 3, 4 , and 5. The geometric mean is a. 15 b. square root of 15 c. 120 d. fifth root of 120 ANS: D PTS: 1 TOP: Descriptive Statistics 4. Geometric mean of five observations is a. the same as weighted mean b. the same as mean c. square root of the product of the 5 observations d. fifth root of the product of the 5 observations ANS: D PTS: 1 TOP: Descriptive Statistics 5. The nth root of the product of the n observations is a. weighted mean b. geometric mean c. product deviation d. the sum of squares ANS: B PTS: 1 TOP: Descriptive Statistics 6. The measure of location which is the most likely to be influenced by extreme values in the data set is the a. range b. median c. mode d. mean ANS: D PTS: 1 TOP: Descriptive Statistics 7. The measure of location which is the most likely to be influenced by extreme values in the data set is the a. range b. median c. mode d. mean ANS: D PTS: 1 TOP: Descriptive Statistics 8. The most important statistical descriptive measure of the location of a data set is the a. mean b. median c. mode d. variance ANS: A PTS: 1 TOP: Descriptive Statistics 9. If two groups of numbers have the same mean, then a. their standard deviations must also be equal b. their medians must also be equal c. their modes must also be equal d. None of these alternatives is correct. ANS: D PTS: 1 TOP: Descriptive Statistics 10. The mean of the sample a. is always smaller than the mean of the population from which the sample was taken b. can never be zero c. can never be negative d. None of these alternatives is correct. ANS: D PTS: 1 TOP: Descriptive Statistics 11. When the smallest and largest percentage of items are removed from a data set and the mean is computed, the mean of the remaining data is a. the median b. the mode c. the trimmed mean d. any of the above ANS: C PTS: 1 TOP: Descriptive Statistics 12. Since the population is always larger than the sample, the value of the sample mean a. is always smaller than the true value of the population mean b. is always larger than the true value of the population mean c. is always equal to the true value of the population mean d. could be larger, equal to, or smaller than the true value of the population mean ANS: D PTS: 1 TOP: Descriptive Statistics 13. Which of the following provides a measure of central location for the data? a. standard deviation b. mean c. variance d. range ANS: B PTS: 1 TOP: Descriptive Statistics 14. When computing the mean of a set of values xi, the value of xi a. can never be zero b. can never be negative c. must always be positive d. can be any value ANS: D PTS: 1 TOP: Descriptive Statistics 15. In computing the mean of a sample, the value of xi is divided by a. n b. n - 1 c. n + 1 d. n - 2 ANS: A PTS: 1 TOP: Descriptive Statistics 16. A numerical value used as a summary measure for a sample, such as sample mean, is known as a a. population parameter b. sample parameter c. sample statistic d. population mean ANS: C PTS: 1 TOP: Descriptive Statistics 17. Since the population size is always larger than the sample size, then the sample statistic a. can never be larger than the population parameter b. can never be equal to the population parameter c. can be smaller, larger, or equal to the population parameter d. can never be smaller than the population parameter ANS: C PTS: 1 TOP: Descriptive Statistics 18. is an example of a a. population parameter b. sample statistic c. population variance d. mode ANS: A PTS: 1 TOP: Descriptive Statistics 19. The mean of a sample a. is always equal to the mean of the population b. is always smaller than the mean of the population c. is computed by summing the data values and dividing the sum by (n - 1) d. is computed by summing all the data values and dividing the sum by the number of items ANS: D PTS: 1 TOP: Descriptive Statistics 20. The hourly wages of a sample of 130 system analysts are given below. mean = 60 mode = 73 median = 74 range = 20 variance = 324 The coefficient of variation equals a. 0.30% b. 30% c. 5.4% d. 54% ANS: B PTS: 1 TOP: Descriptive Statistics 21. The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals a. 13 b. 24 c. 576 d. 28,461 ANS: B PTS: 1 TOP: Descriptive Statistics 22. The median of a sample will always equal the a. mode b. mean c. 50th percentile d. all of the above answers are correct ANS: C PTS: 1 TOP: Descriptive Statistics 23. The median is a measure of a. relative dispersion b. absolute dispersion c. central location d. relative location ANS: C PTS: 1 TOP: Descriptive Statistics 24. The 50th percentile is the a. mode b. median c. mean d. third quartile ANS: B PTS: 1 TOP: Descriptive Statistics 25. The 75th percentile is referred to as the a. first quartile b. second quartile c. third quartile d. fourth quartile ANS: C PTS: 1 TOP: Descriptive Statistics 26. The pth percentile is a value such that at least p percent of the observations are a. less than or equal to this value b. less than this value c. more than or equal to this value d. more than this value ANS: A PTS: 1 TOP: Descriptive Statistics 27. The difference between the largest and the smallest data values is the a. variance b. interquartile range c. range d. coefficient of variation ANS: C PTS: 1 TOP: Descriptive Statistics 28. The first quartile a. contains at least one third of the data elements b. is the same as the 25th percentile c. is the same as the 50th percentile d. is the same as the 75th percentile ANS: B PTS: 1 TOP: Descriptive Statistics 29. When computing the mean, the smallest value a. can never be negative b. can never be zero c. can never be less than the mean d. can be any value ANS: D PTS: 1 TOP: Descriptive Statistics 30. Which of the following is not a measure of central location? a. mean b. median c. variance d. mode ANS: C PTS: 1 TOP: Descriptive Statistics 31. If a data set has an even number of observations, the median a. cannot be determined b. is the average value of the two middle items c. must be equal to the mean d. is the average value of the two middle items when all items are arranged in ascending order ANS: D PTS: 1 TOP: Descriptive Statistics 32. Which of the following is a measure of dispersion? a. percentiles b. quartiles c. interquartile range d. all of the above are measures of dispersion ANS: C PTS: 1 TOP: Descriptive Statistics 33. The value which has half of the observations above it and half the observations below it is called the a. range b. median c. mean d. mode ANS: B PTS: 1 TOP: Descriptive Statistics 34. The most frequently occurring value of a data set is called the a. range b. mode c. mean d. median ANS: B PTS: 1 TOP: Descriptive Statistics 35. The interquartile range is a. the 50th percentile b. another name for the variance c. the difference between the largest and smallest values d. the difference between the third quartile and the first quartile ANS: D PTS: 1 TOP: Descriptive Statistics 36. The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated. mean = 160 mode = 165 median = 170 range = 60 variance = 324 The coefficient of variation equals a. 0.1125% b. 11.25% c. 203.12% d. 0.20312% ANS: B PTS: 1 TOP: Descriptive Statistics 37. The heights (in inches) of 25 individuals were recorded and the following statistics were calculated mean = 70 mode = 73 median = 74 range = 20 variance = 784 The coefficient of variation equals a. 11.2% b. 1120% c. 0.4% d. 40% ANS: D PTS: 1 TOP: Descriptive Statistics 38. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals a. 8 b. 10 c. 6400 d. 4,096 ANS: D PTS: 1 TOP: Descriptive Statistics 39. The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals a. b. c. d. 9 4096 8 6561 ANS: C PTS: 1 TOP: Descriptive Statistics 40. If index i (which is used to determine the location of the pth percentile) is not an integer, its value should be a. squared b. divided by (n - 1) c. rounded down d. rounded up ANS: D PTS: 1 TOP: Descriptive Statistics 41. When the data are skewed to the right, the measure of Skewness will be a. negative b. zero c. positive d. one ANS: C PTS: 1 TOP: Descriptive Statistics 42. When data are positively skewed, the mean will usually be a. greater than the median b. smaller than the median c. equal to the median d. positive ANS: A PTS: 1 TOP: Descriptive Statistics 43. Which of the following is not a measure of dispersion? a. the range b. the 50th percentile c. the standard deviation d. the interquartile range ANS: B PTS: 1 TOP: Descriptive Statistics 44. The interquartile range is used as a measure of variability to overcome what difficulty of the range? a. the sum of the range variances is zero b. the range is difficult to compute c. the range is influenced too much by extreme values d. the range is negative ANS: C PTS: 1 TOP: Descriptive Statistics 45. If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true? a. the data set is a sample b. the data set is a population c. the data set could be either a sample or a population d. the data set is from a census ANS: A PTS: 1 TOP: Descriptive Statistics 46. In computing descriptive statistics from grouped data, a. data values are treated as if they occur at the midpoint of a class b. the grouped data result is more accurate than the ungrouped result c. the grouped data computations are used only when a population is being analyzed d. None of these alternatives is correct. ANS: A PTS: 1 TOP: Descriptive Statistics 47. The measure of dispersion that is influenced most by extreme values is a. the variance b. the standard deviation c. the range d. the interquartile range ANS: C PTS: 1 TOP: Descriptive Statistics 48. When should measures of location and dispersion be computed from grouped data rather than from individual data values? a. as much as possible since computations are easier b. only when individual data values are unavailable c. whenever computer packages for descriptive statistics are unavailable d. only when the data are from a population ANS: B PTS: 1 TOP: Descriptive Statistics 49. The descriptive measure of dispersion that is based on the concept of a deviation about the mean is a. the range b. the interquartile range c. the absolute value of the range d. the standard deviation ANS: D PTS: 1 TOP: Descriptive Statistics 50. The numerical value of the standard deviation can never be a. larger than the variance b. zero c. negative d. smaller than the variance ANS: C PTS: 1 TOP: Descriptive Statistics 51. The sample variance a. is always smaller than the true value of the population variance b. is always larger than the true value of the population variance c. could be smaller, equal to, or larger than the true value of the population variance d. can never be zero ANS: C PTS: 1 TOP: Descriptive Statistics 52. The coefficient of variation is a. the same as the variance b. the standard deviation divided by the mean times 100 c. the square of the standard deviation d. the mean divided by the standard deviation ANS: B PTS: 1 TOP: Descriptive Statistics 53. The variance can never be a. zero b. larger than the standard deviation c. negative d. smaller than the standard deviation ANS: C PTS: 1 TOP: Descriptive Statistics 54. The sum of deviations of the individual data elements from their mean is a. always greater than zero b. always less than zero c. sometimes greater than and sometimes less than zero, depending on the data elements d. always equal to zero ANS: D PTS: 1 TOP: Descriptive Statistics 55. Which of the following symbols represents the standard deviation of the population? a. 2 b. c. d. ANS: B PTS: 1 TOP: Descriptive Statistics 56. Which of the following symbols represents the mean of the population? a. 2 b. c. d. ANS: C PTS: 1 TOP: Descriptive Statistics 57. Which of the following symbols represents the variance of the population? a. 2 b. c. d. ANS: A PTS: 1 TOP: Descriptive Statistics 58. Which of the following symbols represents the size of the population? a. 2 b. c. d. N ANS: D PTS: 1 TOP: Descriptive Statistics 59. Which of the following symbols represents the mean of the sample? a. 2 b. c. d. ANS: D PTS: 1 TOP: Descriptive Statistics 60. Which of the following symbols represents the size of the sample a. 2 b. c. N d. n ANS: D PTS: 1 TOP: Descriptive Statistics 61. The symbol is used to represent a. the variance of the population b. the standard deviation of the sample c. the standard deviation of the population d. the variance of the sample ANS: C PTS: 1 TOP: Descriptive Statistics 62. The symbol 2 is used to represent a. the variance of the population b. the standard deviation of the sample c. the standard deviation of the population d. the variance of the sample ANS: A PTS: 1 TOP: Descriptive Statistics 63. The variance of the sample a. can never be negative b. can be negative c. cannot be zero d. cannot be less than one ANS: A PTS: 1 TOP: Descriptive Statistics 64. The measure of dispersion which is not measured in the same units as the original data is the a. median b. standard deviation c. coefficient of determination d. variance ANS: D PTS: 1 TOP: Descriptive Statistics 65. A numerical measure of linear association between two variables is the a. variance b. covariance c. standard deviation d. coefficient of variation ANS: B PTS: 1 66. Positive values of covariance indicate a. a positive variance of the x values TOP: Descriptive Statistics b. a positive variance of the y values c. the standard deviation is positive d. positive relation between the independent and the dependent variables ANS: D PTS: 1 TOP: Descriptive Statistics 67. A numerical measure of linear association between two variables is the a. variance b. coefficient of variation c. correlation coefficient d. standard deviation ANS: C PTS: 1 TOP: Descriptive Statistics 68. The coefficient of correlation ranges between a. 0 and 1 b. -1 and +1 c. minus infinity and plus infinity d. 1 and 100 ANS: B PTS: 1 TOP: Descriptive Statistics 69. The coefficient of correlation a. is the same as the coefficient of determination b. can be larger than 1 c. cannot be larger than 1 d. cannot be negative ANS: C PTS: 1 TOP: Descriptive Statistics 70. The value of the sum of the deviations from the mean, i.e., must always be a. less than the zero b. negative c. either positive or negative depending on whether the mean is negative or positive d. zero ANS: D PTS: 1 TOP: Descriptive Statistics 71. The numerical value of the variance a. is always larger than the numerical value of the standard deviation b. is always smaller than the numerical value of the standard deviation c. is negative if the mean is negative d. can be larger or smaller than the numerical value of the standard deviation ANS: D PTS: 1 TOP: Descriptive Statistics 72. Since the median is the middle value of a data set it a. must always be smaller than the mode b. must always be larger than the mode c. must always be smaller than the mean d. None of these alternatives is correct. ANS: D PTS: 1 TOP: Descriptive Statistics 73. In a five number summary, which of the following is not used for data summarization? a. b. c. d. the smallest value the largest value the mean the 25th percentile ANS: C PTS: 1 TOP: Descriptive Statistics 74. The relative frequency of a class is computed by a. dividing the midpoint of the class by the sample size b. dividing the frequency of the class by the midpoint c. dividing the sample size by the frequency of the class d. dividing the frequency of the class by the sample size ANS: D PTS: 1 TOP: Descriptive Statistics 75. During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period a. is negative since all the numbers are negative b. must be at least zero c. cannot be computed since all the numbers are negative d. can be either negative or positive ANS: B PTS: 1 TOP: Descriptive Statistics 76. Which of the following is not a measure of dispersion? a. mode b. standard deviation c. range d. interquartile range ANS: A PTS: 1 TOP: Descriptive Statistics 77. If the coefficient of variation is 40% and the mean is 70, then the variance is a. 28 b. 2800 c. 1.75 d. 784 ANS: D PTS: 1 TOP: Descriptive Statistics 78. Given the following information: Standard deviation = 8 Coefficient of variation = 64% The mean would then be a. 12.5 b. 8 c. 0.64 d. 1.25 ANS: A PTS: 1 TOP: Descriptive Statistics 79. Since the mode is the most frequently occurring data value, it a. can never be larger than the mean b. is always larger than the median c. is always larger than the mean d. None of these alternatives is correct. ANS: D PTS: 1 TOP: Descriptive Statistics 80. A group of students had dinner at a local restaurant. The total bill for the dinner was $414.70. Each student paid his/her equal share of the bill, which was $18.85. How many student’s were at the dinner? a. 4 b. 415 c. 19 d. 22 ANS: D PTS: 1 TOP: Descriptive Statistics 81. The standard deviation of a sample was reported to be 20. The report indicated that 7200. What has been the sample size? a. 16 b. 17 c. 18 d. 19 ANS: D PTS: 1 TOP: Descriptive Statistics 82. The variance of a sample was reported to be 144. The report indicated that has been the sample size? a. 49 b. 50 c. 51 d. 52 ANS: C PTS: 1 = = 7200. What TOP: Descriptive Statistics 83. From a population of size 1,000, a random sample of 100 items is selected. The mean of the sample a. must be 10 times smaller than the mean of the population b. must be equal to the mean of the population, if the sample is truly random c. must be 10 times larger than the mean of the population d. can be larger, smaller or equal to the mean of the population ANS: D PTS: 1 TOP: Descriptive Statistics 84. From a population of size 500, a random sample of 50 items is selected. The mode of the sample a. must be 500 b. must be equal to the mode of population, if the sample is truly random c. must be equal to the mean of the population, if the sample is truly random d. can be larger, smaller or equal to the mode of the population ANS: D PTS: 1 TOP: Descriptive Statistics 85. From a population of size 400, a random sample of 40 items is selected. The median of the sample a. must be 200, since 400 divided by 2 is 200 b. must be 10, since 400 divided by 400 is 10 c. must be equal to the median of population, if the sample is truly random d. None of these alternatives is correct. ANS: D PTS: 1 TOP: Descriptive Statistics 86. The geometric mean of 2, 4, 8 is a. 4.67 b. 5.0 c. 16 d. 4.0 ANS: D PTS: 1 TOP: Descriptive Statistics 87. The geometric mean of 1, 1, 8 is a. 10.0 b. 2.0 c. 3.33 d. 3.0 ANS: B PTS: 1 TOP: Descriptive Statistics 88. The geometric mean of 1, 3, 5, and 6 is a. 15.0 b. 5.0 c. 3.08 d. 3.75 ANS: C PTS: 1 TOP: Descriptive Statistics 89. The geometric mean of 1, 2, 4, and 10 is a. 2.99 b. 4.25 c. 17.0 d. 4.0 ANS: A PTS: 1 TOP: Descriptive Statistics Exhibit 3-1 The following data show the number of hours worked by 200 statistics students. Number of Hours 0- 9 10 - 19 20 - 29 30 - 39 Frequency 40 50 70 40 90. Refer to Exhibit 3-1. The class width for this distribution a. is 9 b. is 10 c. is 11 d. varies from class to class ANS: B PTS: 1 TOP: Descriptive Statistics 91. Refer to Exhibit 3-1. The number of students working 19 hours or less a. is 40 b. is 50 c. is 90 d. cannot be determined without the original data ANS: C PTS: 1 TOP: Descriptive Statistics 92. Refer to Exhibit 3-1. The relative frequency of students working 9 hours or less a. is .2 b. is .45 c. is 40 d. cannot be determined from the information given ANS: A PTS: 1 TOP: Descriptive Statistics 93. Refer to Exhibit 3-1. The cumulative relative frequency for the class of 10 - 19 a. is 90 b. is .25 c. is .45 d. cannot be determined from the information given ANS: C PTS: 1 TOP: Descriptive Statistics Exhibit 3-2 A researcher has collected the following sample data 5 6 12 7 6 5 8 12 5 4 94. Refer to Exhibit 3-2. The median is a. 5 b. 6 c. 7 d. 8 ANS: B PTS: 1 TOP: Descriptive Statistics 95. Refer to Exhibit 3-2. The mode is a. 5 b. 6 c. 7 d. 8 ANS: A PTS: 1 TOP: Descriptive Statistics 96. Refer to Exhibit 3-2. The mean is a. 5 b. 6 c. 7 d. 8 ANS: C PTS: 1 97. Refer to Exhibit 3-2. The 75th percentile is a. 5 b. 6 c. 7 d. 8 TOP: Descriptive Statistics ANS: D PTS: 1 TOP: Descriptive Statistics Exhibit 3-3 A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 98. Refer to Exhibit 3-3. The variance is a. 80 b. 4.062 c. 13.2 d. 16.5 ANS: D PTS: 1 TOP: Descriptive Statistics 99. Refer to Exhibit 3-3. The standard deviation is a. 8.944 b. 4.062 c. 13.2 d. 16.5 ANS: B PTS: 1 TOP: Descriptive Statistics 100. Refer to Exhibit 3-3. The coefficient of variation is a. 72.66% b. 81.24% c. 264% d. 330% ANS: B PTS: 1 TOP: Descriptive Statistics 101. Refer to Exhibit 3-3. The range is a. 1 b. 2 c. 10 d. 12 ANS: C PTS: 1 TOP: Descriptive Statistics 102. Refer to Exhibit 3-3. The interquartile range is a. 1 b. 2 c. 10 d. 12 ANS: B PTS: 1 TOP: Descriptive Statistics Exhibit 3-4 The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway. Speed Miles per Hour 50 - 54 55 - 59 Frequency 2 4 60 - 64 65 - 69 70 - 74 75 - 79 5 10 9 5 35 103. Refer to Exhibit 3-4. The mean is a. 35 b. 670 c. 10 d. 67 ANS: D PTS: 1 TOP: Descriptive Statistics 104. Refer to Exhibit 3-4. The variance is a. 6.969 b. 7.071 c. 48.570 d. 50.000 ANS: D PTS: 1 TOP: Descriptive Statistics 105. Refer to Exhibit 3-4. The standard deviation is a. 6.969 b. 7.071 c. 48.570 d. 50.000 ANS: B PTS: 1 TOP: Descriptive Statistics Exhibit 3-5 You are given the following frequency distribution. Class 10-14 15-19 20-24 25-29 30-34 Frequency 1 2 5 8 4 106. Refer to Exhibit 3-5. The mean is a. 500 b. 26.315 c. 30 d. 25 ANS: D PTS: 1 TOP: Descriptive Statistics 107. Refer to Exhibit 3-5. The variance is a. 570 b. 5.477 c. 500 d. 30 ANS: D PTS: 1 TOP: Descriptive Statistics 108. Refer to Exhibit 3-5. The standard deviation is a. 570 b. 5.477 c. 25 d. 30 ANS: B PTS: 1 TOP: Descriptive Statistics 109. Refer to Exhibit 3-5. The coefficient of variation is a. 25% b. 21.91% c. 5.477% d. 30% ANS: B PTS: 1 TOP: Descriptive Statistics Exhibit 3-6 The closing stock price of MNM Corporation for the last 7 trading days is shown below. Day 1 2 3 4 5 6 7 Stock Price 84 87 84 88 85 90 91 110. Refer to Exhibit 3-6. The mean is a. 84 b. 85 c. 86 d. 87 ANS: D PTS: 1 TOP: Descriptive Statistics 111. Refer to Exhibit 3-6. The mode is a. 84 b. 85 c. 86 d. 87 ANS: A PTS: 1 TOP: Descriptive Statistics 112. Refer to Exhibit 3-6. The median is a. 84 b. 85 c. 86 d. 87 ANS: D PTS: 1 TOP: Descriptive Statistics 113. Refer to Exhibit 3-6. The range is a. 7 b. 8 c. 9 d. 91 ANS: A PTS: 1 TOP: Descriptive Statistics 114. Refer to Exhibit 3-6. The variance is a. 2.828 b. 8 c. 9 d. 81 ANS: B PTS: 1 TOP: Descriptive Statistics PROBLEM 1. The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. Day 1 2 3 4 5 6 7 8 9 10 Stock Price 84 87 84 88 85 90 91 83 82 86 For the above sample, compute the following measures. a. The mean b. The median c. The mode d. The variance e. The standard deviation f. The range ANS: a. 86 b. 85.5 c. 84 d. 8.8888 e. 2.9814 f. 9 PTS: 1 TOP: Descriptive Statistics 2. The hourly wages of a sample of eight individuals is given below. Individual A B C D E F G H Hourly Wage (dollars) 27 25 20 10 12 14 17 19 For the above sample, determine the following measures: a. The mean. b. The standard deviation. c. The 25th percentile. ANS: a. b. c. 18 6 13 PTS: 1 TOP: Descriptive Statistics 3. In 2008, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2009, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer. ANS: C.V. for 2008 = 18%, C.V. for 2009 = 17% Therefore 2008 shows a more dispersed distribution. PTS: 1 TOP: Descriptive Statistics 4. Consider the data in the following frequency distribution. Assume the data represent a population. Class 2- 6 7 - 11 12 - 16 17 - 21 Frequency 2 3 4 1 For the above data, compute the following. a. The mean b. The variance c. The standard deviation ANS: a. b. c. 11 21 4.58 PTS: 1 TOP: Descriptive Statistics 5. A private research organization studying families in various countries reported the following data for the amount of time 4-year-old children spent alone with their fathers each day. Country Belgium Canada China Finland Germany Nigeria Sweden United States Time with Dad (minutes) 30 44 54 50 36 42 46 42 For the above sample, determine the following measures: a. The mean b. The standard deviation c. The mode d. The 75th percentile ANS: a. b. c. d. 43 7.56 42 48 PTS: 1 TOP: Descriptive Statistics 6. In 2012, the average donation to the Help Way was $225 with a standard deviation of $45. In 2013, the average donation was $400 with a standard deviation of $60. In which year did the donations show a more dispersed distribution? ANS: The coefficient of variation in 2012 was 20% (more dispersed). The coefficient of variation in 2013 was 15%. PTS: 1 TOP: Descriptive Statistics 7. The following frequency distribution shows the ACT scores of a sample of students: Score 14 - 18 19 - 23 24 - 28 29 - 33 Frequency 2 5 12 1 For the above data, compute the following. a. The mean b. The standard deviation ANS: a. b. 24 3.77 PTS: 1 TOP: Descriptive Statistics 8. The following data show the yearly salaries of football coaches at some state supported universities. University A B C D E F G H Salary (in $1,000) 53 44 68 47 62 59 53 94 For the above sample, determine the following measures. a. The mean yearly salary b. The standard deviation c. The mode d. The median e. The 70th percentile ANS: a. b. c. d. e. 60 15.8 53 56 62 PTS: 1 TOP: Descriptive Statistics 9. The ages of a sample of 8 faculty members selected from the School of Business Administration are shown below. Faculty 1 2 3 4 5 6 7 8 a. b. Age 42 30 73 50 51 37 42 59 Compute the average age. Determine the mode. c. d. Compute the median age. Compute the standard deviation. ANS: a. b. c. d. 48 42 46 13.5 PTS: 1 TOP: Descriptive Statistics 10. The grade point average of the students at UTC is 2.80 with a standard deviation of 0.84. The grade point average of students at UTK is 2.4 with a standard deviation of 0.84. Which university shows a more dispersed grade distribution? ANS: UTK's coefficient of variation = 35%. UTC's coefficient of variation = 30%. Therefore, UTK has a more dispersed grade distribution. PTS: 1 TOP: Descriptive Statistics 11. The following is a frequency distribution for the ages of a sample of employees at a local company. Age 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 a. b. c. d. Frequency 2 3 7 5 1 Determine the average age for the sample. Compute the variance. Compute the standard deviation. Compute the coefficient of variation. ANS: a. b. c. d. 54.5 117.65 10.85 19.91% PTS: 1 TOP: Descriptive Statistics 12. A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of examinations are selected at random and scored. The results are shown below. Grade 93 65 80 97 85 87 97 60 For the above data, determine a. The mean b. The median c. The mode d. The standard deviation e. The coefficient of variation ANS: a. b. c. d. e. 83 86 97 14.01 16.88% PTS: 1 TOP: Descriptive Statistics 13. The number of hours worked per week for a sample of ten students is shown below. Student 1 2 3 4 5 6 7 8 9 10 a. b. c. Hours 20 0 18 16 22 40 8 6 30 40 Determine the median and explain its meaning. Compute the 70th percentile and explain its meaning. What is the mode of the above data? What does it signify? ANS: a. b. c. 19; approximately 50% of the students work at least 19 hours 26; at least 70% of the students work less than or equal to 26 hours per week 40; the most frequent data element PTS: 1 TOP: Descriptive Statistics 14. The frequency distribution below shows the monthly expenditure on gasoline for a sample of 14 individuals. Expenditure Frequency 55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 a. b. 2 3 4 3 2 Compute the mean. Compute the standard deviation. ANS: a. b. 67 6.5 PTS: 1 TOP: Descriptive Statistics 15. The average wage of Tennessee cashiers is $14 per hour with a standard deviation of $4.20. In Georgia, the average wage of cashiers is $16 with a standard deviation of $4.40. In which state do the wages of cashiers appear to be more dispersed? ANS: The coefficient of variation in Tennessee = 30%. The coefficient of variation in Georgia = 27.5%. Therefore, Tennessee shows a more dispersed distribution. PTS: 1 TOP: Descriptive Statistics 16. 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 40 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 ANS: a. b. c. d. e. f. g. 25 25 20 20 35 128.571 11.339 PTS: 1 TOP: Descriptive Statistics 40 10 30 20 10 5 20 17. 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 2 1 2 0 2 1 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 ANS: a. b. c. d. e. f. g. h. 2 1.5 1.25 2 1.5 0.75 0.866 69.28% PTS: 1 TOP: Descriptive Statistics 18. The following is a frequency distribution of grades of a sample of statistics examinations. Grade 50 - 59 60 - 69 70 - 79 80 - 89 90 - 99 Frequency 7 10 22 15 6 Compute the following measures: a. The mean b. The variance c. The standard deviation d. The coefficient of variation ANS: a. b. c. d. 75 130.25 11.41 15.22% PTS: 1 TOP: Descriptive Statistics 2 19. The following shows the number of job losses and gains (in thousands) between 2008 and 2009 for a sample of seven cities. Job Change (in thousands) -11 -7 -6 -5 -5 0 6 City Memphis Nashville Atlanta Chattanooga Birmingham Huntsville Knoxville a. b. c. d. Compute the mean. Determine the mode. Determine the median. Determine the standard deviation. ANS: a. b. c. d. -4000 -5000 -5000 5,477 (rounded) PTS: 1 TOP: Descriptive Statistics 20. For the following frequency distribution, Class 45 - 47 48 - 50 51 - 53 54 - 56 57 - 59 a. b. Frequency 3 6 8 2 1 Compute the mean. Compute the standard deviation. (Assume the data represent a population.) ANS: a. b. 50.8 3.06 PTS: 1 TOP: Descriptive Statistics 21. Below you are given the ages of a sample of 10 college students who are enrolled in statistics. 20 a. b. c. 18 20 22 18 Compute the mean. Compute the variance. Compute the standard deviation. 20 22 17 19 24 d. e. f. g. h. Compute the coefficient of variation. Determine the 25th percentile. Determine the median Determine the 75th percentile. Determine the range. ANS: a. b. c. d. e. f. g. h. 20 4.667 2.16 10.8% 18 20 22 7 PTS: 1 TOP: Descriptive Statistics 22. A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below. 3 a. b. c. d. e. f. g. h. 12 4 7 14 6 2 9 11 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. ANS: a. b. c. d. e. f. g. h. 7.56 17.78 4.22 55.8 4.0 7.0 11 12 PTS: 1 TOP: Descriptive Statistics 23. For the following frequency distribution (assume the data represent a population), Class 70 - 79 80 - 89 90 - 99 100 - 109 Frequency 5 9 11 9 110 - 119 a. b. 6 Compute the mean. Compute the standard deviation. ANS: a. b. 95 12.44 (rounded) PTS: 1 TOP: Descriptive Statistics 24. 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 a. b. c. d. Frequency 1 3 7 6 2 1 Compute the mean. Compute the variance. Compute the standard deviation. Compute the coefficient of variation. ANS: a. b. c. d. 34 35.26 5.94 17.46% PTS: 1 TOP: Descriptive Statistics 25. The following frequency distribution shows the time (in minutes) that a sample of students uses the computer terminals per day. Time 20 - 39 40 - 59 60 - 79 80 - 99 100 - 119 a. b. c. d. Frequency 2 4 6 4 2 Compute the mean. Compute the variance. Compute the standard deviation. Compute the coefficient of variation. ANS: a. b. c. d. 69.5 564.54 23.76 34.19% PTS: 1 TOP: Descriptive Statistics 26. The growth rate in thepopulation of Atlanta for the past five years are shown below. Year Growth Factors 1 1.0298 2 1.0270 3 1.0319 4 1.0258 5 1.0304 a. b. Compute the Geometric mean What has been the percentage growth in the population of Atlanta? ANS: a. b. 1.028977546 2.8977% PTS: 1 TOP: Descriptive Statistics 27. The growth rates in the population of Dalton for the past three years are shown below. Year Growth Factors 1 1.0313 2 1.0429 3 1.0343 a. b. Compute the Geometric mean What has been the percentage growth in the population of Dalton? ANS: a. b. 1.036161368 3.616% PTS: 1 TOP: Descriptive Statistics 28. 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. b. c. d. Determine the mean unpaid balance. Determine the variance. Determine the standard deviation. Compute the coefficient of variation. ANS: a. b. c. d. 74 533.08 (rounded) 23.09 31.20% PTS: 1 TOP: Descriptive Statistics 29. 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 a. b. c. d. Time (In Minutes) 40 28 71 48 49 35 40 57 Compute the mean. Compute the median. Compute the standard deviation. Compute the 75th percentile. ANS: a. b. c. d. 46 44 13.5 53 PTS: 1 TOP: Descriptive Statistics 30. 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? ANS: The coefficient of variation in 2012 was 20% (more dispersed). The coefficient of variation in 2013 was 15%. PTS: 1 TOP: Descriptive Statistics 31. 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 a. b. Unit Price (x) 1 3 5 3 6 8 16 6 Compute and interpret the sample covariance for the above data. Compute and interpret the sample correlation coefficient. ANS: a. b. -47. Since the covariance is negative, it indicates a negative relationship between x and y. -0.922. There is a strong negative relationship between x and y. PTS: 1 TOP: Descriptive Statistics 32. The following observations are given for two variables. y 5 8 18 20 22 30 10 7 a. b. c. d. x 2 12 3 6 11 19 18 9 Compute and interpret the sample covariance for the above data. Compute the standard deviation for x. Compute the standard deviation for y. Compute and interpret the sample correlation coefficient. ANS: a. b. c. d. 19.286 (rounded). Since the covariance is positive, it indicates a positive relationship between x and y. 6.32 8.83 0.345. There is a positive relationship between x and y. The relationship is not very strong. PTS: 1 TOP: Descriptive Statistics 33. Compute the weighted mean for the following data. xi Weight (wi) 9 8 5 3 2 10 12 4 5 3 ANS: 6.676 PTS: 1 TOP: Descriptive Statistics 34. Compute the weighted mean for the following data. xi 19 17 14 13 18 Weight (wi) 12 30 28 10 10 ANS: 16 PTS: 1 TOP: Descriptive Statistics 35. Jason, a freshman at a local college, just completed 15 credit hours. His grade report is presented below. Course Calculus Biology English Music P.E. Credit Hours 5 4 3 2 1 Grades C A D B 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. ANS: 2.6 PTS: 1 TOP: Descriptive Statistics 36. The following data show the yearly salaries of a random sample of Chattanooga residents. Resident A B C D E Salary (In $1,000) 97 48 69 85 92 F G H 48 79 74 For the above sample, determine the following measures (Give your answer in dollars): a. b. c. d. e. The mean yearly salary. The standard deviation. The mode. The median. The 70th percentile ANS: a. b. c. d. e. $74,000 $18,423.59 $48,000 $76,500 $85,000 PTS: 1 TOP: Descriptive Statistics 37. The following frequency distribution shows the yearly tuition (in $1,000s) of a sample of private colleges. Yearly Tuition 12 - 16 17 - 21 22 - 26 27 - 31 Frequency 5 4 3 2 For the above data, compute the mean yearly tuition. (Give your answer in dollars.) ANS: $19,714.29 PTS: 1 TOP: Descriptive Statistics 38. 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) 5 7 9 12 10 13 16 16 a. Unit Price (x) 2 4 8 5 7 8 16 6 Compute and interpret the sample covariance for the above data. b. c. d. Compute the standard deviation for the daily supply. Compute the standard deviation for the unit price. Compute and interpret the sample correlation coefficient. ANS: a. b. c. d. 11.43 (rounded). The covariance is positive. Therefore, there is a positive relationship between x and y. 4 4.175 0.6844. There is a fairly strong positive relationship between x and y. PTS: 1 TOP: Descriptive Statistics 39. The yearly incomes of the top highest paying professions in the United States are shown below. Yearly Income (in $1,000) 136 132 130 126 116 114 110 110 107 99 Profession Surgeons Obstetricians Anesthesiologists Internists Pediatricians Psychiatrists Dentists General Practitioners Chief Executives Airline Pilots For the above sample, determine the following measures (Give your answer in dollars). a. b. c. d. The mean yearly salary The standard deviation The median The mode ANS: a. b. c. d. $118,000 $12,283.68 $115,000 $110,000 PTS: 1 TOP: Descriptive Statistics 40. The population change between 2000 and 2010 for several small cities are shown below. City Chattanooga Collegedale East Ridge Lakeside Population Change (number of residents) 3083 1466 -461 1113 Ridgeside Signal Mountain Soddy-Daisy Walden -11 395 3290 437 For the above sample, determine the following measures. a. b. c. The mean The standard deviation The median ANS: a. b. c. 1,164 1,385.51 775 PTS: 1 TOP: Descriptive Statistics 41. The Michael Painting Company has purchased paint from several suppliers. The purchase price per gallon and the number of gallons purchased are shown below. Supplier A B C D Price Per Gallon ($) 23 25 29 27 Number of Gallons 700 200 100 200 Compute the weighted average price per gallon. ANS: $24.50 PTS: 1 TOP: Descriptive Statistics 42. 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? ANS: The coefficient of variation in 2009 = 16%. The coefficient of variation in 2010= 15%. Therefore, 2005 had a more dispersed distribution. PTS: 1 TOP: Descriptive Statistics 43. The following frequency distribution shows the starting salaries (in $1,000s) of a sample of business students: Starting Salary 22 - 26 27 - 31 32 - 36 Frequency 3 5 8 37 - 41 4 For the above data, compute the mean starting salary: (Give your answer in dollars.) ANS: $32,250 PTS: 1 TOP: Descriptive Statistics 44. In the last month, Nancy purchased gasoline from four different gas stations. The following table shows the price per gallon and the gallons of gasoline that she purchased. Gas Station Texaco Mobil BP Shell Gallons Purchased 20 8 18 12 Price per Gallon ($) 3.95 3.10 4.80 3.99 Determine the average price per gallon that Nancy paid for the gasoline. ANS: $4.10 (rounded) PTS: 1 TOP: Descriptive Statistics 45. 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. ANS: Mean = 14.8 Median = 16 Mode = 17 PTS: 1 TOP: Descriptive Statistics 46. Global Engineers hired the following number of Class 1 engineers during the first six months of the past year. (Assume the data represent a sample.) Month January February March April May June a. b. No. of Class 1 Engineers Hired 3 2 4 2 6 0 Determine the mean, the median, the mode, and the range for the above data. Compute the variance and the standard deviation. c. d. Compute the first and the third quartiles. Compute the z-scores for the months of May and June. ANS: a. Mean = 2.833 Median = 2.5 Mode = 2.0 b. S2 = 4.166 S = 2.041 c. First quartile = 2 Third quartile = 4 d. Z-score for May = 1.55 (rounded) Z-score for June = -1.39 (rounded) PTS: 1 Range = 6 TOP: Descriptive Statistics 47. 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. b. 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: First, compute the Z-score.) ANS: a. 96% b. 75 (1.826)(5) = 65.87 to 84.13 PTS: 1 TOP: Descriptive Statistics 48. 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. c. 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 batteries. (Hint: First compute the Z-score.) ANS: a. 56% b. 75% c. 60 + (2.236)(4). This indicates that at least 80% of the batteries will have lives of 51.056 to 68.944 hours. PTS: 1 TOP: Descriptive Statistics 49. Consider a sample with the following data values. 462 490 350 294 574 Compute the Z scores for the above five observations. ANS: Mean = 434 Standard Deviation = 112 X Z-Score 462 0.25 490 0.5 350 -0.75 294 -1.25 574 1.25 PTS: 1 TOP: Descriptive Statistics 50. The standard deviation of a sample was reported to be 7. The report indicated that What has been the sample size? = 980. ANS: 21 PTS: 1 TOP: Descriptive Statistics 51. The variance of a sample was reported to be 81. The report indicated that has been the sample size? = 972. What ANS: 13 PTS: 1 TOP: Descriptive Statistics 52. The following data show the yearly salaries of a sample of EMBA graduates. EMBA Student A B C D E F G H a. b. c. Salary (in $1,000) 88 97 90 110 114 98 92 95 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 you have determined indicates. ANS: a. b. c. $98,000 $9,355.03 $104,000 Seventy percent of the observations are less than or equal to this value. PTS: 1 TOP: Descriptive Statistics 53. Descriptive statistics for the closing stock prices of two companies for several trading periods are shown below. Baba, Inc. Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count a. b. Maman, Inc. 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. Compare the Skewness of the two and explain what is indicated. ANS: a. Coefficient of variation for Baba, Inc = 27.97% Coefficient of variation for Maman, Inc. = 14.25% Therefore, Baba, Inc. shows a more dispersed stock price distribution. b. Baba, Inc.’s price is skewed to the right (+ 0.04) and Maman, Inc.’s price is skewed to the left (-2.85). PTS: 1 TOP: Descriptive Statistics 54. 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 1 5 9 3 2 For the above data, compute the mean GMAT score. ANS: 550 PTS: 1 TOP: Descriptive Statistics 55. The last semester grades of Nancy, a freshman at a local college are shown below. Course Credit Hours Grades Physics 4 C Calculus 6 A Biology 3 B Music 2 F 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 Nancy’s semester grade point average. ANS: 2.8125 PTS: 1 TOP: Descriptive Statistics 56. The following data show the yearly salaries of a sample of MBA graduates. MBA Student A B C D E F G H a. b. c. Salary (in $1,000) 78 87 80 100 104 88 82 85 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 you have determined indicates. ANS: a. $88,000 b. $9,355.03 c. PTS: 1 $94,000 Seventy percent of the observations are les TOP: Descriptive Statistics 57. Descriptive statistics for the closing stock prices of two companies for several trading periods are shown below. Baba, Inc Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count a. b. 4.00 0.11 3.92 4.19 1.12 1.25 -1.15 0.08 3.95 2.03 5.98 436.32 109 Maman, Inc. Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 15.91 0.29 16.59 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. Compare the Skewness' of the two and explain what is indicated. ANS: a. Coefficient of variation for Baba, Inc = 28% Coefficient of variation for Maman, Inc. = 20.18% Therefore, Baba, Inc. shows a more dispersed stock price distribution. b. Baba, Inc’s price is skewed to the right (+ 0.08) and Maman, Inc’s price is skewed to the left (2.09). PTS: 1 TOP: Descriptive Statistics 58. 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. ANS: 546 PTS: 1 TOP: Descriptive Statistics 59. Last semester grades of Michael, a freshman at a local college are shown below. Course Credit Hours Grades Chemistry 5 C Calculus 5 A English 4 C Music 3 F 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 Michael’s semester grade point average. ANS: 2.33 PTS: 1 TOP: Descriptive Statistics 60. A recent survey of a local neighborhood measured the number of children per household. The results are given below. Household 1 2 3 4 5 6 7 8 9 Children 2 0 1 6 2 2 3 1 2 For the above data compute the following measures. (Round to the nearest tenth, as needed.) a. b. c. The mean Then median The mode ANS: a. 2.1 b. 2 c. 2 PTS: 1 TOP: Descriptive Statistics 61. 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 c. If we consider professor A’s enrollment as an outlier, compute the variance and the standard deviations, excluding Professor A’s class. (Round to the nearest hundredth, as needed.) ANS: a. 1461.47 b. 38.23 c. 32.7 PTS: 1 TOP: Descriptive Statistics 62. Below you are given a sample of ACT scores of 12 college applicants. 19 a. b. c. 23 27 21 32 17 20 29 22 30 25 15 Determine the first quartile. Determine the 75th percentile. Determine the interquartile range. ANS: a. 19.5 (average of 19 and 20) b. 28 (average of 27 and 29) c. 8.5 PTS: 1 TOP: Descriptive Statistics 63. 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. b. c. The mean The standard deviation The 65th percentile (Round to the nearest hundredth, as needed.) ANS: a. 88 b. 7.46 c. 91 PTS: 1 TOP: Descriptive Statistics Score 83 91 79 99 88 81 95 64. Aubree, a college freshman, took 15 hours her first semester. Below is her grade report. Class Physics Biology Statistics Seminar Macroeconomics Credit Hours 4 4 3 1 3 Grade D B B A A Aubree’s university uses a 4-point grading system, i.e., A=4, B=3, C=2, D=1, F=0. a. b. 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 hundredth.) ANS: a. 2.73 b. 3.27 PTS: 1 TOP: Descriptive Statistics 65. 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. b. Compute the geometric mean. What has been the percentage growth in the population of the city between 2009 to 2012? ANS: a.. Geometric Mean = 1.088808 b. 8.88% PTS: 1 TOP: Descriptive Statistics