ch01test

Chapter 1 Introduction and Descriptive StatisticsTrue/False Questions 1. A population is a subset of measurements taken from a large group. Answer: False Type: Concept Difficulty: Easy 2. It is assumed that a sample contains all measurements in which the researcher is interested. Answer: True Type: Concept Difficulty: Medium 3. The first quartile is the 50th percentile. Answer: False Type: Concept Difficulty: Easy 4. The median is the value that occurs most often in a sample of data. Answer: False Type: Concept Difficulty: Easy 5. The interquartile range is the difference between the first and the third quartiles. Answer: True Type: Concept Difficulty: Easy 6. The arithmetic mean assumes an interval level of measurement. Answer: True Type: Concept Difficulty: Medium 7. The mean, median, and the mode will all be equal when the distribution is symmetric. Answer: True Type: Concept Difficulty: Easy 8. The Empirical Rule holds for any set of data, regardless of its shape. Answer: False Type: Concept Difficulty: Easy 9. Chebyshev's Theorem states that at least 8/9 of the observations in a set will lie within 3 standard deviations of the mean. Answer: True Type: Concept Difficulty: Medium 10. The measure of the degree of asymmetry of a distribution is called kurtosis. Answer: False Type: Concept Difficulty: Medium

Aczel, Complete Business Statistics, Sixth Edition

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Chapter 1 Introduction and Descriptive Statistics11. Comparing the high temperature in Alaska this month, with the high temperature a year ago, is an example of using the interval scale of measurement. Answer: True Type: Concept Difficulty: Medium 12. A record of the numbers of models of each of five models of cars sold by a dealership during the past 18 months is an example of ordinal data. Answer: False Type: Concept Difficulty: Easy 13. The mean is more sensitive to skewness than the median. Answer: False Type: Concept Difficulty: Medium 14. Standard deviation is the square root of variance. Answer: True Type: Concept Difficulty: Easy Multiple Choice Questions 15. Classifying students in a statistics course by their gender is an example of what scale of measurement? A) Nominal B) Ordinal C) Interval D) Ratio Answer: A Type: Concept Difficulty: Medium 16. A distribution that is relatively flat and wide is said to be: A) skewed to the right B) symmetric C) platykurtic D) kurtosis E) none of the above Answer: C Type: Concept Difficulty: Easy

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Chapter 1 Introduction and Descriptive Statistics17. The following are the grades a professor gave on the first test in a statistics class: 52, 90, 88, 61, 75, 82, 75, 83, 88, and 86. What was the median score on this test? A) 82 B) 82.5 C) 78.5 D) 88 E) 75 Answer: B Type: Computation Difficulty: Easy 18. A clothes store manager has sales data of trouser sizes for the last month's sales. Which measure of central tendency should the manager use, if the manager is interested in the most sellable size? A) mean B) median C) mode D) standard deviation E) interquartile range Answer: C Type: Concept Difficulty: Medium 19. When do the mean, median and the mode have approximately the same value? A) always B) never C) in all symmetric distributions D) only in symmetric discrete distributions E) when the standard deviation is very small Answer: D Type: Concept Difficulty: Medium 20. The average monthly high temperatures for the past seven months are: 68, 72, 44, 50, 45, and 60. What is the mode? A) 72 B) 50 C) 44 D) 45 E) there is no mode for this data set Answer: E Type: Concept Difficulty: Easy


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Chapter 1 Introduction and Descriptive Statistics21. The mean weight of three gemstones is 20 grams. The weights of two of the stones are 15 grams and 17 grams. What is the weight of the third stone? A) 16 grams B) 10 grams C) 28 grams D) 14 grams E) not enough information to determine the weight of the third stone Answer: C Type: Computation Difficulty: Medium 22. A market research company has collected data on the price of a particular brand of soap in several different locations. The prices are as follows: $0.89, 0.95, 1.25, 1.36, 1.49, 1.65, 1.79, 1.89, 1.99. What are the upper and lower quartiles of soap prices for this brand? A) 1.72, 1.17 B) 1.84, 1.17 C) 1.72, 1.10 D) 2.21, 0.74 E) 1.84, 1.10 Answer: E Type: Computation Difficulty: Medium 23. In a survey conducted among the employees of a local bank, it is found that the following are the number of children each employee has: 1, 0, 2, 2, 0, 1, 0, 1, 4, 3, 6, 4, 2, 0, 1, and 3. What is the mean number of children for these employees? A) 2.5 B) 1.875 C) 1.5 D) 2.0 E) 6.0 Answer: B Type: Computation Difficulty: Easy

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Chapter 1 Introduction and Descriptive StatisticsUse the following to answer questions 24-25: The inventory manager at a computer components store randomly selected the records of 200 hard-drive upgrades from the last six months and observed that upgrades fell into the following capacity categories:C a p a c ) i t y F ( r Ge q B u 2 0 1 0 4 0 8 0 6 0 6 0 8 0 2 0 1 0 0 3 0 e n c y

24. In this instance, hard-drive capacity is an example of a(n) ____________ scale of measurement. A) Continuous B) Discrete C) Nominal D) Ordinal E) Probabilistic Answer: B Type: Concept Difficulty: Easy 25. Based on the inventory manager's sample, the average hard-drive upgrade is for approximately ______ gigabytes; the modal hard-drive upgrade is for ______ gigabytes. A) 60; 40 B) 40; 60 C) 80; 40 D) 80; 60 E) 60; 100 Answer: A Type: Computation Difficulty: Medium


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Chapter 1 Introduction and Descriptive StatisticsUse the following to answer questions 26-27: A census is done in a given region. Following are the populations of the towns in that particular region (in thousands): 35, 46, 52, 63, 64, 71, 77, 82, and 94. 26. What is the median of this data? A) 64 B) 63.5 C) 67.5 D) 59 E) 35 Answer: A Type: Computation Difficulty: Easy 27. Which of the following is closest to the 30th percentile for these data? A) 57.5 B) 63 C) 52.7 D) 53 E) 52 Answer: E Type: Computation Difficulty: Medium 28. Several friends go to a casino and do some gambling. The following are the profits each of these friends make: $120, -$230, $670, -$1020, $250, -$430, and -$60. What is the average profit of this group? A) $100 B) -$100 C) -$1020 D) $397 E) -$397 Answer: B Type: Computation Difficulty: Medium

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Chapter 1 Introduction and Descriptive StatisticsUse the following to answer questions 29-30: The number of bottles filled each day in a bottling plant is observed for a week: 674, 589, 613, 689, 554, 586, and 594. 29. Consider the data given above and find the mean. A) 585 B) 670 C) 586.29 D) 614.14 E) none of the above Answer: D Type: Computation Difficulty: Easy 30. Consider the sample data given above and find the standard deviation. A) 24 B) 45.72 C) 49.39 D) 2090.69 E) 2439.14 Answer: C Type: Computation Difficulty: Medium 31. The mean temperature in three rooms is 69.3 degrees Fahrenheit. If a fourth room is found to have a temperature of 71 degrees, what is the mean of the temperature of the four rooms? A) 69.3 B) 70.15 C) 70.325 D) 69.725 E) none of the above Answer: D Type: Computation Difficulty: Medium


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Chapter 1 Introduction and Descriptive StatisticsUse the following to answer questions 32-33: The numbers that follow are the incomes of professors in a particular college (in thousands of dollars): 25, 28, 30, 32, 38, 45, 53, 54, 54, 56, 61, 63, 64, 67, 71, 74, 82, 85, 97, and 99. 32. Find both the mean, and the mode for these values. A) mean = 57, mode = 54 B) mean = 48.11, mode = 57.5 C) mean = 58.9, mode = 54 D) mean = 58.9, mode = 58.5 E) mean = 58.5, mode = 62 Answer: C Type: Computation Difficulty: Medium 33. What is the median income for this group of professors? A) 56 B) 58.33 C) 58.5 D) 54 E) none of the above Answer: C Type: Computation Difficulty: Easy 34. The following numbers represent the electricity bill each house in a particular area received in the past month: $64, 79, 92, 101, 113, 115, 129, 135, 138, 143, 146, 158, 163, 165, 168, 173, 174, 177, 181, 184, 187, 189, 190, 193, 196, 200, 205, 218, 231, 249, and 278. Which of the following is closest to the 60th percentile for these values? A) 190.2 B) 179.4 C) 181.8 D) 182.5 E) 177 Answer: B Type: Computation Difficulty: Medium

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Chapter 1 Introduction and Descriptive Statistics35. A class of business students received the following test scores on a standardized test: 320, 410, 440, 470, 480, 480, 490, 500, 500, 510, 510, 530, 530, 530, 540, 570, 600, 650, 720, and 790. How many students in this group received a score that was greater than the 75th percentile of this group? A) 56 B) 5 C) 563 D) 15 E) not enough information to answer Answer: B Type: Computation Difficulty: Medium 36. When is the median equal to the 50th percentile in a data set? A) always B) never C) only when the mean and the median are equal D) only in a symmetric distribution E) only in a skewed distribution Answer: A Type: Concept Difficulty: Easy 37. Find the variance of the following set of values: 2, 5, 8, 6, and 1. A) 2.88 B) 4.4 C) 8.3 D) 7 E) 5 Answer: C Type: Computation Difficulty: Medium 38. A salesperson sells the following number of air-conditioners each month, throughout the year: 3, 5, 5, 6, 12, 17, 14, 9, 4, 2, 1, 1. Find both the mean and the median number of air-conditioners this salesperson sold. A) mean = 5.48, median = 7.12 B) mean = 4.5, median = 5 C) mean = 5, median = 5.5 D) mean = 6.43, median = 15.5 E) mean = 6.583, median = 5 Answer: E Type: Computation Difficulty: Medium


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Chapter 1 Introduction and Descriptive Statistics39. Compute the coefficient of variation, if the mean of the set of data is 16 and the variance is 25. A) 0.8 B) 0.3125 C) 1.25 D) 1.5625 E) 0.4 Answer: B Type: Computation Difficulty: Medium 40. Compute the geometric mean for: 8, 5 and 3. A) 4.93 B) 10.95 C) 5.333 D) 5.00 E) 2.5198 Answer: A Type: Computation Difficulty: Medium 41. If a given distribution is known to be symmetric, what percent of the observations are expected to fall within two standard deviations of the mean? A) 68% B) 75% C) 89% D) 95% E) almost all Answer: D Type: Concept Difficulty: Easy 42. A measure of the degree of asymmetry of a frequency distribution is called? A) kurtosis B) skewness C) coefficient of variation D) standard deviation E) ogive Answer: B Type: Concept Difficulty: Medium

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Chapter 1 Introduction and Descriptive Statistics43. In which type of scale are numbers used as labels for different classes? A) nominal B) ordinal C) interval D) ratio E) mean Answer: A Type: Concept Difficulty: Medium 44. Which of the following scales is the strongest type of scale of measurement? A) nominal B) ordinal C) interval D) ratio E) mean Answer: D Type: Concept Difficulty: Medium 45. A survey in which customers taste five different brands of ice cream, and rank their favorites from 1 to 5, would be an example of which type of scale of measurement? A) nominal B) ordinal C) interval D) ratio E) mean Answer: B Type: Concept Difficulty: Medium 46. Which of the following is the graph drawn by connecting the midpoints of the classes of a frequency distribution? A) ogive B) pie chart C) histogram D) frequency polygon E) bar chart Answer: D Type: Concept Difficulty: Easy


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Chapter 1 Introduction and Descriptive Statistics47. The graph of a cumulative frequency distribution is called? A) ogive B) pie chart C) frequency polygon D) histogram E) bar chart Answer: A Type: Concept Difficulty: Easy 48. What is the difference between the variance and standard deviation of a distribution? A) Variance is used with ordinal data and standard deviation with interval data. B) Standard deviation is used with ordinal data and variance deviation with interval data. C) Standard deviation is the positive square of variance. D) Standard deviation is the square root of variance. E) They are basically the same thing. Answer: D Type: Concept Difficulty: Easy 49. What measure of central tendency is most sensitive to skewness? A) Mode B) Median C) Mean D) They are all about the same E) Median and Mean Answer: C Type: Concept Difficulty: Easy 50. What measure of central tendency would be most appropriate for a measurement of salaries if the salaries are normally distributed? A) Mean B) Median C) Mode D) All three; it would depend on your situation Answer: A Type: Concept Difficulty: Medium

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Chapter 1 Introduction and Descriptive Statistics51. What measure of central tendency would be most appropriate for a measurement of salaries when there are a few people in the sample who make over one million dollars, but most of the employees sampled made under $50,000? A) Mean B) Median C) Mode D) All three; it would depend on your situation Answer: B Type: Concept Difficulty: Medium Use the following to answer questions 52-55: A copier services company is considering adding an advanced model to its product line but is concerned about excessive maintenance calls. During a trial introduction in a test market, maintenance personnel recorded X, the number of service visits required to get a particular copier up and running to the customer's satisfaction. These data are summarized in the following table: X 1 2 3 4 5 F r e q 2 0 2 2 0 1 0 5 5 0 5 ( X )

52. Which of the following terms best describes the distribution of required service visits? A) Right-skewed B) Left-skewed C) Symmetrically abnormal D) Upwardly-kurtotic E) Downwardly-kurtotic Answer: A Type: Concept Difficulty: Easy 53. In total, how many service visits were made by maintenance personnel during the trial introduction of this copier? A) 5 B) 11 C) 400 D) 1000 E) None of the above Answer: D Type: Computation Difficulty: Easy


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Chapter 1 Introduction and Descriptive Statistics54. How many copiers were distributed as part of this trial introduction? A) 5 B) 11 C) 400 D) 1000 E) None of the above Answer: C Type: Computation Difficulty: Medium 55. What is the average number of service visits required per copier? A) 1.25 B) 2.50 C) 3.00 D) 5.00 E) None of the above Answer: B Type: Computation Difficulty: Medium Use the following to answer questions 56-57: In a study of its reservation patterns, a national hotel chain randomly sampled the records of 20 of its locations and recorded the number of days last year when the locations had no rooms available: 165, 126, 59, 47, 146, 64, 39, 75, 86, 114, 51, 68, 58, 38, 66, 72, 42, 85, 40, 59 56. The hotel chain's head of market research has concluded that the sample average would be a relatively poor indicator of the population's central tendency in this instance. She based this conclusion on the substantial ______________ exhibited in the sample; in such a case, the sample mean would tend to ______________ the population's central tendency. A) Right skew; overstate B) Right skew; understate C) Left skew; overstate D) Left skew; understate E) Variance; underestimate Answer: A Type: Computation Difficulty: Hard

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Chapter 1 Introduction and Descriptive Statistics57. Given the data in the above sample, which of the following mean/median pairs is correct? A) Sample mean = 65; sample median = 75 B) Sample mean = 65; sample median = 65 C) Sample mean = 75; sample median = 65 D) Sample mean = 75; sample median = 75 E) None of the above Answer: C Type: Computation Difficulty: Hard 58. The average amount of time required to fill orders at a drive-up window has been observed to be 120 seconds, with a standard deviation of 10 seconds. Assuming that the required order-fill time follows a symmetric, bell-shaped distribution, which of the following statements is correct regarding a random sample of 1,000 observations? A) We would expect to see approximately 680 of the order fill-times falling in the interval from 110 seconds to 120 seconds B) We would expect to see approximately 955 of the order fill-times falling in the interval from 100 seconds to 140 seconds C) We would expect to see approximately 27 orders with required fill-times of less than 90 seconds D) We would expect to see approximately 27 orders with required fill-times in excess of 150 seconds E) All of the above are correct Answer: B Type: Computation Difficulty: Medium


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Chapter 1 Introduction and Descriptive Statistics59. Suppose men and women are equally in favor of an upcoming property tax initiative. If, in a random sample of 600 men and 400 women, 240 men were observed to be in favor of the initiative, which of the following charts is most likely representative of what was observed?400 350 300 250Women 50% Men 50%

360

240

200 150 100 50 0 Men Women

A)

B)45%Other 20% Men 40%

40% 35% 30% 25% 20% 15% 10%

Favor

Favor

Women 40%

5% 0% Men Women

C)

D)

Oppose 40% Favor 60%

E) Answer: D Type: Computation Difficulty: Medium

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Chapter 1 Introduction and Descriptive StatisticsShort Answer Questions 60. The difference between the largest value in a data set and the smallest value is called the _________________. Answer: range Type: Concept Difficulty: Easy 61. The standard deviation is always the square root of the __________________. Answer: variance Type: Concept Difficulty: Easy

62. The number of values in a class divided by the total number of values in the sample is called the ________________. Answer: relative frequency Type: Concept Difficulty: Easy

63. The value that occurs most frequently in a data set is called the ________________. Answer: mode Type: Concept Difficulty: Easy Use the following to answer questions 64-65: A test was conducted to find the number of hours a particular brand of battery lasts. Refer to the data given below: 200, 204, 197, 191, 203, 198, 216, 210, 202, 204, 198, 203, 181, 205, 194, and 194. 64. Find the mean hours of operation of the battery. Answer: 200 Type: Computation Difficulty: Medium

65. Find the standard deviation of hours of operation of the battery. Answer: 8.025 Type: Computation Difficulty: Hard

66. What is the mean if the highest and the lowest data are both removed from the set, to remove any extraordinary battery data? Answer: 200.2 Type: Computation Difficulty: Medium


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Chapter 1 Introduction and Descriptive Statistics67. In a dormitory, the following is the number of hours the radio plays each day, in each room: 3.0, 2.4, 3.7, 6.7, 10.6, 1.1, 0.3, 7.4, 8.0, 7.3, 4.5, 3.6, 2.7, 2.4, 3.1, and 1.9. Find both the median number of hours and the mode for the number of hours the radio is played in these rooms. Answer: median = 3.35; mode = 2.4 Type: Computation Difficulty: Medium

68. Compute the coefficient of variation for a data set with a mean of 100 and a variance of 25. Answer: .05 Type: Computation Difficulty: Medium

69. The measure of central tendency that is equal to the 50th percentile is called the ______________. Answer: median Type: Concept Difficulty: Easy

70. What percent of values will be within 2 standard deviations of the mean, in a distribution which is mound-shaped? Answer: 95% Type: Concept Difficulty: Medium

71. Classifications based on political preference would be an example of which type of measurement scale? Answer: nominal Type: Concept Difficulty: Easy

72. The difference between the third and first quartile is called the _______________. Answer: interquartile range Type: Concept Difficulty: Easy

73. The set of all measurements or observations of interest to the statistician is called ______________. Answer: population Type: Concept Difficulty: Easy

Use the following to answer questions 74-75: A machine in a ketchup bottling plant is designed to dispense an average of 12 ounces per bottle, with a variance of 0.5 ounces.

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Chapter 1 Introduction and Descriptive Statistics74. If the machine is operating as designed, and if the distribution of amounts dispensed is relatively symmetric and mound-shaped, what is the proportion of bottles that can be expected to contain between 11.5 and 12.5 ounces? Answer: About 68% Type: Computation Difficulty: Medium

75. If the machine is operating as designed, but the distribution of amounts dispensed is not relatively symmetric or mound-shaped, what is the proportion of bottles that can be expected to contain between 11 and 12 ounces? Answer: At least 75% Type: Computation Difficulty: Medium

Use the following to answer questions 76-77: The following are the valuations (in thousands of dollars) of 16 randomly selected properties sold during the past year in Acmeville: 130 110 130 130 120 140 120 110 150 150 130 140 130 130 120 140 76. Construct a stem-and-leaf diagram of these data. Answer: 11 12 13 14 15 00 000 000000 000 00

Type: Concept Difficulty: Medium 77. Briefly describe the shape of the distribution: ___________________. Answer: Symmetric and mound-shaped Type: Concept Difficulty: Easy


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Chapter 1 Introduction and Descriptive Statistics78. A machine in a ketchup bottling plant is designed to dispense an average of 12 ounces per bottle, with a variance of 0.5 ounces. Find the mean, median, and mode of these data: Mean: _______ Median: _______ Mode: _______ Answer: Mean: 130; Median: 130, Mode: 130 Use the following to answer questions 79-81: The following are the valuations (in thousands of dollars) of 16 randomly selected properties sold during the past year in Acmeville: 130 110 130 130 120 140 120 110 150 150 130 140 130 130 120 140 79. Find the variance and standard deviation of the distribution: Variance: ______ Standard Deviation: _______ Answer: Variance: 146.67; Standard Deviation: 12.11 Difficulty: Medium Type: Concept Type: Concept Difficulty: Medium

80. Based on Chebyshev's theorem, what range would you say should include at least 75% of property valuations? Answer: [105.78,154.22] Type: Concept Difficulty: Hard

81. Based on the empirical rule, what range of valuations would you say should include 95% of property valuations? Answer: [105.78,154.22] Type: Concept Difficulty: Hard

82. You are interested in forming a company running team, however only 10 of your colleagues consent to your crazy idea and their 10K times in minutes are as follows: 64, 47, 60, 54, 57, 39, 45, 62, 61, and 55. What is their mean running time and what is their standard deviation? Answer: Mean = 54.4; Standard Deviation = 7.83 Difficulty: Medium Type: Computation

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Chapter 1 Introduction and Descriptive Statistics83. A quality control consultant randomly sampled 300 bottles from a bottle-filling process and observed a sample average of 50 ml with a standard deviation of 5 ml. Because the consultant observed that none of the bottles sampled had less than 35 ml or more than 65 ml, he concluded that the bottle-filling operation followed a symmetrical, bell-shaped (i.e., normal) distribution. What else would be required for the consultant to make such a conclusion with confidence? Answer: The consultant should also see: 1) approximately 68% (about 204) of the observations falling within the interval 45 ml to 55 ml; and 2) approximately 95% (about 285) of the observations falling within the interval 40 ml to 60 ml. Type: Computation Difficulty: Medium 84. Alan and Karen are moving to a new area of the country and are searching for a new home with the help of Cecilia, a local real estate agent. Prior to their first meeting with Cecilia, Alan and Karen conducted an internet search of homes for sale in their new location and found that home prices in their random sample averaged $380,000. When they asked Cecilia what they should expect to pay for a typical home in their new location, however, Cecilia told them that half of all homes sold for less than $300,000. Assuming that both values were correct and accurately reflected the market, what would be the most likely explanation of such a discrepancy? Answer: Alan and Karen calculated a sample average that was pulled upward by the presence of a few very high-priced homes in the market. Cecilia quoted the median home to avoid overstating the central tendency given the right skew of home prices in this market. Type: Concept Difficulty: Easy Use the following to answer questions 85-86: Mike and Susan recently won a late-model sports car in a sweepstakes drawing. Not wanting the car for themselves, they decided to sell it. An internet car lot shows 20 recent sales of similar cars, with the following final selling prices: 4050, 3750, 3100, 4540, 1800, 4400, 3995, 3670, 3900, 5000 3730, 4130, 4005, 2100, 4120, 4200, 4540, 3775, 3700, 4180 85. Suppose Mike and Susan want a quick sale. What should their approximate price be if they are willing to let their car go at approximately the 10th percentile? Answer: They should price their car at approximately $2,100 Difficulty: Medium Type: Computation


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Chapter 1 Introduction and Descriptive Statistics86. Now suppose Mike and Susan would like their car's sale price to reflect the central tendency of the population of similar cars that are sold. Is there anything exhibited by these data that might make the median preferable to the mean with respect to setting a final sale price? Answer: These data exhibit a strong left skew due to the prices of the three cheapest cars. Thus, the mean of $3,834 is downwardly biased and the median price of $4,000 might be a better estimate. Type: Computation Difficulty: Medium

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