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74 Numerical Descriptive Measures

CHAPTER 3: NUMERICAL DESCRIPTIVE MEASURES

1. Which of the following statistics is not a measure of central tendency?

a) Arithmetic mean. b) Median. c) Mode. d) Q3.

ANSWER: d

TYPE: MC DIFFICULTY: Easy

KEYWORDS: measure of central tendency, arithmetic mean, median, mode, quartiles

2. Which measure of central tendency can be used for both numerical and categorical variables?

a) Arithmetic mean. b) Median. c) Mode.

d) Standard deviation.

ANSWER: c

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: measure of central tendency, mode, arithmetic mean, median

3. Which of the arithmetic mean, median, and mode are resistant measures of central tendency?

a) The arithmetic mean and median only. b) The median and mode only.

c) The mode and arithmetic mean only. d) All the three are resistant measures.

ANSWER: b

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: measure of central tendency, resistant to outliers, mean, median, mode

4. In a right-skewed distribution

a) the median equals the arithmetic mean. b) the median is less than the arithmetic mean. c) the median is larger than the arithmetic mean. d) none of the above.

ANSWER: b

TYPE: MC DIFFICULTY: Easy KEYWORDS: shape

Numerical Descriptive Measures 75

5. Which of the following statements about the median is not true?

a) It is more affected by extreme values than the arithmetic mean. b) It is a measure of central tendency. c) It is equal to Q2.

d) It is equal to the mode in bell-shaped \

ANSWER: a

TYPE: MC DIFFICULTY: Easy

KEYWORDS: median, measure of central tendency, resistant to outliers, quartile

6. In a perfectly symmetrical bell-shaped \

a) the arithmetic mean equals the median. b) the median equals the mode.

c) the arithmetic mean equals the mode. d) All the above.

ANSWER: d

TYPE: MC DIFFICULTY: Easy

KEYWORDS: shape, normal distribution

7. In a perfectly symmetrical distribution

a) the range equals the interquartile range.

b) the interquartile range equals the arithmetic mean. c) the median equals the arithmetic mean. d) the variance equals the standard deviation.

ANSWER: c

TYPE: MC DIFFICULTY: Easy KEYWORDS: shape

8. When extreme values are present in a set of data, which of the following descriptive summary

measures are most appropriate:

a) CV and range.

b) arithmetic mean and standard deviation. c) interquartile range and median. d) variance and interquartile range.

ANSWER: c

TYPE: MC DIFFICULTY: Easy

KEYWORDS: resistant to outliers, coefficient of variation, range, arithmetic mean, standard deviation, interquartile range, median, variance

76 Numerical Descriptive Measures

9. In general, which of the following descriptive summary measures cannot be easily approximated

from a boxplot?

a) The variance. b) The range.

c) The interquartile range. d) The median.

ANSWER: a

TYPE: MC DIFFICULTY: Easy

KEYWORDS: boxplot, variance, range, interquartile range, median

10. The smaller the spread of scores around the arithmetic mean,

a) the smaller the interquartile range. b) the smaller the standard deviation. c) the smaller the coefficient of variation. d) All the above.

ANSWER: d

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: variation, arithmetic mean, interquartile range, standard deviation, coefficient of variation

11. Which descriptive summary measures are considered to be resistant statistics?

a) The arithmetic mean and standard deviation. b) The interquartile range and range. c) The mode and variance.

d) The median and interquartile range.

ANSWER: d

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: resistant to outliers, arithmetic mean, standard deviation, interquartile range, range, mode, variance, median

12. In right-skewed distributions, which of the following is the correct statement?

a) The distance from Q1 to Q2 is larger than the distance from Q2 to Q3. b) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3. c) The arithmetic mean is smaller than the median. d) The mode is larger than the arithmetic mean.

ANSWER: b

TYPE: MC DIFFICULTY: Easy

KEYWORDS: shape, quartiles, arithmetic mean, mode

Numerical Descriptive Measures 77

13. In perfectly symmetrical distributions, which of the following is NOT a correct statement?

a) The distance from Q1 to Q2 equals to the distance from Q2 to Q3.

b) The distance from the smallest observation to Q1 is the same as the distance from Q3 to

the largest observation.

c) The distance from the smallest observation to Q2 is the same as the distance from Q2 to

the largest observation.

d) The distance from Q1 to Q3 is half of the distance from the smallest to the largest

observation.

ANSWER: d

TYPE: MC DIFFICULTY: Easy

KEYWORDS: shape, quartiles, five-number summary, quartiles

14. In left-skewed distributions, which of the following is the correct statement?

a) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.

b) The distance from the smallest observation to Q1 is larger than the distance from Q3 to

the largest observation.

c) The distance from the smallest observation to Q2 is smaller than the distance from Q2 to

the largest observation.

d) The distance from Q1 to Q3 is twice the distance from the Q1 to Q2.

ANSWER: b

TYPE: MC DIFFICULTY: Easy

KEYWORDS: shape, quartiles, five-number summary, quartiles

15. According to the empirical rule, if the data form a \

percent of the observations will be contained within 2 standard deviations around the arithmetic mean.

a) 68.26 b) 88.89 c) 93.75 d) 95.44

ANSWER: d

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: empirical rule, normal distribution

16. According to the empirical rule, if the data form a \

percent of the observations will be contained within 1 standard deviation around the arithmetic mean.

a) 68.26 b) 75.00 c) 88.89 d) 93.75

ANSWER:

78 Numerical Descriptive Measures

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: empirical rule, normal distribution

17. According to the empirical rule, if the data form a \

percent of the observations will be contained within 3 standard deviations around the arithmetic mean.

a) 68.26 b) 75.00 c) 95.0 d) 99.7

ANSWER: d

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: empirical rule, normal distribution

18. Which of the following is NOT a measure of central tendency?

a) The arithmetic mean. b) The median. c) The mode.

d) The interquartile range.

ANSWER: d

TYPE: MC DIFFICULTY: Easy

KEYWORDS: measure of central tendency, arithmetic mean, median, mode, interquartile range

19. Which of the following is NOT sensitive to extreme values?

a) The range.

b) The standard deviation. c) The interquartile range. d) The coefficient of variation.

ANSWER: c

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: resistant to outliers, range, standard deviation, interquartile range, coefficient of variation

20. Which of the following is sensitive to extreme values?

a) The median.

b) The interquartile range. c) The arithmetic mean. d) The 1st quartile.

ANSWER: c

TYPE: MC DIFFICULTY: Moderate

KEYWORDS: resistant to outliers, median, interquartile range, arithmetic mean, quartiles

Numerical Descriptive Measures 79

21. Which of the following is the easiest to compute?

a) The arithmetic mean. b) The median. c) The mode.

d) The standard deviation.

ANSWER: c

TYPE: MC DIFFICULTY: Easy

KEYWORDS: mode, arithmetic mean, median

22. According to the Chebyshev rule, at least 75% of all observations in any data set are contained

within a distance of how many standard deviations around the mean?

a) 1 b) 2 c) 3 d) 4

ANSWER: b

TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule

23. According to the Chebyshev rule, at least 93.75% of all observations in any data set are

contained within a distance of how many standard deviations around the mean?

a) 1 b) 2 c) 3 d) 4

ANSWER: d

TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chebyshev rule

24. According to the Chebyshev rule, at least what percentage of the observations in any data set are

contained within a distance of 3 standard deviations around the mean?

a) 67% b) 75% c) 88.89% d) 99.7%

ANSWER: c

TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule

80 Numerical Descriptive Measures

25. According to the Chebyshev rule, at least what percentage of the observations in any data set are

contained within a distance of 2 standard deviations around the mean?

a) 67% b) 75% c) 88.89% d) 95%

ANSWER: b

TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule

TABLE 3-1

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 uninsured senior citizens were as follows:

60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

26. Referring to Table 3-1, calculate the arithmetic mean age of the uninsured senior citizens to the

nearest hundredth of a year.

ANSWER: 74.04 years

TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean

27. Referring to Table 3-1, identify the median age of the uninsured senior citizens.

ANSWER: 73 years

TYPE: PR DIFFICULTY: Easy KEYWORDS: median

28. Referring to Table 3-1, identify the first quartile of the ages of the uninsured senior citizens.

ANSWER: 65.5 years

TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartiles

29. Referring to Table 3-1, identify the third quartile of the ages of the uninsured senior citizens.

ANSWER: 81.5 years

TYPE: PR DIFFICULTY: Moderate

Numerical Descriptive Measures 81

KEYWORDS: quartiles

30. Referring to Table 3-1, identify the interquartile range of the ages of the uninsured senior citizens.

ANSWER: 16 years

TYPE: PR DIFFICULTY: Moderate KEYWORDS: interquartile range

31. Referring to Table 3-1, identify which of the following is the correct statement.

a) One fourth of the senior citizens sampled are below 65.5 years of age.

b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) The average age of senior citizens sampled is 73.5 years of age. d) All of the above are correct.

ANSWER: a

TYPE: MC DIFFICULTY: Moderate KEYWORDS: quartiles, arithmetic mean

32. Referring to Table 3-1, identify which of the following is the correct statement.

a) One fourth of the senior citizens sampled are below 64 years of age.

b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) 25% of the senior citizens sampled are older than 81.5 years of age. d) All of the above are correct.

ANSWER: c

TYPE: MC DIFFICULTY: Moderate KEYWORDS: quartiles

33. Referring to Table 3-1, what type of shape does the distribution of the sample appear to have?

ANSWER:

Slightly positive or right-skewed. TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape

34. Referring to Table 3-1, calculate the variance of the ages of the uninsured senior citizens correct

to the nearest hundredth of a year squared.

ANSWER: 94.96 years2

TYPE: PR DIFFICULTY: Moderate KEYWORDS: variance

35. Referring to Table 3-1, calculate the standard deviation of the ages of the uninsured senior

citizens correct to the nearest hundredth of a year.

82 Numerical Descriptive Measures

ANSWER: 9.74 years

TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard deviation

36. Referring to Table 3-1, calculate the coefficient of variation of the ages of the uninsured senior

citizens.

ANSWER: 13.16%

TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of variation

37. True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 1.9.

ANSWER: False

TYPE: TF DIFFICULTY: Moderate KEYWORDS: median

38. True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.

ANSWER: False

TYPE: TF DIFFICULTY: Moderate KEYWORDS: median

39. True or False: In a set of numerical data, the value for Q3 can never be smaller than the value for

Q1.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: quartiles

40. True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.

ANSWER: False

TYPE: TF DIFFICULTY: Easy KEYWORDS: quartiles

41. True or False: If the distribution of a data set were perfectly symmetrical, the distance from Q1 to

the median would always equal the distance from Q3 to the median in a boxplot.

ANSWER: True

TYPE: TF DIFFICULTY: Moderate KEYWORDS: boxplot, quartiles, shape

Numerical Descriptive Measures 83

42. True or False: In right-skewed distributions, the distance from Q3 to the largest observation

exceeds the distance from the smallest observation to Q1.

ANSWER: True

TYPE: TF DIFFICULTY: Moderate KEYWORDS: quartiles, shape

43. True or False: In left-skewed distributions, the distance from the smallest observation to Q1

exceeds the distance from Q3 to the largest observation.

ANSWER: True

TYPE: TF DIFFICULTY: Moderate KEYWORDS: quartiles, shape

44. True or False: A boxplot is a graphical representation of a 5-number summary.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: boxplot, five-number summary

45. True or False: The 5-number summary consists of the smallest observation, the first quartile, the

median, the third quartile, and the largest observation.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: five-number summary

46. True or False: In a boxplot, the box portion represents the data between the first and third

quartile values.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot

47. True or False: The line drawn within the box of the boxplot always represents the arithmetic

mean.

ANSWER: False

TYPE: TF DIFFICULTY: Easy

KEYWORDS: boxplot, arithmetic mean

48. True or False: The line drawn within the box of the boxplot always represents the median.

ANSWER: True

84 Numerical Descriptive Measures

TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot, median

49. True or False: In a sample of size 40, the sample mean is 15. In this case, the sum of all

observations in the sample is ?Xi = 600.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean

50. True or False: A population with 200 elements has an arithmetic mean of 10. From this

information, it can be shown that the population standard deviation is 15.

ANSWER: False

TYPE: TF DIFFICULTY: Easy

KEYWORDS: arithmetic mean, standard deviation

51. True or False: In exploratory data analysis, a boxplot can be used to illustrate the median,

quartiles, and extreme values.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: boxplot, five-number summary

52. True or False: An economics professor bases his final grade on homework, two midterm

examinations, and a final examination. The homework counts 10% toward the final grade, while each midterm examination counts 25%. The remaining portion consists of the final examination. If a student scored 95% in homework, 70% on the first midterm examination, 96% on the second midterm examination, and 72% on the final, his final average is 79.8%.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean

53. True or False: The median of a data set with 20 items would be the average of the 10th and the

11th items in the ordered array.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: median, arithmetic mean

Numerical Descriptive Measures 85

54. True or False: The coefficient of variation measures variability in a data set relative to the size of

the arithmetic mean.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: coefficient of variation

55. True or False: The coefficient of variation is expressed as a percentage.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: coefficient of variation

56. True or False: The coefficient of variation is a measure of central tendency in the data.

ANSWER: False

TYPE: TF DIFFICULTY: Easy

KEYWORDS: coefficient of variation, measure of variation

57. True or False: The interquartile range is a measure of variation or dispersion in a set of data.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: interquartile range, measure of variation

58. True or False: The interquartile range is a measure of central tendency in a set of data.

ANSWER: False

TYPE: TF DIFFICULTY: Easy

KEYWORDS: interquartile range, measure of variation

59. True or False: If a set of data is perfectly symmetrical, the arithmetic mean must be identical to

the median.

ANSWER: True

TYPE: TF DIFFICULTY: Easy

KEYWORDS: shape, arithmetic mean, median

60. True or False: The coefficient of variation is a measure of relative variation. ANSWER: True

TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of variation

86 Numerical Descriptive Measures

61. True or False: If the data set is approximately bell-shaped, the empirical rule will more

accurately reflect the greater concentration of data close to the mean as compared to the Chebyshev rule.

ANSWER: True

TYPE: TF DIFFICULTY: Moderate

KEYWORDS: empirical rule, Chebyshev rule, normal distribution

62. If the arithmetic mean of a numerical data set exceeds the median, the data are considered to be

_______ skewed.

ANSWER: positive or right

TYPE: FI DIFFICULTY: Easy

KEYWORDS: shape, arithmetic mean, median

TABLE 3-2

The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings.

11 15 23 29 19 22 21 20 15 25 17

63. Referring to Table 3-2, the arithmetic mean carbohydrates in this sample is ________ grams.

ANSWER: 217/11 = 19.73

TYPE: FI DIFFICULTY: Moderate KEYWORDS: arithmetic mean

64. Referring to Table 3-2, the median carbohydrate amount in the cereal is ________ grams.

ANSWER: 20

TYPE: FI DIFFICULTY: Moderate KEYWORDS: median

65. Referring to Table 3-2, the first quartile of the carbohydrate amounts is ________ grams.

ANSWER: 15

TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles

66. Referring to Table 3-2, the third quartile of the carbohydrate amounts is ________ grams.

ANSWER: 23

TYPE: FI DIFFICULTY: Moderate

Numerical Descriptive Measures 87

KEYWORDS: quartiles

67. Referring to Table 3-2, the range in the carbohydrate amounts is ________ grams.

ANSWER: 18

TYPE: FI DIFFICULTY: Easy KEYWORDS: range

68. Referring to Table 3-2, the interquartile range in the carbohydrate amounts is ________ grams.

ANSWER: 8

TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range

69. Referring to Table 3-2, the variance of the carbohydrate amounts is ________ (grams squared).

ANSWER: 26.02

TYPE: FI DIFFICULTY: Moderate KEYWORDS: variance

70. Referring to Table 3-2, the standard deviation of the carbohydrate amounts is ________ grams.

ANSWER: 5.10

TYPE: FI DIFFICULTY: Moderate KEYWORDS: standard deviation

71. Referring to Table 3-2, the coefficient of variation of the carbohydrate amounts is ________

percent.

ANSWER: 25.86%

TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation

72. Referring to Table 3-2, the five-number summary of the carbohydrate amounts consists of

________, ________, ________, ________, ________.

ANSWER:

11, 15, 20, 23, 29

TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary

88 Numerical Descriptive Measures

73. Referring to Table 3-2, construct a boxplot for the carbohydrate amounts.

Box-and-whisker Plot 1015202530ANSWER:

TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

74. Referring to Table 3-2, what type of shape does the distribution of the sample appear to have?

ANSWER:

Slightly positive or right-skewed. TYPE: PR DIFFICULTY: Moderate

EXPLANATION: The distribution is considered as slightly right-skewed because the length of the right whisker (6) is slighter longer than the length of the left whisker (4). The distribution could also be considered as slight left-skewed since the mean (19.73) is slightly lower than the median (20). KEYWORDS: shape

Numerical Descriptive Measures 89

TABLE 3-3

The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.

Stem Leaves 1H 99 2L 0023 2H 567 3L 034 3H 568 4L 1

Note (1): 1H means the “high teens” – 15, 16, 17, 18, or 19; 2L means the “low twenties” – 20, 21,

22, 23, or 24; 2H means the “high twenties” – 25, 26, 27, 28, or 29, etc.

Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

75. Referring to Table 3-3, the arithmetic mean of the number of vitamin supplements sold in this

sample is ________.

ANSWER: 28

TYPE: FI DIFFICULTY: Easy KEYWORDS: arithmetic mean

76. Referring to Table 3-3, the first quartile of the number of vitamin supplements sold in this

sample is ________.

ANSWER: 20

TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles

77. Referring to Table 3-3, the third quartile of the number of vitamin supplements sold in this

sample is ________.

ANSWER:

90 Numerical Descriptive Measures

TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles

78. Referring to Table 3-3, the median number of vitamin supplements sold in this sample is

________.

ANSWER: 26.5

TYPE: FI DIFFICULTY: Moderate KEYWORDS: median

79. Referring to Table 3-3, the range of the number of vitamin supplements sold in this sample is

________.

ANSWER: 22

TYPE: FI DIFFICULTY: Easy KEYWORDS: range

80. Referring to Table 3-3, the interquartile range of the number of vitamin supplements sold in this

sample is ________.

ANSWER: 15

TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range

81. Referring to Table 3-3, the variance of the number of vitamin supplements sold in this sample is

________.

ANSWER: 54.1

TYPE: FI DIFFICULTY: Easy KEYWORDS: variance

82. Referring to Table 3-3, the standard deviation of the number of vitamin supplements sold in this

sample is ________.

ANSWER: 7.4

TYPE: FI DIFFICULTY: Easy KEYWORDS: standard deviation

83. Referring to Table 3-3, the coefficient of variation of the number of vitamin supplements sold in

this sample is ________ percent.

ANSWER: 26.3%

TYPE: FI DIFFICULTY: Moderate

Numerical Descriptive Measures 91

KEYWORDS: coefficient of variation

84. Referring to Table 3-3, the five-number summary of the data in this sample consists of ________,

________, ________, ________, ________.

ANSWER:

19, 20, 26.5, 35, 41

TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary

85. Referring to Table 3-3, construct a boxplot for the data in this sample.

Box-and-whisker Plot 10203040ANSWER:

TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

86. Referring to Table 3-3, what type of shape does the distribution of the sample appear to have?

ANSWER:

Slightly positive or right-skewed. TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape

TABLE 3-4

The stem-and-leaf display below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days. STEM LEAVES 1H 67889 2L 0011122223333444 2H 5566678899

92 Numerical Descriptive Measures

3L 1122

Note (1): 1H means the “high teens” – 15, 16, 17, 18, or 19; 2L means the “low twenties” – 20, 21, 22, 23, or 24; 2H means the “high twenties” – 25, 26, 27, 28, or 29, etc.

Note (2): For this sample, the sum of the observations is 838, the sum of the squares of the observations is 20,684, and the sum of the squared differences between each observation and the mean is 619.89.

87. Referring to Table 3-4, the arithmetic mean of the customs data is ________.

ANSWER: 23.9

TYPE: FI DIFFICULTY: Easy KEYWORDS: arithmetic mean

88. Referring to Table 3-4, the median of the customs data is ________.

ANSWER: 23

TYPE: FI DIFFICULTY: Moderate KEYWORDS: median

89. Referring to Table 3-4, the first quartile of the customs data is ________.

ANSWER: 21

TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles

90. Referring to Table 3-4, the third quartile of the customs data is ________.

ANSWER: 27

TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles

91. Referring to Table 3-4, the range of the customs data is ________.

ANSWER: 16

TYPE: FI DIFFICULTY: Easy KEYWORDS: range

92. Referring to Table 3-4, the interquartile range of the customs data is ________.

ANSWER: 6

TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range

Numerical Descriptive Measures 93

93. Referring to Table 3-4, the variance of the customs data is ________.

ANSWER: 18.2

TYPE: FI DIFFICULTY: Easy KEYWORDS: variance

94. Referring to Table 3-4, the standard deviation of the customs data is ________.

ANSWER: 4.3

TYPE: FI DIFFICULTY: Easy KEYWORDS: standard deviation

95. Referring to Table 3-4, the coefficient of variation of the customs data is ________ percent.

ANSWER: 17.8% or 18%

TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation

96. Referring to Table 3-4, the five-number summary for the data in the customs sample consists of

________, ________, ________, ________, ________.

ANSWER:

16, 21, 23, 27, 32

TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary

97. Referring to Table 3-4, construct a boxplot of this sample.

Box-and-whisker Plot 101520253035ANSWER:

TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

94 Numerical Descriptive Measures

TABLE 3-5

The rate of return of a Fortune 500 company over the past 15 years are: 3.17%, 4.43%, 5.93%, 5.43%, 7.29%, 8.21%, 6.23%, 5.23%, 4.34%, 6.68%, 7.14%, -5.56%, -5.23%, -5.73%, -10.34%

98. Referring to Table 3-5, compute the arithmetic mean rate of return.

ANWER: 2.48%

TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean

99. Referring to Table 3-5, what is the range of the rate of return?

ANSWER: 18.55%

TYPE: PR DIFFICULTY: Easy KEYWORDS: range

100. Referring to Table 3-5, construct a boxplot for the rate of return.

Box-and-whisker Plot -0.15-0.1-0.0500.050.1ANSWER:

TYPE: PR DIFFICULTY: Easy KEYWORDS: boxplot

101. Referring to Table 3-5, what is the shape of the distribution for the rate of return?

ANSWER: Left-skewed

TYPE: PR DIFFICULTY: Easy KEYWORDS: shape

TABLE 3-6

Numerical Descriptive Measures 95

The rate of return of an Internet Service Provider over a 10 year period are: 10.25%, 12.64%, 8.37%, 9.29%, 6.23%, 42.53%, 29.23%, 15.25%, 21.52%, -2.35%.

102. Referring to Table 3-6, compute the arithmetic mean rate of return.

ANWER: 15.30%

TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean

103. Referring to Table 3-6, construct a boxplot for the rate of return

ANWER:

Box-and-whisker Plot -0.100.10.20.30.40.5TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

104. Referring to Table 3-6, what is the shape of the distribution for the rate of return?

ANSWER: Right-skewed

TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape

105. The Z scores can be used to identify outliers.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: Z scores

106. The larger the Z score, the farther is the distance from the observation to the median.

96 Numerical Descriptive Measures

ANSWER: False

TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z scores

107. As a general rule, an observation is considered an extreme value if its Z score is greater than??3.

ANSWER: False

TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

108. As a general rule, an observation is considered an extreme value if its Z score is greater than?3.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

109. As a general rule, an observation is considered an extreme value if its Z score is less than?3.

ANSWER: False

TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

110. As a general rule, an observation is considered an extreme value if its Z score is less than??3.

ANSWER: True

TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score

111. The Z score of an observation can never be negative.

ANSWER: False

TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z score

112. The Z score of an observation measures how many standard deviations is the value from the

mean.

ANSWER: True

TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z score

Numerical Descriptive Measures 97

TABLE 3-7

Given below is the frequency distribution of the 12-month rate of return achieved by 30 stocks. 12-month Rate of Return Number of Funds 3 ?0.10 but less than 0.0 0.0 but less than 0.1 5 0.1 but less than 0.2 6 0.2 but less than 0.3 10 0.3 but less than 0.4 6

113. Referring to Table 3-7, what is the approximate mean rate of return?

ANSWER: 0.1867

TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate mean

114. Referring to Table 3-7, what is the approximate variance?

ANSWER: 0.0162

TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate variance

115. Referring to Table 3-7, what is the approximate standard deviation?

ANSWER: 0.1273

TYPE: PR DIFFICULTY: Moderate

KEYWORDS: approximate standard deviation

TABLE 3-8

Given below is the frequency distribution of the number of defective tomatoes in 50 different shipments. Defective Items Frequency 0 but less than 5 35 5 but less than 10 7 10 but less than 15 5 15 but less than 20 2 20 but less than 25 1 25 but less than 30 0 Copyright ? 2010 Pearson Education, Inc. Publishing as Prentice Hall

98 Numerical Descriptive Measures

116. Referring to Table 3-8, what is the approximate mean number of defective tomatoes?

ANSWER: 5.2

TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate mean

117. Referring to Table 3-8, what is the approximate variance?

ANSWER: 23.6837

TYPE: PR DIFFICULTY: Moderate KEYWORDS: approximate variance

118. Referring to Table 3-8, what is the approximate standard deviation?

ANSWER: 4.8666

TYPE: PR DIFFICULTY: Moderate

KEYWORDS: approximate standard deviation

TABLE 3-9

In the 2002–2003 academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the 2001–2002 academic year for a sample of 10 public universities were as follows: $1589, $593, $1223, $869, $423, $1720, $708, $1425, $922 and $308.

119. Referring to Table 3-9, what is the mean and median change in the cost?

ANSWER: $978, $895.5

TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean

120. Referring to Table 3-9, what are the five-number summary of the change in the cost?

ANSWER:

$308, $593, $895.5, $1425, and $1720 TYPE: PR DIFFICULTY: Moderate KEYWORDS: five-number summary

121. Referring to Table 3-9, what is the standard deviation of the change in the cost?

ANSWER: $491.8

TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard deviation

Numerical Descriptive Measures 99

122. Referring to Table 3-9, the middle 50% of the change in the cost is spread over what value?

ANSWER: $832

TYPE: PR DIFFICULTY: Moderate KEYWORDS: interquartile range

123. Referring to Table 3-9, what is the coefficient of variation of the change in cost?

ANSWER: 50.29%

TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of variation

124. Referring to Table 3-9, what are the (absolute values of) the Z scores of the change in cost?

ANSWER:

1.24, 0.78, 0.50, 0.22, 1.13, 1.51, 0.55, 0.91, 0.11, 1.36 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Z scores

125. Referring to Table 3-9, are the data skewed? If so, how?

ANSWER:

skewed to the right

TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape

TABLE 3-10

The following table represents the assets in billions of dollars of the five largest bond funds. Bond Fund Assets (Billions $) Vanguard GNMA 19.5 Vanguard Total Bond Mkt. Index 16.8 Bond Fund of America A 13.7 Franklin Calif. Tax-Free Inc. A 12.8 Vanguard Short-Term Corp. 10.9 126. Referring to Table 3-10, what is the mean for this population of the five largest bond funds?

ANSWER: $14.74 billions

TYPE: PR DIFFICULTY: Easy KEYWORDS: population mean

100 Numerical Descriptive Measures

127. Referring to Table 3-10, what are the variance and standard deviation for this population?

ANSWER:

9.2984 squared billion dollars, $3.0493 billions, respectively TYPE: PR DIFFICULTY: Moderate

KEYWORDS: population variance, population standard deviation

TABLE 3-11

The population of eight analysts at a software firm were asked to estimate the reuse rate when developing a new software system. The following data are given as a percentage of the total code written for a software system that is part of the reuse database.

50, 62.5, 37.5, 75.0, 45.0, 47.5, 15.0, 25.0

128. Referring to Table 3-11, what is the mean percentage of the total code that is part of the reuse

database?

ANSWER: 44.69

TYPE: PR DIFFICULTY: Easy KEYWORDS: population mean

129. Referring to Table 3-11, what are the variance and standard deviation of the total code that is

part of the reuse database?

ANSWER:

324.12 and 18.00, respectively

TYPE: PR DIFFICULTY: Moderate

KEYWORDS: population variance, population standard deviation

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