BASIC BUSINESS STATISTICS 13E MARK L. BERENSON - Test Bank

BASIC BUSINESS STATISTICS 13E MARK L. BERENSON – Test Bank

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Numerical Descriptive Measures 3-1
Copyright ©2015 Pearson Education, Inc.
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) Geometric mean.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: measure of central tendency, mode, arithmetic mean, median, geometric mean
3. Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of
central tendency?
a) The arithmetic mean and median only.
b) The median and mode only.
c) The mode and geometric mean only.
d) The arithmetic mean and mode only.
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 greater than the arithmetic mean.
d) none of the above.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: shape
3-2 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
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 Q 2 .
d) It is equal to the mode in bell-shaped “normal” distributions.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: median, measure of central tendency, resistant to outliers, quartile
6. In a perfectly symmetrical bell-shaped “normal” distribution
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
Numerical Descriptive Measures 3-3
Copyright ©2015 Pearson Education, Inc.
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 Q 1 to Q2 is greater than the distance from Q2 to Q3 .
b) The distance from Q 1 to Q2 is less than the distance from Q2 to Q3 .
c) The arithmetic mean is less than the median.
d) The mode is greater than the arithmetic mean.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: shape, quartiles, arithmetic mean, mode
3-4 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
13. In perfectly symmetrical distributions, which of the following is NOT a correct statement?
a) The distance from Q 1 to Q2 equals to the distance from Q 2 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 Q 1 to Q3 is half of the distance from the smallest to the largest
observation.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: five-number summary, shape, quartiles
14. In left-skewed distributions, which of the following is the correct statement?
a) The distance from Q 1 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 less than the distance from Q2 to the
largest observation.
d) The distance from Q 1 to Q3 is twice the distance from the Q1 to Q2.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: , five-number summary, shape, quartiles
15. According to the empirical rule, if the data form a “bell-shaped” normal distribution, _______
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
Numerical Descriptive Measures 3-5
Copyright ©2015 Pearson Education, Inc.
16. According to the empirical rule, if the data form a “bell-shaped” normal distribution, _______
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:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: empirical rule, normal distribution
17. According to the empirical rule, if the data form a “bell-shaped” normal distribution, _______
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 geometric mean.
c) The mode.
d) The interquartile range.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: measure of central tendency, arithmetic mean, geometric mean, 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
3-6 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
20. Which of the following is sensitive to extreme values?
a) The median.
b) The interquartile range.
c) The arithmetic mean.
d) The 1 st quartile.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: resistant to outliers, median, interquartile range, arithmetic mean, quartiles
21. Which of the following is the easiest to compute?
a) The arithmetic mean.
b) The median.
c) The mode.
d) The geometric mean.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: mode, arithmetic mean, median, geometric mean
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
Numerical Descriptive Measures 3-7
Copyright ©2015 Pearson Education, Inc.
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
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
3-8 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
26. A manufacturer of flashlight batteries took a sample of 130 batteries from a day’s production and
used them continuously until they were drained. The number of hours until failure are recorded.
Given below is the boxplot of the number of hours it took to drain each of the 130 batteries. The
distribution of the number of hours is
a) right-skewed
b) left-skewed
c) symmetrical
d) none of the above
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: boxplot
Hours
260 460 660 860 1060
Boxplot
Numerical Descriptive Measures 3-9
Copyright ©2015 Pearson Education, Inc.
27. Data on the change in the cost of tuition, a shared dormitory room, and the most popular meal plan
from one academic year to the next academic year for a sample of 100 public universities are
collected. Below is the boxplot for the change in cost in dollars. The distribution of the change in
cost is
a) right-skewed
b) left-skewed
c) symmetrical
d) none of the above
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: boxplot
SCENARIO 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. The ages of 25 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
28. Referring to Scenario 3-1, calculate the arithmetic mean age of the senior citizens to the nearest
hundredth of a year.
ANSWER:
74.04 years
TYPE: PR DIFFICULTY: Easy
KEYWORDS: arithmetic mean
29. Referring to Scenario 3-1, determine the median age of the senior citizens.
ANSWER:
73 years
TYPE: PR DIFFICULTY: Easy
KEYWORDS: median
Change in
Cost ($)
300 800 1300 1800 2300
Boxplot
3-10 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
30. Referring to Scenario 3-1 determine the first quartile of the ages of the senior citizens.
ANSWER:
65.5 years
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: quartiles
31. Referring to Scenario 3-1 determine the third quartile of the ages of the senior citizens.
ANSWER:
81.5 years
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: quartiles
32. Referring to Scenario 3-1, determine the interquartile range of the ages of the senior citizens.
ANSWER:
16 years
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: interquartile range
33. Referring to Scenario 3-1, determine 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 mean 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
34. Referring to Scenario 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
35. Referring to Scenario 3-1, calculate the skewness statistic for the age of the senior citizens
accurate to two decimal places.
ANSWER:
0.36
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: skewness, shape
Numerical Descriptive Measures 3-11
Copyright ©2015 Pearson Education, Inc.
36. Referring to Scenario 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, skewness
37. Referring to Scenario 3-1, calculate the kurtosis statistic for the age of the senior citizens accurate
to two decimal places.
ANSWER:
-1.01
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: kurtosis, shape
38. Referring to Scenario 3-1, does the distribution of the sample appear to be lepokurtic or
platykurtic?
ANSWER:
lepokurtic
TYPE: PR DIFFICULTY: Easy
KEYWORDS: kurtosis, shape
39. Referring to Scenario 3-1, calculate the variance of the ages of the senior citizens correct to the
nearest hundredth of a year squared.
ANSWER:
94.96 years2
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: variance
40. Referring to Scenario 3-1, calculate the standard deviation of the ages of the senior citizens
correct to the nearest hundredth of a year.
ANSWER:
9.74 years
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: standard deviation
41. Referring to Scenario 3-1, calculate the coefficient of variation of the ages of the senior citizens.
ANSWER:
13.16%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: coefficient of variation
3-12 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
42. 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
43. 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
44. 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
45. 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
46. 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
47. True or False: In right-skewed distributions, the distance from Q3 to the largest value is greater
than the distance from the smallest observation to Q1 .
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: quartiles, shape
Numerical Descriptive Measures 3-13
Copyright ©2015 Pearson Education, Inc.
48. True or False: In left-skewed distributions, the distance from the smallest value to Q1 is greater
than the distance from Q3 to the largest value.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: five-number summary, quartiles, shape
49. True or False: A boxplot is a graphical representation of a five-number summary.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: boxplot, five-number summary
50. True or False: The five-number summary consists of the smallest value, the first quartile, the
median, the third quartile, and the largest value.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: five-number summary
51. 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
52. 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
53. True or False: The line drawn within the box of the boxplot always represents the median.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: boxplot, median
3-14 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
54. 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
55. 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
56. 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
57. 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
58. 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
59. True or False: The coefficient of variation is expressed as a percentage.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: coefficient of variation
Numerical Descriptive Measures 3-15
Copyright ©2015 Pearson Education, Inc.
60. 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
61. 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
62. 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
63. True or False: The geometric mean is a measure of variation or dispersion in a set of data.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: geometric mean, measure of central tendency
64. True or False: The geometric mean is useful in measuring the rate of change of a variable over
time.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: geometric mean
65. 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
66. True or False: The coefficient of variation is a measure of relative variation.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: coefficient of variation
3-16 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
67. 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
68. If the arithmetic mean of a numerical data set is greater than the median, the data are considered
to be _______ skewed.
ANSWER:
positive or right
TYPE: FI DIFFICULTY: Easy
KEYWORDS: shape, arithmetic mean, median
SCENARIO 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
69. Referring to Scenario 3-2, the arithmetic mean carbohydrates in this sample is ________ grams.
ANSWER:
217/11 = 19.73
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: arithmetic mean
70. Referring to Scenario 3-2, the median carbohydrate amount in the cereal is ________ grams.
ANSWER:
20
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: median
71. Referring to Scenario 3-2, the skewness statistic for the carbohydrate amount in the cereal is
________.
ANSWER:
0.09
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: skewness, shape
72. Referring to Scenario 3-2, is the carbohydrate amount in the cereal right- or left-skewed?
ANSWER:
Right-skewed
TYPE: PR DIFFICULTY: Easy
KEYWORDS: skewness, shape
Numerical Descriptive Measures 3-17
Copyright ©2015 Pearson Education, Inc.
73. Referring to Scenario 3-2, the kurtosis statistic for the carbohydrate amount in the cereal is
________.
ANSWER:
-0.06
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: kurtosis, shape
74. Referring to Scenario 3-2, is the carbohydrate amount in the cereal leptokurtic or platykurtic?
ANSWER:
platykurtic
TYPE: PR DIFFICULTY: Easy
KEYWORDS: kurtosis, shape
75. Referring to Scenario 3-2, the first quartile of the carbohydrate amounts is ________ grams.
ANSWER:
15
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: quartiles
76. Referring to Scenario 3-2, the third quartile of the carbohydrate amounts is ________ grams.
ANSWER:
23
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: quartiles
77. Referring to Scenario 3-2, the range in the carbohydrate amounts is ________ grams.
ANSWER:
18
TYPE: FI DIFFICULTY: Easy
KEYWORDS: range
78. Referring to Scenario 3-2, the interquartile range in the carbohydrate amounts is ________ grams.
ANSWER:
8
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: interquartile range
79. Referring to Scenario 3-2, the variance of the carbohydrate amounts is ________ (grams
squared).
ANSWER:
26.02
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: variance
3-18 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
80. Referring to Scenario 3-2, the standard deviation of the carbohydrate amounts is ________
grams.
ANSWER:
5.10
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: standard deviation
81. Referring to Scenario 3-2, the coefficient of variation of the carbohydrate amounts is ________
percent.
ANSWER:
25.86%
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: coefficient of variation
82. Referring to Scenario 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
83. Referring to Scenario 3-2, construct a boxplot for the carbohydrate amounts.
ANSWER:
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: boxplot
Box-and-whisker Plot
10 15 20 25 30
Numerical Descriptive Measures 3-19
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
84. Referring to Scenario 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
85. Referring to Scenario 3-3, the first quartile of the number of vitamin supplements sold in this
sample is ________.
ANSWER:
20
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: quartiles
86. Referring to Scenario 3-3, the third quartile of the number of vitamin supplements sold in this
sample is ________.
ANSWER:
35
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: quartiles
87. Referring to Scenario 3-3, the median number of vitamin supplements sold in this sample is
________.
ANSWER:
26.5
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: median
88. Referring to Scenario 3-3, the skewness statitic of the number of vitamin supplements sold in this
sample is ________.
ANSWER:
0.29
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: skewness, shape
3-20 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
89. Referring to Scenario 3-3, is the number of vitamin supplements sold in this sample right- or left-
skewed?
ANSWER:
Right-skewed
TYPE: PR DIFFICULTY: Easy
KEYWORDS: skewness, shape
90. Referring to Scenario 3-3, the kurtosis statitic of the number of vitamin supplements sold in this
sample is ________.
ANSWER:
-1.32
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: kurtosis, shape
91. Referring to Scenario 3-3, is the number of vitamin supplements sold in this sample lepokurtic or
platykurtic?
ANSWER:
platykurtic
TYPE: PR DIFFICULTY: Easy
KEYWORDS: kurtosis, shape
92. Referring to Scenario 3-3, the range of the number of vitamin supplements sold in this sample is
________.
ANSWER:
22
TYPE: FI DIFFICULTY: Easy
KEYWORDS: range
93. Referring to Scenario 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
94. Referring to Scenario 3-3, the variance of the number of vitamin supplements sold in this sample
is ________.
ANSWER:
54.13
TYPE: FI DIFFICULTY: Easy
KEYWORDS: variance
Numerical Descriptive Measures 3-21
Copyright ©2015 Pearson Education, Inc.
95. Referring to Scenario 3-3, the standard deviation of the number of vitamin supplements sold in
this sample is ________.
ANSWER:
7. 36
TYPE: FI DIFFICULTY: Easy
KEYWORDS: standard deviation
96. Referring to Scenario 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
KEYWORDS: coefficient of variation
97. Referring to Scenario 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
98. Referring to Scenario 3-3, construct a boxplot for the data in this sample.
ANSWER:
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: boxplot
99. Referring to Scenario 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
Box-and-whisker Plot
10 20 30 40
3-22 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-4
The ordered array below represents the number of cargo manifests approved by customs inspectors of
the Port of New York in a sample of 35 days:
16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27,
28, 28, 29, 29, 31, 31, 32, 32
Note: For this sample, the sum of the values is 838, , and the sum of the squared differences between
each value and the mean is 619.89.
100. Referring to Scenario 3-4, the arithmetic mean of the customs data is ________.
ANSWER:
23.9
TYPE: FI DIFFICULTY: Easy
KEYWORDS: arithmetic mean
101. Referring to Scenario 3-4, the median of the customs data is ________.
ANSWER:
23
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: median
102. Referring to Scenario 3-4, the first quartile of the customs data is ________.
ANSWER:
21
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: quartiles
103. Referring to Scenario 3-4, the third quartile of the customs data is ________.
ANSWER:
27
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: quartiles
104. Referring to Scenario 3-4, the range of the customs data is ________.
ANSWER:
16
TYPE: FI DIFFICULTY: Easy
KEYWORDS: range
105. Referring to Scenario 3-4, the interquartile range of the customs data is ________.
ANSWER:
6
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: interquartile range
Numerical Descriptive Measures 3-23
Copyright ©2015 Pearson Education, Inc.
106. Referring to Scenario 3-4, the variance of the customs data is ________.
ANSWER:
18.2
TYPE: FI DIFFICULTY: Easy
KEYWORDS: variance
107. Referring to Scenario 3-4, the standard deviation of the customs data is ________.
ANSWER:
4.3
TYPE: FI DIFFICULTY: Easy
KEYWORDS: standard deviation
108. Referring to Scenario 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
109. Referring to Scenario 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
110. Referring to Scenario 3-4, construct a boxplot of this sample.
ANSWER:
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: boxplot
Box-and-whisker Plot
10 15 20 25 30 35
3-24 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
SCENARIO 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%
111. Referring to Scenario 3-5, compute the arithmetic mean rate of return per year.
ANSWER:
2.48%
TYPE: PR DIFFICULTY: Easy
KEYWORDS: arithmetic mean
112. Referring to Scenario 3-5, compute the geometric mean rate of return per year for the first four
years.
ANSWER:
4.73%
TYPE: PR DIFFICULTY: moderate
KEYWORDS: geometric mean rate of return
113. Referring to Scenario 3-5, what is the range of the rate of return?
ANSWER:
18.55%
TYPE: PR DIFFICULTY: Easy
KEYWORDS: range
114. Referring to Scenario 3-5, construct a boxplot for the rate of return.
ANSWER:
TYPE: PR DIFFICULTY: Easy
KEYWORDS: boxplot
115. Referring to Scenario 3-5, what is the shape of the distribution for the rate of return?
ANSWER:
Left-skewed
TYPE: PR DIFFICULTY: Easy
KEYWORDS: shape
Box-and-whisker Plot
-0.15 -0.1 -0.05 0 0.05 0.1
Numerical Descriptive Measures 3-25
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-6
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%.
116. Referring to Scenario 3-6, compute the arithmetic mean rate of return per year.
ANSWER:
15.30%
TYPE: PR DIFFICULTY: Easy
KEYWORDS: arithmetic mean
117. Referring to Scenario 3-6, compute the geometric mean rate of return per year for the first three
years.
ANSWER:
10.41%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: geometric mean rate of return
118. Referring to Scenario 3-6, construct a boxplot for the rate of return
ANSWER:
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: boxplot
119. Referring to Scenario 3-6, what is the shape of the distribution for the rate of return?
ANSWER:
Right-skewed
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: boxplot, shape
120. You were told that the 1st , 2 nd and 3 rd quartiles of female students’ weight at a major university
are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh more than 138 lbs?
ANSWER:
25 percent
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: quartile
-0.1 0.1 0.3 0.5
Boxplot
3-26 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
121. You were told that the 1st , 2 nd and 3 rd quartiles of female students’ weight at a major university
are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh less than 95 lbs?
ANSWER:
25 percent
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: quartile
122. You were told that the 1st , 2 nd and 3 rd quartiles of female students’ weight at a major university
are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh between 95 and 138 lbs?
ANSWER:
50 percent
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: quartile
123. You were told that the 1st , 2 nd and 3 rd quartiles of female students’ weight at a major university
are 95 lbs, 125 lbs, and 138 lbs. What percentage of the students weigh more than 125 lbs?
ANSWER:
50 percent
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: quartile
124. The Z scores can be used to identify outliers.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Z scores
125. The larger the Z score, the farther is the distance from the value to the median.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Z scores
126. As a general rule, a value is considered an extreme value if its Z score is greater than −3.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Z score
127. As a general rule, a value is considered an extreme value if its Z score is greater than 3.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Z score
Numerical Descriptive Measures 3-27
Copyright ©2015 Pearson Education, Inc.
128. As a general rule, a value is considered an extreme value if its Z score is less than 3.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Z score
129. As a general rule, a value is considered an extreme value if its Z score is less than −3.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Z score
130. The Z score of a value can never be negative.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Z score
131. The Z score of a value measures how many standard deviations the value is from the mean.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Z score
132. The 12-month rate of returns over a three year period of a particular stock is 0.099, −0.289, and
0.089. The geometric mean rate of return per year for this stock is _______.
ANSWER:
−5.24% or −0.0524
TYPE: FI DIFFICULTY: moderate
KEYWORDS: geometric mean rate of return
133. The rate of return for the S&P 500 over a four year period is −0.029, −0.061, −0.493, and
−0.286. The geometric mean rate of return per year is _______.
ANSWER:
−24.20% or −0.2420
TYPE: FI DIFFICULTY: moderate
KEYWORDS: geometric mean rate of return
134. The rate of return for a stock over a three year period is 0.527, 0.145, and 0.684. The geometric
mean rate of return is _______.
ANSWER:
43.33% or 0.4333
TYPE: FI DIFFICULTY: moderate
KEYWORDS: geometric mean rate of return
3-28 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-7
In a recent 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 previous academic year for a sample of 10 public universities were as
follows: $1,589, $593, $1,223, $869, $423, $1,720, $708, $1425, $922 and $308.
135. Referring to Scenario 3-7, what is the mean and median change in the cost?
ANSWER:
$978, $895.5
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: mean
136. Referring to Scenario 3-7, what is 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
137. Referring to Scenario 3-7, what is the standard deviation of the change in the cost?
ANSWER:
$491.8
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: standard deviation
138. Referring to Scenario 3-7, what is the interquartile range of the change in the cost?
ANSWER:
$832
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: interquartile range
139. Referring to Scenario 3-7, what is the coefficient of variation of the change in cost?
ANSWER:
50.29%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: coefficient of variation
140. Referring to Scenario 3-7, what is the skewness statistic of the change in the cost?
ANSWER:
0.22
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: skewness, shape
Numerical Descriptive Measures 3-29
Copyright ©2015 Pearson Education, Inc.
141. Referring to Scenario 3-7, is the change in the cost right- or left-skewed?
ANSWER:
Right-skewed
TYPE: PR DIFFICULTY: Easy
KEYWORDS: skewness, shape
142. Referring to Scenario 3-7, what is the kurtosis statistic of the change in the cost?
ANSWER:
-1.32
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: kurtosis, shape
143. Referring to Scenario 3-7, is the change in the cost lepokurtic or platykurtic?
ANSWER:
platykurtic
TYPE: PR DIFFICULTY: Easy
KEYWORDS: skewness, shape
144. Referring to Scenario 3-7, 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
145. Referring to Scenario 3-7, are the data skewed? If so, how?
ANSWER:
skewed to the right
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: shape
3-30 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-8
The time period from 2010 to 2013 saw a great deal of volatility in the value of stocks. The data in
the following table represent the total rate of return of our companies from 2010 to 2013.
Year Company A Company B Company C Company D
2013 25.30 26.40 45.40 29.40
2012 -15.01 -22.10 -21.58 -20.90
2011 -5.44 -11.90 -1.03 -10.97
2010 -6.20 -9.10 -3.02 -10.89
146. Referring to Scenario 3-8, calculate the geometric mean rate of return per year for Company A.
ANSWER:
-1.42
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: geometric mean rate of return
147. Referring to Scenario 3-8, calculate the geometric mean rate of return per year for Company B.
ANSWER:
-5.77%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: geometric mean rate of return
148. Referring to Scenario 3-8, calculate the geometric mean rate of return per year for Company C.
ANSWER:
2.28%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: geometric mean rate of return
149. Referring to Scenario 3-8, calculate the geometric mean rate of return per year for Company D.
ANSWER:
-5.07%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: geometric mean rate of return
Numerical Descriptive Measures 3-31
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-9
The following table represents the assets in billions of dollars of the five largest bond funds sometime
in the past.
Bond Fund Assets (Billions $)
PIMCO Total Return Fund 246
Vanguard Total Bond Market Index Fund 110
Templeton Global Bond Fund 57
Vanguard Total Bond Market Index Fund II 56
Vanguard Inflation-Protected Securities 43
150. Referring to Scenario 3-9, what is the mean for this population of the five largest bond funds?
ANSWER:
$102.4 billions
TYPE: PR DIFFICULTY: Easy
KEYWORDS: population mean
151. Referring to Scenario 3-9, what are the variance and standard deviation for this population?
ANSWER:
5,684.24 squared billion dollars, $75.39 billions, respectively
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: population variance, population standard deviation
SCENARIO 3-10
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
152. Referring to Scenario 3-10, 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
153. Referring to Scenario 3-10, 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
3-32 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-11
Given below are the closing prices for the Dow Jones Industrial Average (DJIA) and the Standard &
Poor’s (S&P) 500 Index over a 10-week sometime in the past.
Dow Jones 10,421 10,110 9,862 10,475 9,920 10,592 11,213 10,933 11,134 10,316
S&P 500 1,379 1,356 1,343 1,410 1,389 1,463 1,529 1,499 1,516 1,355
154. Referring to Scenario 3-11, what is the sample covariance between the DJIA and the S&P 500
index?
ANSWER:
31594.7333
TYPE: PR DIFFICULTY: Easy
KEYWORDS: covariance
155. Referring to Scenario 3-11, what is the sample correlation coefficient between the DJIA and the
S&P 500 index?
ANSWER:
0.9274
TYPE: PR DIFFICULTY: Easy
KEYWORDS: coefficient of correlation
156. Referring to Scenario 3-11, how will you classify the linear relationship between the DJIA and
the S&P 500 index?
a) Weak
b) Moderate
c) Strong
d) No relationship
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
157. Referring to Scenario 3-11, for the week when the DJIA is high, you will expect the S&P index
in that week to
a) be about the same value as the DJIA
b) be low
c) be high
d) have no relationship with the DJIA value
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
Numerical Descriptive Measures 3-33
Copyright ©2015 Pearson Education, Inc.
158. Referring to Scenario 3-11, you will expect an increase in the DJIA to be associated with
a) an increase in the S&P 500 index
b) a decrease in the S&P 500 index
c) no predictable change in the DJIA
d) no predictable change in the S&P 500 index
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
SCENARIO 3-12
Given below are the rating and performance scores of 15 laptop computers.
Performance
Score
115 191 153 194 236 184 184 216
Overall
Rating
74 78 79 80 84 76 77 92
Performance
Score
185 183 189 202 192 141 187
Overall
Rating
83 78 77 78 78 73 77
159. Referring to Scenario 3-12, what is the sample covariance between the performance scores and
the rating?
ANSWER:
88.8905
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: covariance
160. Referring to Scenario 3-12, what is the sample correlation coefficient between the performance
scores and the rating?
ANSWER:
0.6629
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: coefficient of correlation
3-34 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
161. Referring to Scenario 3-12, how will you classify the linear relationship between the
performance scores and the rating?
a) Weak
b) Moderate
c) Strong
d) No relationship
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
162. Referring to Scenario 3-12, for a laptop computer that has a high rating, you will expect its
performance score to
a) be about the same as its rating
b) be low
c) be high
d) have no relationship with its rating
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
163. Referring to Scenario 3-12, you will expect a decrease in the performance score of one laptop
computer to be associated with
a) an increase in its rating
b) a decrease in its rating
c) no predictable change in its rating
d) no predictable change in the performance score of another laptop computer
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
Numerical Descriptive Measures 3-35
Copyright ©2015 Pearson Education, Inc.
SCENARIO 3-13
Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the
current leader in the energy drink market. Given below are the exam scores and the number of 12-
ounce energy drinks consumed within a week prior to the exam of 10 college students.
Exam Scores 75 92 84 64 64 86 81 61 73 93
Number of Drinks 5 3 2 4 2 7 3 0 1 0
164. Referring to Scenario 3-13, what is the sample covariance between the exam scores and the
number of energy drinks consumed?
ANSWER:
3.7667
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: covariance
165. Referring to Scenario 3-13, what is the sample correlation coefficient between the exam scores
and the number of energy drinks consumed?
ANSWER:
0.1450
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: coefficient of correlation
166. Referring to Scenario 3-13, how will you classify the linear relationship between the exam
scores and the number of energy drinks consumed?
a) Weak
b) Moderate
c) Strong
d) No relationship
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation
167. Referring to Scenario 3-13, for a student who has consumed a high number of energy drinks
within the week prior to the exam, you will expect his/her exam score to
a) be noticeably higher than the exam score had he/she not consume as much energy drink.
b) be noticeably lower than the exam score had he/she not consume as much energy drink.
c) not be noticeably different from the amount of energy drinks that he/she consumed.
d) not be noticeably different from the exam score had he/she not consumed as much.
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: coefficient of correlation, interpretation
3-36 Numerical Descriptive Measures
Copyright ©2015 Pearson Education, Inc.
168. Referring to Scenario 3-13, you will expect a decrease in the amount of energy drink consumed
within the week prior to the exam to be associated with
a) no predictable change in the amount of energy drink consumed after the exam
b) an increase in the exam score
c) a decrease in the exam score
d) no predictable change in the exam score
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: coefficient of correlation, interpretation