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
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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
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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
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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
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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
Copyright ? 2010 Pearson Education, Inc. Publishing as Prentice Hall