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