Applied Statistics in Business And Economics 5th Edition by Doane -Test Bank
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Sample Test
Chapter 04
Descriptive Statistics
True / False Questions
1. A
data set with two values that are tied for the highest number of occurrences is
called bimodal.
True False
2. The
midrange is not greatly affected by outliers.
True False
3. The
second quartile is the same as the median.
True False
4. A
trimmed mean may be preferable to a mean when a data set has extreme values.
True False
5. One
benefit of the box plot is that it clearly displays the standard deviation.
True False
6. It is
inappropriate to apply the Empirical Rule to a population that is right-skewed.
True False
7. Given
the data set 10, 5, 2, 6, 3, 4, 20, the median value is 5.
True False
8. Given
the data set 2, 5, 10, 6, 3, the median value is 3.
True False
9. When
data are right-skewed, we expect the median to be greater than the mean.
True False
10. The
sum of the deviations around the mean is always zero.
True False
11. The
midhinge is a robust measure of center when there are outliers.
True False
12. Chebyshev’s
Theorem says that at most 50 percent of the data lie within 2 standard
deviations of the mean.
True False
13. Chebyshev’s
Theorem says that at least 95 percent of the data lie within 2 standard
deviations of the mean.
True False
14. If
there are 19 data values, the median will have 10 values above it and 9 below
it since n is odd.
True False
15. If
there are 20 data values, the median will be halfway between two data values.
True False
16. In a
left-skewed distribution, we expect that the median will be greater than the
mean.
True False
17. If
the standard deviations of two samples are the same, so are their coefficients
of variation.
True False
18. A
certain health maintenance organization (HMO) examined the number of office
visits by its members in the last year. This data set would probably be skewed
to the left due to low outliers.
True False
19. A
certain health maintenance organization (HMO) examined the number of office
visits by its members in the last year. For this data set, the mean is probably
not a very good measure of a “typical” person’s office visits.
True False
20. Referring
to this box plot of ice cream fat content, the median seems more “typical” of
fat content than the midrange as a measure of center.
True False
21. Referring
to this box plot of ice cream fat content, the mean would exceed the median.
True False
22. Referring
to this box plot of ice cream fat content, the skewness would be negative.
True False
23. Referring
to this graph of ice cream fat content, the second quartile is about 61.
True False
24. The
range as a measure of variability is very sensitive to extreme data values.
True False
25. In
calculating the sample variance, the sum of the squared deviations around the
mean is divided by n – 1 to avoid underestimating the unknown population
variance.
True False
26. Outliers
are data values that fall beyond ±2 standard deviations from the mean.
True False
27. The
Empirical Rule assumes that the distribution of data follows a normal curve.
True False
28. The
Empirical Rule can be applied to any distribution, unlike Chebyshev’s theorem.
True False
29. When
applying the Empirical Rule to a distribution of grades, if a student scored
one standard deviation below the mean, then she would be at the 25th percentile
of the distribution.
True False
30. Kurtosis
cannot be judged accurately by looking at a histogram.
True False
31. A
platykurtic distribution is more sharply peaked (i.e., thinner tails) than a
normal distribution.
True False
32. A
leptokurtic distribution is more sharply peaked (i.e., thinner tails) than a
normal distribution.
True False
33. A
positive kurtosis coefficient in Excel indicates a leptokurtic condition in a
distribution.
True False
34. A
sample consists of the following data: 7, 11, 12, 18, 20, 22, 43. Using the
“three standard deviation” criterion, the last observation (X = 43) would be
considered an outlier.
True False
Multiple Choice Questions
35. The
coefficient of variation is
100.
measured on a scale from 0 to 100.
1. a
unit-free statistic.
1. helpful
when the sample means are zero.
1. a
measure of correlation for two variables.
36. Which
is not an advantage of the method of medians to find Q1 and Q3?
1. Ease
of interpolating quartile positions
1. Ease
of application in small data sets
1. Intuitive
definitions without complex formulas
1. Same
method as Excel’s =QUARTILE.EXC function.
37. Which
is a characteristic of the mean as a measure of center?
1. Deviations
do not sum to zero when there are extreme values.
1. It is
less reliable than the mode when the data are continuous.
1. It
utilizes all the information in a sample.
1. It is
usually equal to the median in business data.
38. The
position of the median is:
1. n/2
in any sample.
1. n/2
if n is even.
1. n/2
if n is odd.
1. (n +
1)/2 in any sample.
39. Which
is a characteristic of the trimmed mean as a measure of center?
1. It is
similar to the mean if there are offsetting high and low extremes.
1. It is
especially helpful in a small sample.
1. It
does not require sorting the sample.
1. It is
basically the same as the midrange.
40. Which
is not a characteristic of the geometric mean as a measure of center?
1. It is
similar to the mean if the data are skewed right.
1. It
mitigates the effects of large data values.
1. It is
useful in business data to calculate average growth rates.
1. It
cannot be calculated when the data contain negative or zero values.
41. Which
is not a characteristic of the standard deviation?
1. It is
always the square root of the variance.
1. It is
not applicable when data are continuous.
1. It
can be calculated when the data contain negative or zero values.
1. Its
physical interpretation is not as easy as the MAD.
42. Chebyshev’s
Theorem:
1. applies
to all samples.
1. applies
only to samples from a normal population.
1. gives
a narrower range of predictions than the Empirical Rule.
1. is
based on Sturges’ Rule for data classification.
43. Which
of the following is not a valid description of an outlier?
1. A
data value beyond the outer fences
1. A data
value that is very unusual
1. A
data value that lies below Q1 or above Q3
1. A
data value several standard deviations from the mean.
44. If
samples are from a normal distribution with μ = 100 and σ = 10, we expect:
110.
about 68 percent of the data within 90 to 110.
120.
almost all the data within 80 to 120.
130.
about 95 percent of the data within 70 to 130.
75. about
half the data to exceed 75.
45. In a
sample of 10,000 observations from a normal population, how many would you
expect to lie beyond three standard deviations of the mean?
1. None
of them
1. About
27
1. About
100
1. About
127
46. The
Excel formula for the standard deviation of a sample array named Data is:
1. =STDEV.S(Data).
1. =STANDEV(Data).
1. =STDEV.P(Data).
1. =SUM(Data)/(COUNT(Data)-1).
47. Which
is not true of an outlier?
1. It is
likely to be from a different population.
1. It
suggests an error in recording the data.
1. It is
best discarded to get a better mean.
1. It is
an anomaly that may tell the researcher something.
48. Estimating
the mean from grouped data will tend to be most accurate when:
1. observations
are distributed uniformly within classes.
1. there
are few classes with wide class limits.
1. the
sample is not very large and bins are wide.
1. the
standard deviation is large relative to the mean.
49. Which
is true of the kurtosis of a distribution?
1. A
distribution that is flatter than a normal distribution (i.e., thicker tails)
is mesokurtic.
1. A
distribution that is more peaked than a normal distribution (i.e., thinner
tails) is platykurtic.
50. It is
risky to assess kurtosis if the sample size is less than 50.
1. The
expected range of the kurtosis coefficient increases as n increases.
50. Which
is true of skewness?
1. In
business data, positive skewness is unusual.
1. In a
negatively skewed distribution, the mean is likely to exceed the median.
1. Skewness
often is evidenced by one or more outliers.
1. The
expected range of Excel’s skewness coefficient increases as n increases.
51. Which
is not true of the Empirical Rule?
1. It
applies to any distribution.
1. It
can be applied to fewer distributions than Chebyshev’s Theorem.
1. It
assumes that the distribution of data follows a bell-shaped, normal curve.
1. It predicts
more observations within μ ± kσ than Chebyshev’s Theorem.
52. Which
is a correct statement concerning the median?
1. In a
left-skewed distribution, we expect that the median will exceed the mean.
1. The
sum of the deviations around the median is zero.
1. The
median is an observed data value in any data set.
1. The
median is halfway between Q1 and Q3 on a box plot.
53. Which
statement is true?
1. With
nominal data we can find the mode.
1. Outliers
distort the mean but not the standard deviation.
1. Business
and economic data are rarely skewed to the right.
1. If we
sample a normal population, the sample skewness coefficient is exactly 0.
54. Exam
scores in a small class were 10, 10, 20, 20, 40, 60, 80, 80, 90, 100, 100. For
this data set, which statement is incorrect concerning measures of center?
60. The
median is 60.00.
1. The
mode is not helpful.
1. The 5
percent trimmed mean would be awkward.
35. The
geometric mean is 35.05.
55. Exam
scores in a small class were 0, 50, 50, 70, 70, 80, 90, 90, 100, 100. For this
data set, which statement is incorrect concerning measures of center?
70. The
median is 70.
1. The
mode is not helpful.
1. The
geometric mean is useless.
70. The
mean is 70.
56. Exam
scores in a random sample of students were 0, 50, 50, 70, 70, 80, 90, 90, 90,
100. Which statement is incorrect?
29. The
standard deviation is 29.61.
1. The
data are slightly left-skewed.
1. The
midrange and mean are almost the same.
90. The
third quartile is 90.
57. For
U.S. adult males, the mean height is 178 cm with a standard deviation of 8 cm
and the mean weight is 84 kg with a standard deviation of 8 kg. Elmer is 170 cm
tall and weighs 70 kg. It is most nearly correct to say that:
1. Elmer’s
weight is more unusual than his height.
1. Elmer
is heavier than he is tall.
1. Height
and weight have the same degree of variation.
1. Height
has more variation than weight.
58. John
scored 85 on Prof. Hardtack’s exam (Q1 = 40 and Q3 = 60). Based on the fences,
which is correct?
1. John
is an extreme outlier.
1. John
is an outlier.
1. John
is not an outlier.
1. John
is in the 85th percentile.
59. John
scored 35 on Prof. Johnson’s exam (Q1 = 70 and Q3 = 80). Based on the fences,
which is correct?
1. John
is unusual but not an outlier.
1. John
is an outlier.
1. John
is neither unusual nor an outlier.
1. John
is in the 30th percentile.
60. A
population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The
population variance is:
6. 6.07.
36. 36.82.
5. 5.16.
22. 22.86.
61. Consider
the following data: 6, 7, 17, 51, 3, 17, 23, and 69. The range and the median
are:
17. 69
and 17.5.
17. 66
and 17.5.
17. 66
and 17.
17. 69
and 17.
62. When
a sample has an odd number of observations, the median is the:
1. observation
in the center of the data array.
1. average
of the two observations in the center of the data array.
1. value
of the most frequent observation.
3. average
of Q1 and Q3.
63. As a
measure of variability, compared to the range, an advantage of the standard
deviation is:
1. being
calculated easily through the use of a formula.
1. considering
only the data values in the middle of the data array.
1. describing
the distance between the highest and lowest values.
1. considering
all data values.
64. Which
two statistics offer robust measures of center when outliers are present?
1. Mean
and mode.
1. Median
and trimmed mean.
1. Midrange
and geometric mean.
1. Variance
and standard deviation.
65. Which
Excel function is designed to calculate z = (x – μ)/σ for a column of data?
1. =STANDARDIZE
1. =NORM.DIST
1. =STDEV.P
1. =AVEDEV
66. Which
Excel function would be least useful to calculate the quartiles for a column of
data?
1. =STANDARDIZE
1. =PERCENTILE.EXC
1. =QUARTILE.EXC
1. =RANK
67. A
sample of 50 breakfast customers of McDonald’s showed the spending below. Which
statement is least likely to be correct?
1. The
median is very close to the midhinge.
5. The
median purchase is slightly less than $5.
7. About
75 percent of the customers spend less than $7.
1. The
mean is a reasonable measure of center.
68. VenalCo
Market Research surveyed 50 individuals who recently purchased a certain CD,
revealing the age distribution shown below. Which statement is least
defensible?
1. The
mean age probably exceeds the median age.
1. The
mode would be a reasonable measure of center.
1. The
data are somewhat skewed to the left.
1. The
CD is unlikely to appeal to retirees.
69. Given
a sample of three items (X = 4, 6, 5), which statement is incorrect?
5. The
geometric mean is 5.2.
1. The standard
deviation is 1.
1. The
coefficient of variation is 20 percent.
1. The
quartiles are useless.
70. A
sample of customers from Barnsboro National Bank shows an average account
balance of $315 with a standard deviation of $87. A sample of customers from
Wellington Savings and Loan shows an average account balance of $8350 with a
standard deviation of $1800. Which statement about account balances is correct?
1. Barnsboro
Bank has more variation.
1. Wellington
S&L has more variation.
1. Both
have the same variation.
71. Histograms
are best used to:
1. provide
a visual estimate of the standard deviation.
1. show
the quartiles of the data set.
1. assess
the shape of the distribution.
1. reveal
the interquartile range of the data set.
72. The ______________
shows the relationship between two variables.
1. box
plot
1. bar
chart
1. histogram
1. scatter
plot
73. If
the mean and median of a population are the same, then its distribution is:
1. normal.
1. skewed.
1. symmetric.
1. uniform.
74. In
the following data set {7, 5, 0, 2, 7, 15, 5, 2, 7, 18, 7, 3, 0}, the value 7
is:
1. the
mean.
1. the
mode.
1. both
the mode and median.
1. both
the mean and mode.
75. The
median of 600, 800, 1000, 1200 is:
800.
800.
1000. 1000.
900.
900.
950.
950.
76. The
25th percentile for waiting time in a doctor’s office is 19 minutes. The 75th
percentile is 31 minutes. The interquartile range is:
1. 12
minutes.
1. 16
minutes.
1. 22
minutes.
1. impossible
to determine without knowing n.
77. The
25th percentile for waiting time in a doctor’s office is 19 minutes. The 75th
percentile is 31 minutes. Which is incorrect regarding the fences?
1. The
upper inner fence is 49 minutes.
1. The
upper outer fence is 67 minutes.
1. A
waiting time of 45 minutes exceeds the upper inner fence.
1. A
waiting time of 70 minutes would be an outlier.
78. When
using Chebyshev’s Theorem, the minimum percentage of sample observations that
will fall within two standard deviations of the mean will be __________ the
percentage within two standard deviations if a normal distribution is assumed
(Empirical Rule).
1. smaller
than
1. greater
than
1. the
same as
79. Which
distribution is least likely to be skewed to the right by high values?
1. Annual
incomes of n passengers on a flight from New York to London
1. Weekend
gambling losses of n customers at a major casino
1. Accident
damage losses by n renters of an auto rental company
1. Cost
of a plain McDonald’s hamburger in n U.S. cities
80. Based
on daily measurements, Bob’s weight has a mean of 200 pounds with a standard
deviation of 16 pounds, while Mary’s weight has a mean of 125 pounds with a
standard deviation of 15 pounds. Who has the smaller relative variation?
1. Bob
1. Mary
1. They
are the same.
81. Frieda
is 67 inches tall and weighs 135 pounds. Women her age have a mean height of 65
inches with a standard deviation of 2.5 inches and a mean weight of 125 pounds
with a standard deviation of 10 pounds. In relative terms, it is correct to say
that:
1. Frieda
is taller and thinner than women in her age group.
1. for
this group of women, weight has greater variation than height.
1. Frieda’s
height is more unusual than her weight.
1. the
variation coefficient exceeds 10 percent for both height and weight.
82. Which
statement is false?
1. The
coefficient of variation cannot be used when the mean is zero.
1. The
standard deviation is in the same units as the mean (e.g., kilograms).
1. The
mean from a frequency tabulation may differ from the mean from raw data.
1. The
skewness coefficient is zero in a sample from any normal distribution.
83. The
values of xmin and xmax can be inferred accurately except in a:
1. box
plot.
1. dot
plot.
1. histogram.
1. scatter
plot.
84. Which
of the following statements is likely to be true?
1. The median
personal income of California taxpayers would probably be near the mean.
1. The
interquartile range offers a measure of income inequality among California
residents.
1. For
income, the sum of squared deviations about the mean is negative about half the
time.
1. For
personal incomes in California, outliers in either tail would be equally
likely.
85. Which
statistics offer robust (resistant to outliers) measures of center?
1. Mean,
midrange, mode.
1. Median,
midhinge, trimmed mean.
1. Trimmed
mean, midrange, midhinge.
1. Mean,
mode, quartiles.
86. The
Empirical Rule says that:
1. most
business data sets are normally distributed.
1. outliers
are within three standard deviations of the mean.
1. in
most business data we expect the mean and median to be similar.
1. about
32 percent of the data are beyond one standard deviation from the mean.
87. Three
randomly chosen Seattle students were asked how many round trips they made to
Canada last year. Their replies were 3, 4, 5. The geometric mean is:
3. 3.877.
4. 4.000.
3. 3.915.
4. 4.422.
88. Three
randomly chosen California students were asked how many times they drove to
Mexico last year. Their replies were 4, 5, 6. The geometric mean is:
3. 3.87.
5. 5.00.
5. 5.42.
4. 4.93.
89. Three
randomly chosen Colorado students were asked how many times they went rock
climbing last month. Their replies were 5, 6, 7. The standard deviation is:
1. 1.212.
1. 0.816.
1. 1.000.
1. 1.056.
90. Patient
survival times after a certain type of surgery have a very right-skewed
distribution due to a few high outliers. Consequently, which statement is most
likely to be correct?
1. Median
> Midrange
1. Mean
< Median
1. Mean
> Midrange
1. Mean
> Trimmed Mean
91. So
far this year, stock A has had a mean price of $6.58 per share with a standard
deviation of $1.88, while stock B has had a mean price of $10.57 per share with
a standard deviation of $3.02. Which stock is more volatile?
1. Stock
A
1. Stock
B
1. They
are the same.
92. Outliers
are indicated using fences on a
1. box
plot.
1. dot
plot.
1. histogram.
1. Pareto
chart.
93. Which
is not a measure of variability?
1. Mean
absolute deviation (MAD)
1. Range
1. Coefficient
of variation
1. Trimmed
mean
94. Twelve
randomly chosen students were asked how many times they had missed class during
a certain semester, with this result: 3, 2, 1, 2, 1, 5, 9, 1, 2, 3, 3, 10. The
geometric mean is:
1.
2. 2.604
1. 1.517
1.
95. Twelve
randomly chosen students were asked how many times they had missed class during
a certain semester, with this result: 3, 2, 1, 2, 1, 5, 9, 1, 2, 3, 3, 10. The
median is:
7. 7.0.
3. 3.0.
3. 3.5.
2. 2.5.
96. One
disadvantage of the range is that:
1. only
extreme values are used in its calculation.
1. it is
expressed in different units than the mean.
1. it
does not exist for some data sets.
1. it is
undefined if any X values are 0 or negative.
97. Which
is a characteristic of the standard deviation?
1. It is
not greatly affected by outliers.
1. It is
measured in the same units as the mean.
1. It measures
dispersion around the median.
1. It
has a natural, concrete meaning.
98. Twelve
randomly chosen students were asked how many times they had missed class during
a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For
this sample, the geometric mean is:
2. 2.158.
1. 1.545.
2. 2.376.
3. 3.017.
99. Twelve
randomly chosen students were asked how many times they had missed class during
a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18. For
this sample, the median is:
2. 2.
3. 3.
3. 3.5.
2. 2.5.
100.
Twelve randomly chosen students were asked how many times they
had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3,
4, 3, 1, 1, 5, 18. For this sample, which measure of center is least
representative of the “typical” student?
1. Mean
1. Median
1. Mode
1. Midrange
101.
Here are statistics on order sizes of Megalith Construction
Supply’s shipments of two kinds of construction materials last year.
Which order sizes have greater variability?
1. Girders
1. Rivets
1. They
are the same.
1. Cannot
be determined without knowing n
102.
The quartiles of a distribution are most clearly revealed in
which display?
1. Box
plot
1. Scatter
plot
1. Histogram
1. Dot
plot
103.
The sum of the deviations around the mean is:
1. greater
than zero if data are right-skewed.
1. smaller
when the units are smaller (e.g., milligrams versus kilograms).
1. always
zero.
1. dependent
on the sample size.
104.
What does the graph below (profit/sales ratios for 25 Fortune
500 companies) reveal?
1. That
the median exceeds the mean.
1. That
the data are slightly left-skewed.
8. That
the interquartile range is about 8.
1. That
the distribution is bell-shaped.
105.
Find the sample correlation coefficient for the following data.
1. .8911
1. .9132
1. .9822
1. .9556
106.
Heights of male students in a certain statistics class range
from Xmin = 61 to Xmax = 79. Applying the Empirical Rule, a reasonable estimate
of σ would be:
2. 2.75.
3. 3.00.
3. 3.25.
3. 3.50.
107.
A reporter for the campus paper asked five randomly chosen
students how many occupants, including the driver, ride to school in their
cars. The responses were 1, 1, 1, 1, 6. The coefficient of variation is:
1. 25 percent.
1. 250
percent.
1. 112
percent.
1. 100
percent.
108.
A smooth distribution with one mode is negatively skewed (skewed
to the left). The median of the distribution is $65. Which of the following is
a reasonable value for the distribution mean?
1. $76
1. $54
1. $81
1. $65
109.
In a positively skewed distribution, the percentage of
observations that fall below the median is:
1. about
50 percent.
1. less
than 50 percent.
1. more
than 50 percent.
1. can’t
tell without knowing n.
110.
Which is a weakness of the mode?
1. It
does not apply to qualitative data.
1. It is
inappropriate for continuous data.
1. It is
hard to calculate when n is small.
1. It is
usually about the same as the median.
111.
The mode is least appropriate for:
1. continuous
data.
1. categorical
data.
1. discrete
data.
1. Likert
scale data.
112.
Craig operates a part-time snow-plowing business using a 2002
GMC 2500 HD extended cab short box truck. This box plot of Craig’s MPG on 195
tanks of gas does not support which statement?
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