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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 rightskewed.
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 rightskewed, 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 leftskewed 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 unitfree 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 bellshaped, 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 leftskewed 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 leftskewed.
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 rightskewed 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.
1.517
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 rightskewed.
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 leftskewed.
8.
That the interquartile range is about 8.
1.
That the distribution is bellshaped.
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. is:
In a positively skewed distribution, the percentage of observations that fall below the median
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 parttime snowplowing 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?