Chapter 5—Measures of Variability
MULTIPLE CHOICE QUESTIONS
5.1 + Which of the following is NOT a measure of variability?
5.2 Dispersion refers to
5.3 + An outlier
5.4 If we eliminate the top and bottom 25% of the data and take the range of what
remains we have the
5.5 A trimmed sample is one that
5.6 + The population variance is
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5.7 + We generally like the standard deviation when we are trying to describe a sample
of data because
5.8 + When calculating the standard deviation we divide by N-1 rather than N because
the result is
5.9 The variance can best be thought of as the
5.10 What do we mean by an unbiased statistic?
5.11 The difference between s and is that is
5.12 The vertical line in the center of a box plot
5.13 In a boxplot the width of the box encompasses
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5.14 The whiskers in a boxplot
5.15 + Data points at the extremes of the distribution have
5.16 Data points that lie outside the whiskers in a boxplot are often referred to as
5.17 + If the whiskers on a boxplot are much longer on the right than on the left, we
would suspect that the distribution is
5.18 + People in the stock market refer to a measure called the “standard deviation,”
although it is calculated somewhat differently from the one discussed here. It is a
good guess that this measure refers to
5.19 + Which of the following sets of data is likely to have the smallest standard
deviation?
5.20 If we multiply a set of data by a constant, such as converting feet to inches, we
will
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5.21 As you increase the number of observations in a sample from 50 to 500, you are
most likely to
5.22 The university counseling center has treated a large number of students for
depression. They find that the standard deviation of depression scores for their
pool of students is substantially higher after treatment than before treatment. The
most likely explanation is
5.23 + The standard deviation for the numbers 8, 9, and 10 is
5.24 If we know that a set of test scores has a mean of 75 and a standard deviation of 8,
we would conclude that
5.25 + You would obtain a negative value for the variance if
5.26 The range is
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5.27 + Which of the following is NOT a method of describing data that reduces the role
of outliers on the measurement of a data set’s variability?
5.28 The problem with measuring dispersion by merely averaging all the deviations
between each score and the overall mean is that
5.29 + A data set of intelligence scores was collected from high school seniors. The IQ
scores ranged from 82 to 113. Which of the following is probably NOT a
reasonable estimate of the standard deviation?
5.30 The equation
2
1+locationmedian
is used to calculate the
5.31 The US Census Bureau collected data on family composition and found that
samples from different parts of the country gave very different results for the
mean number of family members living in households. If all of the data were
combined to one data set,
5.32 + The interquartile range
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5.33 If the average adult male in the United States is 5’ 9” tall, and the standard
deviation for height is 2”, approximately how many adult males would you expect
5.34 Errors that can lead to outliers can occur in
5.35+ The disadvantage of using an interquartile range is that
5.36 Given the numbers 1, 2, and 3, the standard deviation is
5.37 If I continue to draw observations from a population and recalculate the mean
each time I add an observation, the mean will approach _______ as the sample
size increases.
5.38 A “hinge” is another word for
5.39 A boxplot is better than a statistic such as the mean when your purpose is
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5.40 We normally compute the variance using N – 1 in the denominator because
5.41 The population variance is
5.42 Data points at the extremes of the distribution have
TRUE/FALSE QUESTIONS
the center.
the range.
susceptible to distortion due to outliers.
deviation.
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Answer the next two questions based on the following box-plot.
20
18
16
14
12
10
OPEN-ENDED QUESTIONS
5.53 Answer the following questions based on this set of numbers:
1 2 2 3 3 3 4 5
a) What is the range?
b) What is the variance?
c) What is the standard deviation?
5.54 A sample of 20 families reported how many children they have. Answer the
following questions based on the summary table below.
Number of children
0
2
4
Number of families
3
7
1
a) What is the range?
b) What is the variance?
c) What is the standard deviation?
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5.55 Based on the same data, calculate:
a) The median location
b) The median
c) The hinge location
d) The upper hinge
e) The lower hinge
f) H spread
g) Lower fence
h) Upper fence
i) Lower adjacent value
j) Upper adjacent value
5.56 Create a box plot for the above data.
5.57 Create two sets of scores with equal ranges, but different variances.
5.58 What happens to the standard deviation when a constant is added to each score?
Use the following set of data, and a constant of 2 to illustrate your answer.
1 2 3 4
5.59 Answer the following questions based on this distribution of exam scores.
120100806040200
1
a) What is the median?
b) Are there outliers?
c) Does the distribution seem skewed? If so, is it positively, or negatively
skewed?
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5.60 Compare the distribution of exam scores for students who did and did not read the
textbook prior to taking the exam. Discuss measures of variability and of central
tendency.
1116N =
Read textDid not read text
120
110
100
90
80
70
60
50
40
30
20
10
0
1
5.61 Given the following distribution, which would be the least useful measure of
central tendency? Explain your answer.
Number of Children
10.0 – 11.0
9.0 – 10.0
8.0 – 9.0
7.0 – 8.0
6.0 – 7.0
5.0 – 6.0
4.0 – 5.0
3.0 – 4.0
2.0 – 3.0
1.0 – 2.0
0.0 – 1.0
14
12
10
8
6
4
2
0
5.62 Construct two small sets of data that have the same mean, but a different standard
deviation.
Answers to Open-ended Questions
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