Chapter 3 – Descriptive Statistics: Numerical Measures
Multiple Choice
1. The interquartile range is the difference between the
a.
first and second quartiles
b.
first and third quartiles
c.
second and third quartiles
d.
second and fourth quartiles
2. The coefficient of determination is equal to the
a.
absolute value of the correlation coefficient
b.
squared value of the correlation coefficient
c.
square-root of the correlation coefficient
d.
inverse value of the correlation coefficient
3. Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains
outliers?
a.
b.
c.
d.
a
4. An important measure of location for categorical data is the
a.
mean
b.
median
c.
mode
d.
margin
c
5. The measure of variability easiest to compute, but seldom used as the only measure, is the
a.
range
b.
interquartile range
c.
standard deviation
d.
variance
a
6. In computing descriptive statistics for grouped data, the ____ are used to approximate the data values in each class.
a.
class lower limits
Chapter 3 – Descriptive Statistics: Numerical Measures
b.
class upper limits
c.
class midpoints
d.
class ranges
c
7. Which of the following is not a measure of variability of a single variable?
a.
range
b.
covariance
c.
standard deviation
d.
coefficient of variation
8. The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within one
standard deviation of the mean is approximately
a.
33
b.
50
c.
68
d.
95
c
9. A box plot is a graphical representation of data that is based on
a.
the empirical rule
b.
z-scores
c.
a histogram
d.
a five-number summary
10. The coefficient of variation indicates how large the standard deviation is relative to the
a.
mean
b.
median
c.
range
d.
variance
a
11. Which of the following descriptive statistics is not measured in the same units as the data?
a.
35th percentile
b.
standard deviation
c.
variance
d.
interquartile range
c
12. A numerical measure computed from a sample, such as sample mean, is known as a
a.
population parameter
b.
sample parameter
c.
sample statistic
d.
population mean
c
13. A numerical measure, such as a mean, computed from a population is known as a
a.
population parameter
b.
sample parameter
c.
sample statistic
d.
sample mean
a
14. Since the population size is always larger than the sample size, then the sample statistic
a.
can never be larger than the population parameter
b.
can never be equal to the population parameter
c.
can never be zero
d.
None of the other answers are correct.
15. μ is an example of a
a.
population parameter
b.
sample statistic
c.
population variance
d.
mode
a
16. The mean of a sample is
a.
always equal to the mean of the population
b.
always smaller than the mean of the population
c.
computed by summing the data values and dividing the sum by (n − 1)
d.
computed by summing all the data values and dividing the sum by the number of items
17. The mean of the sample
a.
is always larger than the mean of the population from which the sample was taken
b.
is always smaller than the mean of the population from which the sample was taken
Chapter 3 – Descriptive Statistics: Numerical Measures
c.
can never be zero
d.
None of the other answers are correct.
18. Since the population is always larger than the sample, the value of the sample mean
a.
is always smaller than the true value of the population mean
b.
is always larger than the true value of the population mean
c.
is always equal to the true value of the population mean
d.
could be larger, equal to, or smaller than the true value of the population mean
19. After the data has been arranged from smallest value to largest value, the value in the middle is called the
a.
range
b.
median
c.
mean
d.
None of the other answers are correct.
20. If a data set has an even number of observations, the median
a.
can not be determined
b.
is the average value of the two middle items
c.
must be equal to the mean
d.
is the average value of the two middle items when all items are arranged in ascending order
21. Since the median is the middle value of a data set, it must always be
a.
smaller than the mode
b.
larger than the mode
c.
smaller than the mean
d.
None of the other answers are correct.
22. The most frequently occurring value of a data set is called the
a.
range
b.
mode
c.
mean
d.
None of the other answers are correct.
23. Since the mode is the most frequently occurring data value, it
a.
can never be larger than the mean
b.
is always larger than the median
c.
is always larger than the mean
d.
None of the other answers are correct.
24. Excel’s __________ function can be used to compute the mean.
a.
MAX
b.
AVERAGE
c.
MEDIAN
d.
MODE
25. Excel’s __________ function can be used to compute the median.
a.
MAX
b.
AVERAGE
c.
MEDIAN
d.
MODE
c
26. Excel’s __________ function can be used to compute the mode.
a.
MAX
b.
AVERAGE
c.
MEDIAN
d.
MODE.SNGL
27. Excel provides functions for computing the
a.
mean
b.
median
c.
mode
d.
Excel provides functions for all of these.
28. In computing the pth percentile, if the index i is an integer the pth percentile is the
a.
data value in position i
b.
data value in position i + 1
c.
average of data values in position i and i + 1
c
29. The 50th percentile is the
a.
mode
b.
median
c.
mean
d.
third quartile
30. The 75th percentile is also the
a.
first quartile
b.
second quartile
c.
third quartile
d.
fourth quartile
c
31. The first quartile
a.
contains at least one third of the data elements
b.
is the same as the 25th percentile
c.
is the same as the 50th percentile
d.
is the same as the 75th percentile
32. Which of the following is not a measure of location?
a.
mean
b.
median
c.
variance
d.
mode
c
33. The median of a sample will always equal the
a.
mode
b.
mean
c.
50th percentile
d.
all of these answers are correct
c
34. The measure of location that is the most likely to be influenced by extreme values in the data set is the
a.
range
b.
median
Chapter 3 – Descriptive Statistics: Numerical Measures
c.
mode
d.
mean
d
1
Exhibit 3-1
A researcher has collected the following sample data.
5
12
6
8
5
6
7
5
12
4
35. Refer to Exhibit 3-1. The median is
a.
5
b.
6
c.
7
d.
8
b
1
36. Refer to Exhibit 3-1. The mode is
a.
5
b.
6
c.
7
d.
8
a
1
37. Refer to Exhibit 3-1. The mean is
a.
5
b.
6
c.
7
d.
8
c
1
38. Refer to Exhibit 3-1. The 75th percentile is
a.
5
b.
6
c.
7
d.
8
d
1
Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
3
5
12
3
2
39. Refer to Exhibit 3-2. The variance is
a.
80
b.
4.062
c.
13.2
d.
16.5
d
1
40. Refer to Exhibit 3-2. The standard deviation is
a.
8.944
b.
4.062
c.
13.2
d.
16.5
b
1
41. Refer to Exhibit 3-2. The coefficient of variation is
a.
72.66%
b.
81.24%
c.
264%
d.
330%
b
1
42. Refer to Exhibit 3-2. The range is
a.
1
b.
2
c.
10
d.
12
c
1
43. Refer to Exhibit 3-2. The interquartile range is
a.
1
b.
2
c.
10
d.
12
b
1
Exhibit 3-3
Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500
and a standard deviation of $2,500.
44. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Chapter 3 – Descriptive Statistics: Numerical Measures
a.
37.5
b.
2
c.
-2
d.
0.92
b
1
45. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $28,000 is
a.
28
b.
1.8
c.
-1.8
d.
0.78
c
1
Exhibit 3-4
The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.
Speed (MPH)
Frequency
50 − 54
2
55 − 59
4
60 − 64
5
65 − 69
10
70 − 74
9
75 − 79
5
35
46. Refer to Exhibit 3-4. The mean is
a.
35
b.
670
c.
10
d.
67
d
1
47. Refer to Exhibit 3-4. The variance is
a.
6.969
b.
7.071
c.
48.570
d.
50.000
d
1
48. Refer to Exhibit 3-4. The standard deviation is
a.
6.969
b.
7.071
c.
48.570
Chapter 3 – Descriptive Statistics: Numerical Measures
d.
50.000
49. The difference between the largest and the smallest data values is the
a.
variance
b.
interquartile range
c.
range
d.
coefficient of variation
c
50. The interquartile range is
a.
the 50th percentile
b.
another name for the variance
c.
the difference between the largest and smallest values
d.
the difference between the third quartile and the first quartile
51. The interquartile range is used as a measure of variability to overcome what difficulty of the range?
a.
the sum of the range variances is zero
b.
the range is difficult to compute
c.
the range is influenced too much by extreme values
d.
the range is negative
c
52. The sample variance
a.
is always smaller than the true value of the population variance
b.
is always larger than the true value of the population variance
c.
could be smaller, equal to, or larger than the true value of the population variance
d.
can never be zero
c
53. The variance of the sample
a.
can never be negative
b.
can be negative
c.
cannot be zero
d.
cannot be less than one
a
54. The population variance can never be
Chapter 3 – Descriptive Statistics: Numerical Measures
a.
zero
b.
larger than the standard deviation
c.
negative
d.
all of these are correct
c
1
55. The sum of deviations of the individual data elements from their mean is
a.
always greater than zero
b.
always less than zero
c.
sometimes greater than and sometimes less than zero, depending on the data elements
d.
always equal to zero
d
1
56. The value of the sum of the squared deviations from the mean, i.e., must always be
a.
less than the mean
b.
negative
c.
either positive or negative depending on whether the mean is negative or positive
d.
at least zero
d
1
57. If the variance of a data set is correctly computed with the formula using n − 1 in the denominator, which of the
following is true?
a.
the data set is a sample
b.
the data set is a population
c.
the data set could be either a sample or a population
d.
the data set is from a census
a
1
58. During a cold winter, the temperature stayed below zero for ten days (ranging from –20 to -5). The variance of the
temperatures of the ten day period
a.
is negative since all the numbers are negative
b.
must be at least zero
c.
can not be computed since all the numbers are negative
d.
can be either negative or positive
b
1
59. The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals
a.
0
b.
4096
c.
8
Chapter 3 – Descriptive Statistics: Numerical Measures
d.
6,561
c
60. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals
a.
8
b.
10
c.
6,400
d.
4,096
61. The numerical value of the standard deviation can never be
a.
larger than the variance
b.
zero
c.
negative
d.
all of these statements are correct
c
62. Excel’s __________ function can be used to compute the sample variance.
a.
MAX
b.
MODE
c.
VAR.S
d.
STDEV
c
63. Excel’s __________ function can be used to compute the population variance.
a.
MAX
b.
MODE
c.
VAR
d.
None of the other answers are correct.
64. Excel’s __________ function can be used to compute the sample standard deviation.
a.
MAX
b.
MODE
c.
VAR
d.
STDEV.S
65. Excel’s __________ function can be used to compute the population standard deviation.
Chapter 3 – Descriptive Statistics: Numerical Measures
a.
MAX
b.
MODE
c.
STDEV
d.
None of the other answers are correct.
66. The coefficient of variation is
a.
the same as the variance
b.
the square root of the variance
c.
the square of the standard deviation
d.
None of the other answers are correct.
67. The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated
mean = 160
range = 60
mode = 165
variance = 324
median = 170
The coefficient of variation equals
a.
0.1125%
b.
11.25%
c.
203.12%
d.
0.20312%
68. Which of the following is a measure of dispersion?
a.
percentiles
b.
quartiles
c.
interquartile range
d.
all of these are measures of dispersion
c
69. Which of the following is not a measure of dispersion?
a.
the range
b.
the 50th percentile
c.
the standard deviation
d.
the interquartile range
70. The measure of dispersion that is influenced most by extreme values is
Chapter 3 – Descriptive Statistics: Numerical Measures
a.
the variance
b.
the standard deviation
c.
the range
d.
the interquartile range
ANSWER:
c
POINTS:
71. The descriptive measure of dispersion that is based on the concept of a deviation about the mean is
a.
the range
b.
the interquartile range
c.
both the range and the interquartile range
d.
the standard deviation
ANSWER:
POINTS:
72. If two groups of numbers have the same mean, then their
a.
standard deviations must also be equal
b.
medians must also be equal
c.
modes must also be equal
d.
None of the other answers are correct.
ANSWER:
POINTS:
73. The descriptive measure that is not measured in the same units as the original data is the
a.
median
b.
standard deviation
c.
mode
d.
variance
ANSWER:
POINTS:
74. Which of the following symbols represents the size of the population?
a.
σ 2
b.
σ
c.
μ
d.
N
ANSWER:
POINTS:
75. Which of the following symbols represents the size of the sample?
a.
σ 2
b.
σ
c.
N
d.
n
Chapter 3 – Descriptive Statistics: Numerical Measures
76. Which of the following symbols represents the mean of the population?
a.
σ 2
b.
σ
c.
μ
d.
77. Which of the following symbols represents the mean of the sample?
a.
σ 2
b.
σ
c.
μ
d.
78. Which of the following symbols represents the variance of the population?
a.
σ 2
b.
σ
c.
μ
d.
79. The symbol σ 2 is used to represent the
a.
variance of the population
b.
standard deviation of the sample
c.
standard deviation of the population
d.
None of the other answers are correct.
80. Which of the following symbols represents the standard deviation of the population?
a.
σ 2
b.
σ
c.
μ
d.
81. The symbol σ is used to represent the
Chapter 3 – Descriptive Statistics: Numerical Measures
a.
variance of the population
b.
standard deviation of the sample
c.
standard deviation of the population
d.
None of the other answers are correct.
c
82. The __________ denotes the number of standard deviations xi is from the mean .
a.
range
b.
median
c.
z-score
d.
third quartile
c
83. A(n) __________ is an unusually small or unusually large data value.
a.
sample statistic
b.
median
c.
z-score
d.
outlier
84. __________ can be used to make statements about the proportion of data values that must be within a specified
number of standard deviations of the mean.
a.
Chebyshev’s theorem
b.
The empirical rule
c.
A five-number summary
d.
A box plot
a
85. __________ can be used to determine the percentage of data values that must be within one, two, and three standard
deviations of the mean for data having a bell-shaped distribution.
a.
Chebyshev’s theorem
b.
empirical rule
c.
five-number summary
d.
box plot
86. In a five-number summary, which of the following is not used for data summarization?
a.
the smallest value
b.
the largest value
c.
the median