BSTAT2 2nd Edition By Gerald Keller – Test Bank
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Sample Test
CHAPTER 3: NUMERICAL DESCRIPTIVE TECHNIQUES
TRUE/FALSE
1. The
mean is affected by extreme values but the median is not.
ANS:
T
NAT: Analytic; Descriptive Statistics
2. The
mean is a measure of variability.
ANS:
F
NAT: Analytic; Descriptive Statistics
3. In a
histogram, the proportion of the total area which must be to the left of the
median is more than 0.50 if the distribution is positively skewed.
ANS: F
NAT: Analytic; Descriptive Statistics
4. A
data sample has a mean of 107, a median of 122, and a mode of 134. The
distribution of the data is positively skewed.
ANS:
F
NAT: Analytic; Descriptive Statistics
5. m is
a population parameter and is a sample statistic.
ANS:
T
NAT: Analytic; Descriptive Statistics
6. In a
bell shaped distribution, there is no difference in the values of the mean,
median, and mode.
ANS: T
NAT: Analytic; Descriptive Statistics
7. Lily
has been keeping track of what she spends to eat out. The last week’s
expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49,
$14.53, and $7.66. The mean amount Lily spends on meals is $8.35.
ANS:
T
NAT: Analytic; Descriptive Statistics
8. In a
negatively skewed distribution, the mean is smaller than the median and the
median is smaller than the mode.
ANS:
T
NAT: Analytic; Descriptive Statistics
9. The
median of a set of data is more representative than the mean when the mean is
larger than most of the observations.
ANS:
T
NAT: Analytic; Descriptive Statistics
10.
The value of the mean times the number of observations equals
the sum of the observations.
ANS:
T
NAT: Analytic; Descriptive Statistics
11.
In a histogram, the proportion of the total area which must be
to the left of the median is less than 0.50 if the distribution is negatively
skewed.
ANS:
F
NAT: Analytic; Descriptive Statistics
12.
In a histogram, the proportion of the total area which must be
to the right of the mean is exactly 0.50 if the distribution is symmetric and
unimodal.
ANS:
T
NAT: Analytic; Descriptive Statistics
13.
Suppose a sample of size 50 has a sample mean of 20. In this
case, the sum of all observations in the sample is 1,000.
ANS:
T
NAT: Analytic; Descriptive Statistics
14.
The median of an ordered data set with 30 items would be the
average of the 15th and the 16th observations.
ANS:
T
NAT: Analytic; Descriptive Statistics
15.
If the median, median and mode are all equal, the histogram must
be symmetric and bell shaped.
ANS:
F
NAT: Analytic; Descriptive Statistics
16.
The value of the standard deviation may be either positive or
negative, while the value of the variance will always be positive.
ANS:
F
NAT: Analytic; Descriptive Statistics
17.
The difference between the largest and smallest observations in
an ordered data set is called the range.
ANS:
T
NAT: Analytic; Descriptive Statistics
18.
The standard deviation is expressed in terms of the original
units of measurement but the variance is not.
ANS:
T
NAT: Analytic; Descriptive Statistics
19.
The data set 10, 20, 30 has the same variance as the data set
100, 200, 300.
ANS:
F
NAT: Analytic; Descriptive Statistics
20.
The Empirical Rule states that the percentage of observations in
a data set (providing that the data set is bell shaped) that fall within one
standard deviation of their mean is approximately 75%.
ANS:
F
NAT: Analytic; Descriptive Statistics
21.
A population with 200 elements has a variance of 20. From this
information, it can be shown that the population standard deviation is 10.
ANS: F
NAT: Analytic; Descriptive Statistics
22.
If two data sets have the same range, the distances from the
smallest to largest observations in both sets will be the same.
ANS:
T
NAT: Analytic; Descriptive Statistics
23.
The coefficient of variation is a measure of variability.
ANS:
T
NAT: Analytic; Descriptive Statistics
24.
The standard deviation is the positive square root of the
variance.
ANS: T
NAT: Analytic; Descriptive Statistics
25.
If two data sets have the same standard deviation, they must
have the same coefficient of variation.
ANS:
F
NAT: Analytic; Descriptive Statistics
26.
The units for the variance are the same as the units for the
original data (for example, feet, inches, etc.).
ANS:
F
NAT: Analytic; Descriptive Statistics
27.
The variance is more meaningful and easier to interpret compared
to the standard deviation.
ANS:
F
NAT: Analytic; Descriptive Statistics
28.
The range is considered the weakest measure of variability.
ANS:
T
NAT: Analytic; Descriptive Statistics
29.
The coefficient of variation allows us to compare two sets of
data based on different measurement units.
ANS:
T
NAT: Analytic; Descriptive Statistics
30.
If the observations are in the millions, a standard deviation of
10 would be considered small. If the observations are all less than 50, a
standard deviation of 10 would be considered large.
ANS:
T
NAT: Analytic; Descriptive Statistics
31.
The distance between the 25th percentile
and the median is always the same as the distance between the median and the 75th percentile.
ANS:
F
NAT: Analytic; Descriptive Statistics
32.
The interquartile range will always exceed that of the range.
ANS:
F
NAT: Analytic; Descriptive Statistics
33.
The interquartile range is found by taking the difference
between the 1st and 3rd quartiles and dividing that value by 2.
ANS:
F
NAT: Analytic; Descriptive Statistics
34.
Quartiles divide the observations in a data set into four parts
with the same amount of data in each part.
ANS:
T
NAT: Analytic; Descriptive Statistics
35.
The length of the box in a box plot portrays the interquartile
range.
ANS:
T
NAT: Analytic; Descriptive Statistics
36.
Expressed in percentiles, the interquartile range is the
difference between the 25th and 75th percentiles.
ANS:
T
NAT: Analytic; Descriptive Statistics
37.
If the distribution of a data set were perfectly symmetric, the
distance from Q1 to
the median would always equal the distance from Q3 to
the median in a box plot.
ANS:
T
NAT: Analytic; Descriptive Statistics
38.
The first and second quartiles of a data set can never be equal.
ANS:
F
NAT: Analytic; Descriptive Statistics
39.
The value for Q3 can
never be smaller than the value for Q1.
ANS:
T
NAT: Analytic; Descriptive Statistics
40.
In symmetric data, the value for Q2 is
always halfway between Q1 and Q3.
ANS:
T
NAT: Analytic; Descriptive Statistics
41.
Percentiles can be converted into quintiles and deciles, where
quintiles divide the data into fifths and deciles divide the data into tenths.
ANS: T
NAT: Analytic; Descriptive Statistics
42.
The 5-number summary consists of the smallest observation, the
first quartile, the median, the third quartile, and the largest observation.
ANS:
T
NAT: Analytic; Descriptive Statistics
43.
A box plot is a graphical representation of the 5-number
summary.
ANS:
T
NAT: Analytic; Descriptive Statistics
44.
The interquartile range is an interval of numbers starting
at Q1 and
ending at Q3.
ANS:
F
NAT: Analytic; Descriptive Statistics
45.
The line drawn within the box of a box plot always represents
the mean.
ANS:
F
NAT: Analytic; Descriptive Statistics
46.
The line drawn within the box of a box plot always represents
the median.
ANS:
T
NAT: Analytic; Descriptive Statistics
47.
The interquartile range is a measure of variability in a set of
data.
ANS:
T
NAT: Analytic; Descriptive Statistics
48.
Expressed in percentiles, the fifth decile is the 50th percentile
or the median.
ANS:
T
NAT: Analytic; Descriptive Statistics
49.
If the covariance of x and y is 26.16, and the
standard deviation of x is
32.7, then the slope of the least squares line is b1 =.80.
ANS:
F
NAT: Analytic; Descriptive Statistics
50.
If , , n =
12, and the slope equals 0.5, then the y-intercept
of the least squares line is b0 =
276.08.
ANS:
T
NAT: Analytic; Descriptive Statistics
51.
If the coefficient of correlation r = 0, there can be
no linear relationship between the dependent variable y and the
independent variable x.
ANS:
T
NAT: Analytic; Descriptive Statistics
52.
If the coefficient of correlation r = 0, there can be
no relationship whatsoever between the dependent variable y and the
independent variable x.
ANS:
F
NAT: Analytic; Descriptive Statistics
53.
If the coefficient of correlation r = -.81, the
standard deviations of x and y are 20 and 25,
respectively, then cov(x, y) must be -405.0.
ANS:
T
NAT: Analytic; Descriptive Statistics
54.
The advantage that the coefficient of correlation has over the
covariance is that the former has set lower and upper limits.
ANS:
T
NAT: Analytic; Descriptive Statistics
55.
If the standard deviations of x and y are 12.5 and 10.8, respectively, and
the covariance is 118.8, then the coefficient of correlation r is 0.88.
ANS:
T
NAT: Analytic; Descriptive Statistics
56.
Generally speaking, if two variables are unrelated, the
covariance will be a number close to zero.
ANS:
T
NAT: Analytic; Descriptive Statistics
57.
If the standard deviation of x is 18, the covariance of x and y is 120, the
coefficient r =
0.90, then the standard deviation of y is
54.87.
ANS:
F
NAT: Analytic; Descriptive Statistics
58.
Three measures of the linear relationship between x and y are the
coefficient of correlation, the coefficient of determination, and the
coefficient of variation.
ANS:
F
NAT: Analytic; Descriptive Statistics
59.
The coefficient of correlation r is a number that indicates the
direction and the strength of the linear relationship between the dependent
variable y and
the independent variable x.
ANS:
T
NAT: Analytic; Descriptive Statistics
60.
The variance is a measure of the linear relationship between two
variables
ANS:
F
NAT: Analytic; Descriptive Statistics
61.
A perfect straight line sloping upward would produce a
correlation coefficient value of 1.0.
ANS: T
NAT: Analytic; Descriptive Statistics
62.
When the standard deviation is expressed as a percentage of the
mean, the result is the coefficient of correlation.
ANS:
F
NAT: Analytic; Descriptive Statistics
63.
If the coefficient of correlation r = ±1, then the
best-fit linear equation will actually include all of the observations.
ANS:
T
NAT: Analytic; Descriptive Statistics
MULTIPLE CHOICE
64.
Which of the following statistics is a measure of central
location?
|
a. |
The mean |
|
b. |
The median |
|
c. |
The mode |
|
d. |
All of these choices are true. |
ANS:
D
NAT: Analytic; Descriptive Statistics
65.
Which measure of central location is meaningful when the data
are ordinal?
|
a. |
The mean |
|
b. |
The median |
|
c. |
The mode |
|
d. |
All of these choices are meaningful for
ordinal data. |
ANS:
C
NAT: Analytic; Descriptive Statistics
66.
Which of the following statements about the mean is not always correct?
|
a. |
The sum of the deviations from the mean
is zero. |
|
b. |
Half of the observations are on either
side of the mean. |
|
c. |
The mean is a measure of the central
location. |
|
d. |
The value of the mean times the number
of observations equals the sum of all observations. |
ANS:
B
NAT: Analytic; Descriptive Statistics
67.
Which of the following statements is true for the following
observations: 9, 8, 7, 9, 6, 11, and 13?
|
a. |
The mean, median and mode are all
equal. |
|
b. |
Only the mean and median are equal. |
|
c. |
Only the mean and mode are equal |
|
d. |
Only the median and mode are equal. |
ANS:
A
NAT: Analytic; Descriptive Statistics
68.
In a histogram, the proportion of the total area which must be
to the left of the median is:
|
a. |
exactly 0.50. |
|
b. |
less than 0.50 if the distribution is
negatively skewed. |
|
c. |
more than 0.50 if the distribution is
positively skewed. |
|
d. |
unknown. |
ANS:
A
NAT: Analytic; Descriptive Statistics
69.
Which measure of central location can be used for both interval
and nominal variables?
|
a. |
The mean |
|
b. |
The median |
|
c. |
The mode |
|
d. |
All of these choices are true. |
ANS:
C
NAT: Analytic; Descriptive Statistics
70.
Which of these measures of central location is not sensitive to
extreme values?
|
a. |
The mean |
|
b. |
The median |
|
c. |
The mode |
|
d. |
All of these choices are true. |
ANS:
B
NAT: Analytic; Descriptive Statistics
71.
In a positively skewed distribution:
|
a. |
the median equals the mean. |
|
b. |
the median is less than the mean. |
|
c. |
the median is larger than the mean. |
|
d. |
the mean can be larger or smaller than
the median. |
ANS:
B
NAT: Analytic; Descriptive Statistics
72.
Which of the following statements about the median is not true?
|
a. |
It is more affected by extreme values
than the mean. |
|
b. |
It is a measure of central location. |
|
c. |
It is equal to Q2. |
|
d. |
It is equal to the mode in a bell
shaped distribution. |
ANS:
A
NAT: Analytic; Descriptive Statistics
73.
Which of the following summary measures is sensitive to extreme
values?
|
a. |
The median |
|
b. |
The interquartile range |
|
c. |
The mean |
|
d. |
The first quartile |
ANS:
C
NAT: Analytic; Descriptive Statistics
74.
In a perfectly symmetric bell shaped “normal” distribution:
|
a. |
the mean equals the median. |
|
b. |
the median equals the mode. |
|
c. |
the mean equals the mode. |
|
d. |
All of these choices are true. |
ANS:
D
NAT: Analytic; Descriptive Statistics
75.
Which of the following statements is true?
|
a. |
When the distribution is positively
skewed, mean > median > mode. |
|
b. |
When the distribution is negatively
skewed, mean < median < mode. |
|
c. |
When the distribution is symmetric and
unimodal, mean = median = mode. |
|
d. |
When the distribution is symmetric and
bimodal, mean = median = mode. |
ANS:
C
NAT: Analytic; Descriptive Statistics
76.
In a histogram, the proportion of the total area which must be
to the right of the mean is:
|
a. |
less than 0.50 if the distribution is
negatively skewed. |
|
b. |
exactly 0.50. |
|
c. |
more than 0.50 if the distribution is
positively skewed. |
|
d. |
exactly 0.50 if the distribution is
symmetric and unimodal. |
ANS:
D
NAT: Analytic; Descriptive Statistics
77.
The average score for a class of 30 students was 75. The 15 male
students in the class averaged 70. The 15 female students in the class averaged:
|
a. |
85. |
|
b. |
80 |
|
c. |
75 |
|
d. |
70 |
ANS:
B
NAT: Analytic; Descriptive Statistics
78.
A sample of 20 observations has a standard deviation of 3. The
sum of the squared deviations from the sample mean is:
|
a. |
20. |
|
b. |
23. |
|
c. |
29. |
|
d. |
171. |
ANS:
D
NAT: Analytic; Descriptive Statistics
79.
If two data sets have the same range:
|
a. |
the distances from the smallest to
largest observations in both sets will be the same. |
|
b. |
the smallest and largest observations
are the same in both sets. |
|
c. |
both sets will have the same standard
deviation. |
|
d. |
both sets will have the same
interquartile range. |
ANS:
A
NAT: Analytic; Descriptive Statistics
80.
The Empirical Rule states that the approximate percentage of
measurements in a data set (providing that the data set has a bell shaped
distribution) that fall within two standard deviations of their mean is
approximately:
|
a. |
68%. |
|
b. |
75%. |
|
c. |
95%. |
|
d. |
99%. |
ANS: C
NAT: Analytic; Descriptive Statistics
81.
Which of the following summary measures is affected most by
extreme values?
|
a. |
The median. |
|
b. |
The mean. |
|
c. |
The range. |
|
d. |
The interquartile range. |
ANS: C
NAT: Analytic; Descriptive Statistics
82.
Which of the following is a measure of variability?
|
a. |
The interquartile range |
|
b. |
The variance |
|
c. |
The coefficient of variation |
|
d. |
All of these choices are true. |
ANS: D
NAT: Analytic; Descriptive Statistics
83.
The smaller the spread of scores around the mean:
|
a. |
the smaller the variance of the data
set. |
|
b. |
the smaller the standard deviation of
the data set. |
|
c. |
the smaller the coefficient of
variation of the data set. |
|
d. |
All of these choices are true. |
ANS:
D
NAT: Analytic; Descriptive Statistics
84.
Is a standard deviation of 10 a large number indicating great
variability, or is it small number indicating little variability? To answer
this question correctly, one should look carefully at the value of the:
|
a. |
mean. |
|
b. |
standard deviation. |
|
c. |
coefficient of variation. |
|
d. |
mean dividing by the standard
deviation. |
ANS: C
NAT: Analytic; Descriptive Statistics
85.
Which of the following types of data has no measure of
variability?
|
a. |
Interval data |
|
b. |
Nominal data |
|
c. |
Bimodal data |
|
d. |
None of these choices. |
ANS: B
NAT: Analytic; Descriptive Statistics
86.
Which of the following statements is true regarding the data set
8, 8, 8, 8, and 8?
|
a. |
The range equals 0. |
|
b. |
The standard deviation equals 0. |
|
c. |
The coefficient of variation equals 0. |
|
d. |
All of these choices are true. |
ANS:
D
NAT: Analytic; Descriptive Statistics
87.
When extreme values are present in a set of data, which of the
following descriptive summary measures are most appropriate?
|
a. |
Coefficient of variation and range |
|
b. |
Mean and standard deviation |
|
c. |
Interquartile range and median |
|
d. |
Variance and interquartile range |
ANS:
C
NAT: Analytic; Descriptive Statistics
88.
The length of the box in the box plot portrays the:
|
a. |
median. |
|
b. |
interquartile range. |
|
c. |
range. |
|
d. |
third quartile. |
ANS:
B
NAT: Analytic; Descriptive Statistics
89.
In a negatively skewed distribution, which of the following is
the correct statement?
|
a. |
The distance from Q1 to Q2 is smaller than the
distance from Q2 to Q3 |
|
b. |
The distance from the smallest
observation to Q1 is larger than the
distance from Q3 to the largest
observation |
|
c. |
The distance from the smallest
observation to Q2 is smaller than the
distance from Q2 to the largest
observation |
|
d. |
The distance from Q1 to Q3 is twice the distance
from the Q1 to Q2 |
ANS:
B
NAT: Analytic; Descriptive Statistics
90.
In a perfectly symmetric distribution, which of the following statements
is false?
|
a. |
The distance from Q1 to Q2 equals to the
distance from Q2 to Q3 |
|
b. |
The distance from the smallest
observation to Q1 is the same as the
distance from Q3 to the largest
observation |
|
c. |
The distance from the smallest observation
to Q2 is the same as the
distance from Q2 to the largest
observation |
|
d. |
The distance from Q1 to Q3 is half of the
distance from the smallest to the largest observation |
ANS:
D
NAT: Analytic; Descriptive Statistics
91.
Which of the following summary measures cannot be easily
approximated from a box plot?
|
a. |
The range |
|
b. |
The interquartile range |
|
c. |
The second quartile |
|
d. |
The standard deviation |
ANS:
D
NAT: Analytic; Descriptive Statistics
92.
The interquartile range is the difference between the:
|
a. |
largest and smallest numbers in the
data set. |
|
b. |
25th percentile and the 75th percentile. |
|
c. |
median and the mean. |
|
d. |
None of these choices. |
ANS: B
NAT: Analytic; Descriptive Statistics
93.
In a positively skewed distribution, which of the following is
the correct statement?
|
a. |
The distance from Q1 to Q2 is larger than the
distance from Q2 to Q3 |
|
b. |
The distance from Q1 to Q2 is smaller than the
distance from Q2 to Q3 |
|
c. |
The distance from Q1 to Q2 is twice the distance
from Q2 to Q3 |
|
d. |
The distance from Q1 to Q2 is half the distance
from Q2 to Q3. |
ANS:
B
NAT: Analytic; Descriptive Statistics
94.
Which measures of central location and variability are
considered to be resistant to extreme values?
|
a. |
The mean and standard deviation. |
|
b. |
The mode and variance. |
|
c. |
The median and interquartile range. |
|
d. |
None of these choices. |
ANS:
C
NAT: Analytic; Descriptive Statistics
95.
Which of the following measures of variability is not sensitive
to extreme values?
|
a. |
The range |
|
b. |
The standard deviation |
|
c. |
The interquartile range |
|
d. |
The coefficient of variation |
ANS:
C
NAT: Analytic; Descriptive Statistics
96.
Which of the following statements is true?
|
a. |
The lower or first quartile is
labeled Q1 and is equal to the
25th percentile. |
|
b. |
The second quartile is labeled Q2 and is equal to the
median. |
|
c. |
The upper or third quartile is
labeled Q3 and is equal to the
75th percentile. |
|
d. |
All of these choices are true. |
ANS:
D
NAT: Analytic; Descriptive Statistics
97.
Assuming a linear relationship between X and Y, if the coefficient of
correlation (r)
equals -0.75, this means that:
|
a. |
there is very weak correlation |
|
b. |
the slope b1 is = -0.75 |
|
c. |
the value of X is always
greater than the value of Y |
|
d. |
None of these choices are true |
ANS:
B
NAT: Analytic; Descriptive Statistics
98.
Generally speaking, if two variables are unrelated (as one
increases, the other shows no pattern), the covariance will be:
|
a. |
a large positive number. |
|
b. |
a large negative number. |
|
c. |
a positive or negative number close to
zero. |
|
d. |
None of these choices. |
ANS:
C
NAT: Analytic; Descriptive Statistics
99.
Which of the following is a property of r, the coefficient of
correlation?
|
a. |
r always lies between 0 and 1. |
|
b. |
r has no units. |
|
c. |
If you switch the values of X and Y, the sign of r changes. |
|
d. |
All of these choices are true. |
ANS:
B
NAT: Analytic; Descriptive Statistics
100.
Which of the following are measures of the linear relationship
between two variables?
|
a. |
The covariance |
|
b. |
The coefficient of correlation |
|
c. |
The variance |
|
d. |
Both a and b |
ANS:
D
NAT: Analytic; Descriptive Statistics
101.
The strength of the linear relationship between two interval
variables can be measured by the:
|
a. |
coefficient of variation. |
|
b. |
coefficient of correlation. |
|
c. |
slope of the regression line. |
|
d. |
Y-intercept. |
ANS:
B
NAT: Analytic; Descriptive Statistics
COMPLETION
102.
Another word for the mean of a data set is the
____________________.
ANS: average
NAT: Analytic; Descriptive Statistics
103.
The size of a sample is denoted by the letter
____________________, and the size of a population is denoted by the letter
____________________.
ANS: n; N
NAT: Analytic; Descriptive Statistics
104.
The sample mean is denoted by ____________________ and the
population mean is denoted by ____________________.
ANS: ; m x
NAT: Analytic; Descriptive Statistics
105.
There are three measures of central location; the mean, the
____________________ and the ____________________.
ANS:
median; mode
mode; median
NAT: Analytic; Descriptive Statistics
106.
The ____________________ is calculated by finding the middle of
the data set, when the data are ordered from smallest to largest.
ANS: median
NAT: Analytic; Descriptive Statistics
107.
The ____________________ is the least desirable of all the
measures of central location.
ANS: mode
NAT: Analytic; Descriptive Statistics
108.
The ____________________ is not as sensitive to extreme values
as the ____________________.
ANS:
median; mean
median; average
NAT: Analytic; Descriptive Statistics
109.
The ____________________ mean is used whenever we wish to find
the “average” growth rate, or rate of change, in a variable over time.
ANS: geometric
NAT: Analytic; Descriptive Statistics
110.
The ____________________ mean of n returns (or
growth rates) is the appropriate mean to calculate if you wish to estimate the
mean rate of return (or growth rate) for any single period in the future.
ANS: arithmetic
NAT: Analytic; Descriptive Statistics
111.
If a data set contains an even number of observations, the
median is found by taking the ____________________ of these two numbers.
ANS:
average
arithmetic mean
NAT: Analytic; Descriptive Statistics
112.
If a data set is composed of 5 different numbers, there are
____________________ modes.
ANS:
0
no
zero
NAT: Analytic; Descriptive Statistics
113.
According to the Empirical Rule, if the data form a bell shaped
normal distribution, approximately ____________________ percent of the
observations will be contained within 2 standard deviations around the mean.
ANS: 95
NAT: Analytic; Descriptive Statistics
114.
According to the Empirical Rule, if the data form a bell shaped
normal distribution approximately ____________________ percent of the
observations will be contained within 1 standard deviation around the mean.
ANS: 68
NAT: Analytic; Descriptive Statistics
115.
According to the Empirical Rule, if the data form a bell shaped
normal distribution approximately ____________________ percent of the
observations will be contained within 3 standard deviations around the mean.
ANS: 99.7
NAT: Analytic; Descriptive Statistics
116.
There are three statistics used to measure variability in a data
set; the range, the ____________________ and the ____________________.
ANS:
variance; standard deviation
standard deviation; variance
NAT: Analytic; Descriptive Statistics
117.
The ____________________ is the square root of the
____________________.
ANS: standard deviation; variance
NAT: Analytic; Descriptive Statistics
118.
The ____________________ is the least effective of all the
measures of variability.
ANS: range
NAT: Analytic; Descriptive Statistics
119.
The ____________________ uses both the mean and the standard
deviation to interpret standard deviation for bell shaped histograms.
ANS: Empirical Rule
NAT: Analytic; Descriptive Statistics
120.
A statistic that interprets the standard deviation relative to
the size of the numbers in the data set is called the ____________________ of ____________________.
ANS: coefficient; variation
NAT: Analytic; Descriptive Statistics
121.
The range, variance, standard deviation, and coefficient of
variation are to be used only on ____________________ data.
ANS: interval
NAT: Analytic; Descriptive Statistics
122.
If the first and second quartiles are closer to each other than
are the second and third quartiles, the shape of the histogram based on the
quartiles is ____________________.
ANS: positively skewed
NAT: Analytic; Descriptive Statistics
123.
If the first and second quartiles are farther apart than the
second and third quartiles, the shape of the histogram based on the quartiles
is ____________________.
ANS: negatively skewed
NAT: Analytic; Descriptive Statistics
124.
____________________ are extremely large or extremely small
observations.
ANS: Outliers
NAT: Analytic; Descriptive Statistics
125.
The middle line inside the box in a box plot represents the
____________________.
ANS: median
NAT: Analytic; Descriptive Statistics
126.
Any points that lie outside the whiskers on a box plot are
called ____________________.
ANS: outliers
NAT: Analytic; Descriptive Statistics
127.
The ____________________ measures the spread between the middle
50% of the observations.
ANS: interquartile range
NAT: Analytic; Descriptive Statistics
128.
The 10th ____________________ is the value for which 10% of the
observations are less than that value.
ANS: percentile
NAT: Analytic; Descriptive Statistics
129.
A percentile is a measure of ____________________ standing.
ANS: relative
NAT: Analytic; Descriptive Statistics
130.
Q2 is
another name for the ____________________.
ANS: median
NAT: Analytic; Descriptive Statistics
131.
The ____________________ of the correlation indicates the
direction of a linear relationship.
ANS: sign
NAT: Analytic; Descriptive Statistics
132.
The magnitude of the correlation measures the
____________________ of a linear relationship.
ANS: strength
NAT: Analytic; Descriptive Statistics
133.
The ____________________ of a linear relationship is hard to
interpret from the covariance, but it is easy to interpret from the
correlation.
ANS:
magnitude
strength
NAT: Analytic; Descriptive Statistics
SHORT ANSWER
Strip Mall Rent
Monthly rent data in dollars for a sample of 10 stores in a
small town in South Dakota are as follows: 220, 216, 220, 205, 210, 240, 195,
235, 204, and 250.
134.
{Strip Mall Rent Narrative} Compute the sample monthly average
rent.
ANS:
= $219.50
NAT: Analytic; Descriptive Statistics
135.
{Strip Mall Rent Narrative} Compute the sample median.
ANS:
$218
NAT: Analytic; Descriptive Statistics
136.
{Strip Mall Rent Narrative} What is the mode?
ANS:
$220
NAT: Analytic; Descriptive Statistics
Pets Survey
A sample of 40 families were asked how many pets they owned.
Their responses are summarized in the following table.
|
Number of Pets |
0 |
1 |
2 |
3 |
4 |
5 |
|
Number of Families |
3 |
20 |
5 |
4 |
2 |
2 |
137.
{Pets Survey Narrative} Determine the mean, the median, and the
mode of the number of pets owned per family.
ANS:
= [(0 ´ 3) + (1 ´ 20) + (2 ´ 5) + (3 ´ 4) + (4 ´ 2) + (5 ´
2)]/25 = 1.50 pets, median = 1 pet, mode = 1 pet.
NAT: Analytic; Descriptive Statistics
138.
{Pets Survey Narrative} Explain what the mean, median, and mode
tell you about this particular data set.
ANS:
The “average” number of pets owned was 1.80 pets. (This
represents the overall average, rather than the number of pets for the average
family.) Half the families own at most one pet, and the other half own at least
one pet. The most frequent number of pets owned was one pet.
NAT: Analytic; Descriptive Statistics
139.
How do the mean, median and mode compare to each other when the
distribution is:
|
a. |
symmetric? |
|
b. |
negatively skewed? |
|
c. |
positively skewed? |
ANS:
|
a. |
mean = median = mode |
|
b. |
mean < median < mode |
|
c. |
mean > median > mode |
NAT: Analytic; Descriptive Statistics
140.
A basketball player has the following points for seven games:
20, 25, 32, 18, 19, 22, and 30. Compute the following measures of central
location:
|
a. |
mean |
|
b. |
median |
|
c. |
mode |
ANS:
|
a. |
= 23.714 |
|
b. |
median = 22.0 |
|
c. |
There is no mode |
NAT: Analytic; Descriptive Statistics
Computers
The following data represent the number of computers owned by a
sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
141.
{Computers Narrative} Compute the mean number of computers.
ANS:
= 1.90
NAT: Analytic; Descriptive Statistics
142.
{Computers Narrative} Compute the median number of computers.
ANS:
Median = 1.5
NAT: Analytic; Descriptive Statistics
143.
{Computers Narrative} Is the distribution of the number of
computers symmetric or skewed? Why?
ANS:
The distribution is positively skewed because the mean is larger
than the median.
NAT: Analytic; Descriptive Statistics
Weights of Workers
The following data represent the number of employees of a sample
of 25 companies: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168,
163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
144.
{Weights of Workers Narrative} Construct a stem and leaf display
for the number of workers.
ANS:
|
Stem |
Leaf |
|
13 |
47 |
|
14 |
0568 |
|
15 |
124667 |
|
16 |
2345889 |
|
17 |
123447 |
NAT: Analytic; Descriptive Statistics
145.
{Weights of Workers Narrative} Find the median number of
workers.
ANS:
Median = 162 workers
NAT: Analytic; Descriptive Statistics
146.
{Weights of Workers Narrative} Find the mean number of workers.
ANS:
NAT: Analytic; Descriptive Statistics
147.
{Weights of Workers Narrative} Is the distribution of the number
of workers symmetric or skewed? Why?
ANS:
The distribution is negatively skewed because the mean is
smaller than the median, and the stem and leaf display also shows this negative
skewness.
NAT: Analytic; Descriptive Statistics
148.
The number of hours a college student spent studying during the
final exam week was recorded as follows: 7,6, 4, 9, 8, 5, and 10. Compute
for the data and the value in an appropriate unit.
ANS:
= 7 hours
NAT: Analytic; Descriptive Statistics
Hours Worked per Week
The following data represent the hours worked per week of a
sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42,
33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
149.
{Hours Worked per Week Narrative} Construct a stem and leaf
display for the hours.
ANS:
|
Stem |
Leaf |
|
2 |
0378 |
|
3 |
1355689 |
|
4 |
022344789 |
|
5 |
236 |
|
6 |
14 |
NAT: Analytic; Descriptive Statistics
150.
{Hours Worked per Week Narrative} Find the median hours.
ANS:
Median = 42 hours
NAT: Analytic; Descriptive Statistics
151.
{Hours Worked per Week Narrative} Compute the sample mean hours.
ANS:
= 41.2 hours
NAT: Analytic; Descriptive Statistics
152.
{Hours Worked per Week Narrative} Find the modal hours.
ANS:
Modes are 35, 42, and 44
NAT: Analytic; Descriptive Statistics
153.
{Hours Worked per Week Narrative} Compare the mean and median
hours for these employees and use them to discuss the shape of the
distribution.
ANS:
The mean and median are 41.2 hours, 42 hours, respectively. They
are very close to each other, which tells us the distribution of hours is
approximately symmetric.
NAT: Analytic; Descriptive Statistics
Salaries of Employees
The following data represent the yearly salaries (in thousands
of dollars) of a sample of 13 employees of a firm: 26.5, 23.5, 29.7, 24.8,
21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
154.
{Salaries of Employees Narrative} Compute the mean salary.
ANS:
= 24.692 thousand dollars
NAT: Analytic; Descriptive Statistics
155.
{Salaries of Employees Narrative} Compute the median salary.
ANS:
median = 24.3 thousand dollars
NAT: Analytic; Descriptive Statistics
156.
{Salaries of Employees Narrative} Compare the mean salary with
the median salary and use them to describe the shape of the distribution.
ANS:
The mean is $24,692 thousand dollars, and the median is $24,300
thousand dollars. The mean is slightly higher than the median. This tells us
that the data are slightly positively skewed, but close to symmetric.
NAT: Analytic; Descriptive Statistics
157.
A sample of 12 construction workers has a mean age of 25 years.
Suppose that the sample is enlarged to 14 construction workers, by including
two additional workers having common age of 25 each. Find the mean of the
sample of 14 workers.
ANS:
= 25 years
NAT: Analytic; Descriptive Statistics
158.
The mean of a sample of 15 measurements is 35.6 feet. Suppose
that the sample is enlarged to 16 measurements, by including one additional
measurement having a value of 42 feet. Find the mean of the sample of the 16
measurements.
ANS:
= 36 feet.
NAT: Analytic; Descriptive Statistics
Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65
years of age whose net worth is too high to qualify for Medicaid and who have
no private health insurance. The ages of 22 uninsured senior citizens were as
follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 86,
87, 91, 92, 94, and 97.
159.
{Ages of Senior Citizens Narrative} Calculate the mean age of
the uninsured senior citizens
ANS:
= 78.0 years.
NAT: Analytic; Descriptive Statistics
160.
{Ages of Senior Citizens Narrative} Calculate the median age of
the uninsured senior citizens.
ANS:
76.5 years.
NAT: Analytic; Descriptive Statistics
161.
{Ages of Senior Citizens Narrative} Explain why there is no mode
for this data set.
ANS:
There is no mode because every age is different.
NAT: Analytic; Descriptive Statistics
162.
A basketball player has the following points for seven games:
20, 25, 32, 18, 19, 22, and 30. Compute the following measures of variability.
|
a. |
Standard deviation |
|
b. |
Coefficient of variation |
|
c. |
Compare the standard deviation and
coefficient of variation and use them to discuss the variability in the data. |
ANS:
|
a. |
s = 5.499 |
|
b. |
cv = 0.232 |
|
c. |
The standard deviation is 5.499 and the
coefficient of variation is 0.232. The coefficient of variation is smallest
because the mean is larger than the standard deviation. |
NAT: Analytic; Descriptive Statistics
163.
The following data represent the number of children in a sample
of 10 families from a certain community: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
|
a. |
Compute the range. |
|
b. |
Compute the variance. |
|
c. |
Compute the standard deviation. |
|
d. |
Compute the coefficient of variation. |
|
e. |
Explain why in this case range >
variance > standard deviation > coefficient of variation. |
ANS:
|
a. |
5 |
|
b. |
2.77 |
|
c. |
1.66 |
|
d. |
0.87 |
|
e. |
The range is the difference between the
largest and smallest observation, which compares the numbers to each other;
the variance is in essence “the average squared deviation from mean”, which compares
the numbers to the mean. The standard deviation is less than the variance
because it’s the square root of a number larger than one. The coefficient of
variation is even smaller because the mean is larger than the standard
deviation. |
NAT: Analytic; Descriptive Statistics
164.
The following data represent the number of children in a sample
of 10 families from a certain community: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
|
a. |
Compute the range. |
|
b. |
Compute the variance. |
|
c. |
Compute the standard deviation. |
|
d. |
Compute the coefficient of variation. |
|
e. |
Explain why in this case range >
variance > standard deviation > coefficient of variation. |
ANS:
|
a. |
5 |
|
b. |
2.77 |
|
c. |
1.66 |
|
d. |
0.87 |
|
e. |
The range is the difference between the
largest and smallest observation, which compares the numbers to each other;
the variance is in essence “the average squared deviation from mean”, which
compares the numbers to the mean. The standard deviation is less than the
variance because it’s the square root of a number larger than one. The
coefficient of variation is even smaller because the mean is larger than the
standard deviation. |
NAT: Analytic; Descriptive Statistics
Weights of Teachers
The following data represent the weights in pounds of a sample
of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168,
163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
165.
{Weights of Teachers Narrative} Compute the sample variance, and
sample standard deviation.
ANS:
s2 = 156.12,
and s =
12.49
NAT: Analytic; Descriptive Statistics
166.
{Weights of Teachers Narrative} Compute the range and
coefficient of variation.
ANS:
Range = 43,
cv = 12.49 / 159.04 = 0.079
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