Deck 3: Averages and Variation

Question 1

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. The sample means for x and y are 10.40 and 9.20, respectively.
$$\begin{array} { l l l l l l l l l l l } x : & 13 & 0 & 36 & 22 & 32 & 24 & 25 & - 13 & - 13 & - 22 \\y : & 7 & - 2 & 27 & 16 & 23 & 17 & 16 & - 2 & - 3 & - 7\end{array}$$ Compute a 75% Chebyshev interval around the mean for x-values and also for y-values. Round your answers to the nearest hundredth.

A)for x-values: -10.16 to 51.52 and for y-values: -2.95 to 33.50
B)for x-values: -30.72 to 22.55 and for y-values: -15.10 to 21.35
C)for x-values: -15.10 to 33.50 and for y-values: -30.72 to 51.52
D)for x-values: -30.72 to 22.55 and for y-values: -2.95 to -13.90
E)for x-values: -30.72 to 51.52 and for y-values: -15.10 to 33.50

Answer 1

for x-values: -30.72 to 51.52 and for y-values: -15.10 to 33.50

Question 2

Given the sample data below, use the defining formula to compute the sample standard deviation. $$\begin{array} { l l l l l l } 28 & 32 & 15 & 29 & 19 & 14\end{array}$$

A)7.79
B)27.40
C)50.48
D)60.57
E)7.11

Answer 2

7.79

Question 3

Find the sample variance for the following sample data. Round your answer to the nearest hundredth. $$s ^ { 2 }$$ $\begin{array}{llllll}x: & 24 & 16 & 13 & 31 & 28\end{array}$

A)47.44
B)78.80
C)98.50
D)59.30
E)79.46

Answer 3

59.30

Question 4

Compute the population standard deviation $\sigma$ for the following sample data, assuming the sample comprises the entire population. Round your answer to the nearest hundredth. x:
21
17
15
35
27

A)8.12
B)10.36
C)2.30
D)9.27
E)9.22

Question 5

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. The sample means for x and y are 11.00 and 8.90, respectively.
$$\begin{array} { l l l l l l l l l l l } x : & 12 & 0 & 37 & 24 & 32 & 26 & 27 & - 12 & - 12 & - 24 \\y : & 9 & - 3 & 26 & 15 & 25 & 18 & 15 & - 3 & - 4 & - 9\end{array}$$ Compute the coefficient of variation for each fund. Round your answers to the nearest tenth.

A)for x-values: , and for y-values: $116.5 \%$ $144.0 \%$
B)for x-values: , and for y-values: $192.9 \%$ $238.4 \%$
C)for x-values: , and for y-values: $144.0 \%$ $192.9 \%$
D)for x-values: , and for y-values: $116.5 \%$ $238.4 \%$
E)for x-values: , and for y-values: $192.9 \%$ $144.0 \%$

Question 6

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute. $$\sum x$$ $$\begin{array} { l l l l l l l l l l l } x : & 14 & 0 & 36 & 24 & 31 & 26 & 27 & - 14 & - 14 & - 24 \\y : & 8 & - 1 & 26 & 17 & 25 & 18 & 17 & - 1 & - 2 & - 8\end{array}$$

A)134
B)106
C)154
D)75
E)130

Question 7

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute. $$\sum y$$ $$\begin{array} { l l c l l l l l l l l } x : & 12 & 0 & 39 & 25 & 33 & 27 & 28 & - 12 & - 12 & - 25 \\y : & 7 & - 1 & 29 & 15 & 26 & 18 & 15 & - 1 & - 2 & - 7\end{array}$$

A)106
B)100
C)99
D)101
E)107

Question 8

Compute the population variance for the following sample data, assuming the sample comprises the entire population. Round your answer to the nearest hundredth. $$\sigma ^ { 2 }$$ $\begin{array}{llllll}x: & 21&20&11&35&26\end{array}$

A)77.30
B)117.20
C)93.76
D)61.84
E)59.13

Question 9

The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Assume there is a physician at the park clinic in Grand Canyon Village. Suppose the physician has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon. Compute a 5% trimmed mean for Upper Canyon and Lower Canyon. Round your answer to the nearest thousandth. Upper Canyon: Number of injuries per Landing Point Between North Canyon and Phantom Ranch $\begin{array} { l l l l l l l l l l l } 4 & 5 & 3 & 3 & 5 & 6 & 7 & 10 & 5 & 3 & 5 \end{array}$
Lower Canyon: Number of injuries per Landing Point Between Bright Angel and Lava Falls
$$\begin{array} { l l l l l l l l l l l l l l } 9 & 3 & 3 & 0 & 7 & 8 & 4 & 12 & 5 & 0 & 3 & 11 & 4 & 3\end{array}$$

A)The 5% trimmed mean for Lower Canyon is 3.333 and for Upper Canyon is 5.417.
B)The 5% trimmed mean for Lower Canyon is 2.727 and for Upper Canyon is 4.643.
C)The 5% trimmed mean for Lower Canyon is 2.636 and for Upper Canyon is 3.786.
D)The 5% trimmed mean for Lower Canyon is 3.222 and for Upper Canyon is 4.333.
E)The 5% trimmed mean for Lower Canyon is 4.333 and for Upper Canyon is 3.222.

Question 10

Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth. $\begin{array}{llllll}x: & 24 & 17 & 15 & 33 & 25\end{array}$

A)7.16
B)8.57
C)9.58
D)6.40
E)9.60

Question 11

At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were Find the interquartile range.
$$\begin{array} { l l l l l l l l l l } 27 & 3 & 7 & 20 & 28 & 38 & 31 & 45 & 19 & 11 \\9 & 19 & 35 & 30 & 33 & 16 & 25 & 37 & 13 & 38\end{array}$$

A)46.5
B)19.5
C)22.5
D)48.5
E)21.5

Question 12

How hot does it get in Death Valley? Assume that the following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures were taken from May to November in the vicinity of Furnace Creek. Compute the median for these ground temperatures. Round your answer to the nearest tenth. $$\left( { } ^ { \circ } F \right)$$ $$\begin{array} { l l l l l l l } 148 & 153 & 167 & 172 & 196 & 178 & 193 \\196 & 178 & 178 & 167 & 162 & 153 & 145\end{array}$$

A)160.0
B)167.0
C)194.5
D)339.0
E)169.5

Question 13

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute a 75% Chebyshev interval around the mean for x-values and also for y-values. Round your answers to the nearest hundredth. $$\begin{array} { l l l l l l l l l l l } x : & 12 & 0 & 39 & 24 & 33 & 26 & 27 & - 12 & - 12 & - 24 \\y & 8 & - 5 & 28 & 15 & 25 & 18 & 15 & - 5 & - 6 & - 8\end{array}$$

A)for x-values: -10.29 to 54.48 and for y-values: -5.14 to 35.78
B)for x-values: -31.88 to 24.94 and for y-values: -18.78 to 22.14
C)for x-values: -31.88 to 54.48 and for y-values: -18.78 to 35.78
D)for x-values: -31.88 to 24.94 and for y-values: -5.14 to -15.98
E)for x-values: -18.78 to 35.78 and for y-values: -31.88 to 54.48

Question 14

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the coefficient of variation for each fund. Round your answers to the nearest tenth. $$\begin{array} { l c c c c c c c c c c } x : & 12 & 0 & 38 & 23 & 34 & 25 & 26 & - 12 & - 12 & - 23 \\y : & 10 & - 5 & 28 & 15 & 24 & 16 & 15 & - 5 & - 6 & - 10\end{array}$$

A)for x-values: , and for y-values: $123.1 \%$ $166.6 \%$
B)for x-values: , and for y-values: $190.8 \%$ $166.6 \%$
C)for x-values: , and for y-values: $$166.6 \%$$ $190.8 \%$
D)for x-values: , and for y-values: $123.1 \%$ $258.3 \%$
E)for x-values: , and for y-values: $190.8 \%$ $258.3 \%$

Question 15

Find the range for the following sample data. $\begin{array}{llllll}x: & 24 & 18 & 15 & 31 & 29\end{array}$

A)11
B)7
C)3
D)2
E)16

Question 16

In your biology class, your final grade is based on several things: a lab score, score on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 20% of your total grade, each major test is worth 27.5%, and the final exam is worth 25%. Compute the weighted average for the following scores: 91 on the lab, 83 on the first major test, 92 on the second major test, and 84 on the final exam. Round your answer to the nearest hundredth.

A)89.08
B)85.93
C)87.68
D)87.33
E)84.85

Question 17

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute. $$\sum x ^ { 2 }$$ $$\begin{array} { l l l l l l l l l l l } x : & 14 & 0 & 38 & 23 & 33 & 25 & 26 & - 14 & - 14 & - 23 \\y : & 9 & - 5 & 28 & 17 & 24 & 16 & 17 & - 5 & - 6 & - 9\end{array}$$

A)5088
B)4755
C)4951
D)5480
E)4391

Question 18

The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Assume there is a physician at the park clinic in Grand Canyon Village. Suppose the physician has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon. The mean, median, and mode for Upper Canyon are 5.091, 5.0, and 5, respectively.
Upper Canyon: Number of injuries per Landing Point Between
North Canyon and Phantom Ranch
$\begin{array} { l l l l l l l l l l l } 4 & 5 & 3 & 3 & 5 & 6 & 7 & 10 & 5 & 3 & 5 \end{array}$
Lower Canyon: Number of injuries per Landing Point Between
Bright Angel and Lava Falls
$\begin{array} { l l l l l l l l l l l l l l } 9 & 3 & 3 & 0 & 7 & 8 & 4 & 12 & 5 & 0 & 3 & 11 & 4 & 3 \end{array}$ The mean, median, and mode for Lower Canyon are 5.214, 4.0, and 3, respectively.
Compare the mean, median, and mode found in Upper Canyon and Lower Canyon, respectively.

A)Lower Canyon mean is smaller than Upper Canyon, Lower Canyon median is smaller than Upper Canyon, and Lower Canyon mode is smaller than Upper Canyon.
B)Lower Canyon mean is greater than Upper Canyon, Lower Canyon median is greater than Upper Canyon, and Lower Canyon mode is smaller than Upper Canyon.
C)Lower Canyon mean is greater than Upper Canyon, Lower Canyon median is smaller than Upper Canyon, and Lower Canyon mode is greater than Upper Canyon.
D)Lower Canyon mean is greater than Upper Canyon, Lower Canyon median is smaller than Upper Canyon, and Lower Canyon mode is smaller than Upper Canyon.
E)Lower Canyon mean is greater than Upper Canyon, Lower Canyon median is greater than Upper Canyon, and Lower Canyon mode is greater than Upper Canyon.

Question 19

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth. $$\begin{array} { l l l l l l l l l l l } x : & 13 & 0 & 37 & 25 & 32 & 27 & 28 & - 13 & - 13 & - 25 \\y & 8 & - 2 & 26 & 16 & 26 & 18 & 16 & - 2 & - 3 & - 8\end{array}$$

A)and $\bar { x } = 68.5$ $\bar { y } = 9.9$
B)and $\bar { x } = 11.1$ $\bar { y } = 9.5$
C)and $\bar { x } = 161.0$ $\bar { y } = 10.6$
D)and $\bar { x } = 39.5$ $\bar { y } = 13.0$
E)and $\bar { x } = 9.5$ $\bar { y } = 11.1$

Question 20

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute. $$\sum y ^ { 2 }$$ $$\begin{array} { l l l l l l l l l l l } x : & 12 & 0 & 37 & 24 & 35 & 26 & 27 & - 12 & - 12 & - 24 \\y : & 8 & - 5 & 28 & 15 & 25 & 16 & 15 & - 5 & - 6 & - 8\end{array}$$

A)2304
B)2240
C)2265
D)2268
E)2329

Question 21

Suppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state offers the lowest premium? Which state offers the highest premium?

A)Texas has the lowest premium and Pennsylvania has the highest.
B)California has the lowest premium and Texas has the highest.
C)Pennsylvania has the lowest premium and Texas has the highest.
D)Texas has the lowest premium and California has the highest.
E)none of these choices

Question 22

Suppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state has the highest median premium?

A)Pennsylvania has the highest median premium.
B)California has the highest median premium.
C)Texas as well as California have the highest median premium.
D)Texas has the highest median premium.
E)none of these choices

Question 23

Suppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state has the smallest range of premiums?

A)Texas has the smallest range of premiums.
B)California has the smallest range of premiums.
C)Texas as well as Pennsylvania have the smallest range.
D)Pennsylvania has the smallest range of premiums.
E)none of these choices

Question 24

Suppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state has the smallest interquartile range?

A)California has the smallest interquartile range.
B)Texas has the smallest interquartile range.
C)Pennsylvania as well as California have the smallest interquartile range.
D)Pennsylvania has the smallest interquartile range.
E)none of these choices

Question 25

What percentage of the general U.S. population have bachelor's degrees? Suppose that the Statistical Abstract of the United States, 120th Edition, gives the following percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order. Illinois has a bachelor's degree percentage rate of about 18%. Into what quartile does this rate fall?
$$\begin{array} { l l l l l l l l l l } 17 & 18 & 18 & 18 & 19 & 20 & 20 & 20 & 21 & 21 \\21 & 21 & 21 & 22 & 22 & 22 & 22 & 22 & 23 & 23 \\24 & 24 & 24 & 24 & 24 & 25 & 25 & 25 & 25 & 26 \\26 & 26 & 26 & 26 & 26 & 27 & 27 & 27 & 28 & 28 \\28 & 29 & 29 & 31 & 31 & 32 & 32 & 34 & 35 & 38\end{array}$$

A)second quartile
B)first quartile
C)third quartile
D)first quartile as well as second quartile
E)none of these choices

Question 26

At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were A box-and-whisker plot of the data is shown below.
$$\begin{array} { l l l l l l l l l l } 24 & 2 & 5 & 16 & 26 & 37 & 28 & 48 & 14 & 8 \\6 & 24 & 32 & 27 & 29 & 11 & 22 & 33 & 9 & 37\end{array}$$ Find the interquartile range.

A)39.0
B)25.0
C)20.5
D)40.5
E)22.0