Question 1

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
-When investigating times required for drive-through service, the following results (in seconds) were obtained.

$\begin{array}{l|l|l|l|l|l|l|l|l}
\text { Restaurant A } & 120 & 123 & 153 & 128 & 124 & 118 & 154 & 110 \
\hline \text { Restaurant B } & 115 & 126 & 147 & 156 & 118 & 110 & 145 & 137
\end{array}$

A) Restaurant A: $44 \mathrm { sec } ; 260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }$
Restaurant B: $46 \mathrm { sec } ; 245.64 \mathrm { sec } ^ { 2 } ; 15.67 \mathrm { sec }$
There is more variation in the times for restaurant A.

B) Restaurant A: 46 sec; $260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }$
Restaurant B: $44 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }$
There is more variation in the times for restaurant $\mathrm { B }$.

C) Restaurant A: $44 \mathrm { sec } ; 298.34 \mathrm { sec } ^ { 2 } ; 17.27 \mathrm { sec }$
Restaurant B: $46 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }$
There is more variation in the times for restaurant A.

D) Restaurant A: $44 \mathrm { sec } ; 260.79 \mathrm { sec } ^ { 2 } ; 16.15 \mathrm { sec }$
Restaurant B: $46 \mathrm { sec } ; 285.64 \mathrm { sec } ^ { 2 } ; 16.90 \mathrm { sec }$
There is more variation in the times for restaurant $B$.

Accepted Answer

The answer of Find the range, variance, and standard deviation...

Question 2

Which score has the highest relative position: a score of 46 on a test for which $\bar { x } = 43$ and s $= 6$, a score of $4.3$ on a test for which $\bar { x } = 3.8$ and $s = 0.9$ or a score of $378.5$ on a test for which $\bar { x } = 351$ and $\mathrm { s } = 55 ?$
A) A score of 46
B) A score of 4.3
C) A score of 378.5

Accepted Answer

The relative position is determined by the z-score, calculated as $ z = \frac{x - \bar{x}}{s} $. For each score:  A) $ z = \frac{46 - 43}{6} = 0.5 $  B) $ z = \frac{4.3 - 3.8}{0.9} \approx 0.56 $  C) $ z = \frac{378.5 - 351}{55} \approx 0.5 $  The score of 4.3 has the highest z-score, indicating the highest relative position.

Question 3

The mean of a set of data is 374.92 and its standard deviation is 105.19. Find the z score for a value of 327.83.
A) -0.49
B) -0.45
C) -0.15
D) -0.40

Accepted Answer

The answer of The mean of a set of data...

Question 4

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values.
-The weights (in pounds) of six dogs are listed below. Find the mean weight. $$\begin{array} { l l l l l l } 
39 & 30 & 91 & 15 & 133 & 88
\end{array}$$
A) 65.5 lb
B) 66.5 lb
C) 79.2 lb
D) 66 lb

Accepted Answer

The mean is the sum of the values divided by the number of values. In this case, the mean is (39 + 30 + 91 + 15 + 133 + 88) / 6 = 396 / 6 = 66.

Question 5

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data.
-$$\begin{array} { l l l l l l } 
24.4 & 11.8 & 38.9 & 29.7 & 11.2 & 14.6
\end{array}$$
A) 2842.7
B) 34.3
C) 3468.5
D) 11.19

Accepted Answer

To find the standard deviation, first calculate the mean of the data. Then, find the squared differences from the mean, average those, and take the square root. The standard deviation for this data set is approximately 11.19.

Question 6

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
-The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set.

$\begin{array} { l l l l l l l l l l } 5.5 & 5.7 & 5.8 & 5.9 & 6.1 & 6.1 & 6.3 & 6.4 & 6.5 & 6.6 \end{array}$
$\begin{array} { l l l l l l l l l l } 6.7 & 6.7 & 6.7 & 6.9 & 7.0 & 7.0 & 7.0 & 7.1 & 7.2 & 7.2 \end{array}$
$\begin{array} { l l l l l l l l l l l } 7.4 & 7.5 & 7.7 & 7.7 & 7.8 & 8.0 & 8.1 & 8.1 & 8.3 & 8.7 \end{array}$
A)

B)

C)

D)

Accepted Answer

The answer of Construct a boxplot for the given data....

Question 7

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place.
-Listed below are the systolic blood pressures (in $\mathrm { mm } \mathrm { Hg }$ ) for a sample of men aged 20-29 and for a sample of men aged 60-69.

$\begin{array}{llllll}
\text { Men aged 20-29: } 117 & 125 & 133 & 118 & 131 & 123 \
\text { Men aged 60-69: } 130 & 151 & 138 & 125 & 164 & 139
\end{array}$

A) Men aged 20-29: 5.5%
Men aged 60-69: 10.5%
There is substantially more variation in blood pressures of the men aged 60-69.

B) Men aged 20-29: $8.7 \%$
Men aged 60-69: 4.6%
There is more variation in blood pressures of the men aged 20-29.

C) Men aged 20-29: 5.3%
Men aged 60-69: $10.1 \%$
There is substantially more variation in blood pressures of the men aged 60-69.

D) Men aged 20-29: 5.0%
Men aged 60-69: 8.2%
There is substantially more variation in blood pressures of the men aged $60 - 69$.

Accepted Answer

The answer of Find the coefficient of variation for each...

Quiz 3: Statistics for Describing, Exploring, and Comparing Data

Which score has the highest relative position: a score of 46 on a test for which $\bar { x } = 43$ and s $= 6$ , a score of $4.3$ on a test for which $\bar { x } = 3.8$ and $s = 0.9$ or a score of $378.5$ on a test for which $\bar { x } = 351$ and $\mathrm { s } = 55 ?$

The mean of a set of data is 374.92 and its standard deviation is 105.19. Find the z score for a value of 327.83.

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. - $\begin{array} { l l l l l l } 24.4 & 11.8 & 38.9 & 29.7 & 11.2 & 14.6\end{array}$

Quiz 3: Statistics for Describing, Exploring, and Comparing Data

The mean of a set of data is 374.92 and its standard deviation is 105.19. Find the z score for a value of 327.83.

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. - 24.411.838.929.711.214.6\begin{array} { l l l l l l } 24.4 & 11.8 & 38.9 & 29.7 & 11.2 & 14.6\end{array}24.4​11.8​38.9​29.7​11.2​14.6​

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. - $\begin{array} { l l l l l l } 24.4 & 11.8 & 38.9 & 29.7 & 11.2 & 14.6\end{array}$