Question 1

The range and standard deviation of the data set below are 35 and 12.47 respectively.  $5,24,25,26,40$  If the 26 is replaced with 39, how will this affect the range? How will this affect the standard deviation. Use your answers to explain why the standard deviation is preferable to the range as a measure of variation.

Accepted Answer

The answer of The range and standard deviation of the...

Question 2

Find the mode(s)for the given sample data.
-81, 35, 32, 35, 29, 81

Accepted Answer

A) 81 
B) 81, 35 
C) 35 
D) 48.8

Question 3

Determine the quartile or interquartile range as specified.
-The normal annual precipitation (in inches)is given below for 21 different U.S. cities. Find the first quartile, 
$\mathrm { Q } _ { 1 } \text {. }$ 
$\begin{array} { l l l l l l l } 39.1 & 16.4 & 25.4 & 18.4 & 27.1 & 27.8 & 30.6 \end{array}$
$\begin{array} { l l l l l l l l } 15.2 & 42.6 & 18.4 & 13.5 & 19.8 & 32.3 & 10.0 \end{array}$
$\begin{array} { l l l l l l l } 14.8 & 33.6 & 12.9 & 35.0 & 22.3 & 11.2 & 51.7 \end{array}$

Accepted Answer

A) $15.2 \mathrm { in } .$ 
B)  $14.8 \mathrm { in } .$ 
C)  $14.900 \mathrm { in }$. 
D)  $15.00 \mathrm { in }$.

Question 4

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)

Accepted Answer

A) A score of 304 
B) A score of 43.5 
C) Both scores have the same relative position.

Question 5

Consider the following sample of exam scores, arranged in increasing order: $\begin{array} { l l l l l l } 22 & 35 & 44 & 55 & 67 & 70 \end{array}$
$\begin{array} { l l l l l l } 78 & 81 & 81 & 82 & 84 & 88 \end{array}$
$\begin{array} { l l l l l l } 88 & 89 & 90 & 90 & 91 & 92 \end{array}$
$\begin{array} { l l l l l l } 92 & 93 & 93 & 94 & 94 & 95 \ 95 & 96 & 96 & 97 & 99 & 100 \end{array}$
$\begin{array} { l l l l l l } 95 & 96 & 96 & 97 & 99 & 100 \end{array}$
Note: $\bar { x } = 82.4$ and $s = 19.5$

Accepted Answer

A) (i) Use Chebychev's rule to obtain a lower bound on the percentage of observations that lie within 2 standard deviations to either side of the mean.
(ii) Use the data to obtain the exact percentage of observations that lie within  standard deviations to either side of the mean. Compare this answer with part (i).
  (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $43.4$ and $121.4$;
(ii) 26 of the thirty observations (87\%) lie within the interval $43.4$ to $121.4$. "At least $75 \%$ " means $75 \%$ or more, and $87 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. 
B)  (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $40.4$ and $123.4$;
(ii) 27 of the thirty observations ( $90 \%$ ) lie within the interval $40.4$ to $123.4$. "At least $75 \%$ " means $75 \%$ or more, and $90 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. 
C)  (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $43.4$ and $121.4$;
(ii) 28 of the thirty observations ( $93 \%$ ) lie within the interval $43.4$ to $121.4$. "At least $75 \% "$ means $75 \%$ or more, and $93 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. 
D)  (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $53.4$ and $116.4$;
(ii) 28 of the thirty observations ( $93 \%$ ) lie within the interval $53.4$ to $116.4$. "At least $75 \%$ " means $75 \%$ or more, and $93 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data.

Question 6

Find the range for the given data set.
-The weights, in pounds, of 18 randomly selected adults are given below. $\begin{array} { l l l l l l } 120 & 165 & 187 & 143 & 119 & 132 \ 127 & 156 & 179 & 159 & 180 & 202 \ 114 & 146 & 151 & 168 & 173 & 144 \end{array}$

Accepted Answer

A) $78 \mathrm { lb }$ 
B)  $114 \mathrm { lb }$ 
C)  $202 \mathrm { lb }$ 
D)  $88 \mathrm { lb }$

Question 7

Find the range for the given data set.
-28, 39, 17, 45, 52

Accepted Answer

A) 35 
B) 17 
C) 52 
D) 11

Question 8

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions Being compared have approximately the same shape.)

Accepted Answer

A) A score of 92 
B) A score of 688 
C) Both scores have the same relative position.

Question 9

Solve the problem.
-Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation.

Accepted Answer

A) IL and MA have very comparable salaries. The average salaries for these states are just above $40K, and their variations are very close. NV is very comparable to IL and MA. The upper
50% of salaries for NV corresponds to the lower 50% of WA salaries. 
B) IL and MA don't have very comparable salaries. The average salaries for these states are just below $40K, and their variations are different. NV is not very comparable to either IL or MA.
The upper 50% of salaries for WA corresponds to the lower 50% of NV salaries. 
C) IL and MA have very comparable salaries. The average salaries for these states are just below $40K, but their variations are different. NV is not very comparable to either IL or MA. The
Upper 50% of salaries for NV corresponds to the lower 50% of WA salaries. 
D) IL and MA have very comparable salaries. The average salaries for these states are just below $40K, and their variations are very close. NV is not very comparable to either IL or MA. The
Upper 50% of salaries for NV corresponds to the lower 50% of WA salaries.

Question 10

Find the population standard deviation. Round to one decimal place as needed. 
$0,3,5,7,7$

Accepted Answer

A) 7 
B)  2.7 
C)  10.6 
D)  1.6

Question 11

Identify potential outliers, if any, for the given data.
-The weekly salaries (in dollars)of sixteen government workers are listed below. 
$\begin{array} { l l l l } 690 & 584 & 813 & 643 \ 728 & 558 & 458 & 597 \ 498 & 651 & 685 & 360 \ 526 & 787 & 475 & 986 \end{array}$

Accepted Answer

A) 360,986 
B)  360 
C)  986 
D)  None

Question 12

The median of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

Accepted Answer

The answer of The median of a data set is...

Question 13

Obtain the population standard deviation, Ϭ, for the given data. Assume that the data represent population data. Round your final answer to one more decimal place than that used for the Observations. The normal annual precipitation (in inches)is given below for 8 different U.S. cities. 
$\begin{array} { l l l l } 6.7 & 8.3 & 5.7 & 14.2 \end{array}$
$\begin{array} { r r r r } 15.2 & 13.7 & 17.0 & 14.3 \end{array}$

Accepted Answer

A) $4.03 \mathrm { in }$. 
B)  $6.22 \mathrm { in } .$ 
C)  $4.30 \mathrm { in }$. 
D)  $16.20 \mathrm { in }$.

Question 14

Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

Accepted Answer

The answer of Do you think it is possible to...

Question 15

A variable x has the possible observations shown below. 
$\text { Possible observations of } \mathrm{x}$ : -3  -1 0 1 1 2 4 4 5
Determine the standardized version of $x$.
Round the values of $\mu$ and $\sigma$ to one decimal place.

Accepted Answer

A) $z = \frac { x - 1.4 } { 2.6 }$ 
B)  $x = \frac { z - 1.4 } { 2.6 }$ 
C)  ${ z } = \frac { \mathrm { x } - 1.4 } { 2.5 }$ 
D)  $z = \frac { x - 2.5 } { 1.4 }$

Question 16

Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place thanthat used for the observations.
-The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score. $\begin{array} { l l l l l } 589 & 532 & 359 & 349 & 497 \end{array}$
$\begin{array} { l l l l l } 340 & 353 & 626 & 470 & 482 \end{array}$

Accepted Answer

A) 459.7 
B)  450.7 
C)  469.1 
D)  476

Question 17

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Accepted Answer

A) 0.78 
B) 1.01 
C) 0.64 
D) 0.71

Question 18

Find the range for the given data set.
-Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. $\begin{array} { l l l l l } 
5 & 20 & 4 & 14 & 10
\end{array}$

Accepted Answer

A) 5 
B) 20 
C) 4 
D) 16

Question 19

Construct and interpret a boxplot or a modified boxplot as specified.
-The weights (in ounces)of 27 tomatoes are listed below. Construct a modified boxplot for the data. $\begin{array} { l l l l l l l l l } 1.7 & 2.0 & 2.2 & 2.2 & 2.4 & 2.5 & 2.5 & 2.5 & 2.6 \ 2.6 & 2.6 & 2.6 & 2.6 & 2.7 & 2.8 & 2.8 & 2.8 & 2.9 \ 2.9 & 2.9 & 3.0 & 3.0 & 3.1 & 3.1 & 3.3 & 3.6 & 4.2 \end{array}$

Accepted Answer

A)

The data is left-skewed and has one potential outlier. 
B)

The data is roughly symmetrical, possibly bell-shaped, with no potential outliers. 
C)

The data is roughly symmetrical and has two potential outliers. 
D)

The data is highly right-skewed with three potential outliers.

Question 20

Obtain the five-number summary for the given data.
-The weekly salaries (in dollars)of sixteen government workers are listed below. 
$\begin{array} { l l l l } 690 & 609 & 813 & 644 \ 728 & 571 & 473 & 614 \ 529 & 678 & 685 & 460 \ 552 & 787 & 507 & 826 \end{array}$

Accepted Answer

A) 460, 540.5, 629.0, 709, 826 dollars 
B)  460,534.75,629.0,718.5,826 dollars 
C)  460,529,614,690,826 dollars 
D)  460,534.75,614,718.5,826 dollars

Exam 3: Descriptive Measures

Find the mode(s) for the given sample data. -81, 35, 32, 35, 29, 81

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)

Find the range for the given data set. -The weights, in pounds, of 18 randomly selected adults are given below. $\begin{array} { l l l l l l } 120 & 165 & 187 & 143 & 119 & 132 \\ 127 & 156 & 179 & 159 & 180 & 202 \\ 114 & 146 & 151 & 168 & 173 & 144 \end{array}$

Find the range for the given data set. -28, 39, 17, 45, 52

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions Being compared have approximately the same shape.)

Solve the problem. -Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation.

Find the population standard deviation. Round to one decimal place as needed. $0,3,5,7,7$

Identify potential outliers, if any, for the given data. -The weekly salaries (in dollars) of sixteen government workers are listed below. $\begin{array} { l l l l } 690 & 584 & 813 & 643 \\ 728 & 558 & 458 & 597 \\ 498 & 651 & 685 & 360 \\ 526 & 787 & 475 & 986 \end{array}$

The median of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

A variable x has the possible observations shown below. $\text { Possible observations of } \mathrm{x}$ : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of $x$ . Round the values of $\mu$ and $\sigma$ to one decimal place.

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Find the range for the given data set. -Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. $\begin{array} { l l l l l } 5 & 20 & 4 & 14 & 10\end{array}$

Obtain the five-number summary for the given data. -The weekly salaries (in dollars) of sixteen government workers are listed below. $\begin{array} { l l l l } 690 & 609 & 813 & 644 \\ 728 & 571 & 473 & 614 \\ 529 & 678 & 685 & 460 \\ 552 & 787 & 507 & 826 \end{array}$

Exam 3: Descriptive Measures

Find the mode(s) for the given sample data. -81, 35, 32, 35, 29, 81

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)

Find the range for the given data set. -28, 39, 17, 45, 52

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions Being compared have approximately the same shape.)

Solve the problem. -Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation.

Find the population standard deviation. Round to one decimal place as needed. 0,3,5,7,70,3,5,7,70,3,5,7,7

The median of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

A variable x has the possible observations shown below. Possible observations of x\text { Possible observations of } \mathrm{x} Possible observations of x : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of xxx . Round the values of μ\muμ and σ\sigmaσ to one decimal place.

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Find the range for the given data set. -Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. 52041410\begin{array} { l l l l l } 5 & 20 & 4 & 14 & 10\end{array}5​20​4​14​10​

Find the population standard deviation. Round to one decimal place as needed. $0,3,5,7,7$

A variable x has the possible observations shown below. $\text { Possible observations of } \mathrm{x}$ : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of $x$ . Round the values of $\mu$ and $\sigma$ to one decimal place.

Find the range for the given data set. -Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. $\begin{array} { l l l l l } 5 & 20 & 4 & 14 & 10\end{array}$