Question 1

In a data set containing n values, the 67th percentile can be found as follows: $$\mathrm { P } _ { 67 } = \frac { 67 } { 100 } \cdot \mathrm { n }$$ ?

Accepted Answer

The formula given calculates the position of the 67th percentile in a sorted data set, not the actual value of the 67th percentile. The value at this position is the 67th percentile.

Question 2

Find the mode(s) for the given sample data.
-Listed below are the lengths (in inches) of each snake in the Clarmont Zoo's reptile house. $$\begin{array} { l l l l l l l l l l l } 
9 & 15 & 99 & 13 & 16 & 101 & 40 & 10 & 14 & 17 & 102
\end{array}$$

Accepted Answer

The mode is the value that appears most frequently in a data set. In this case, no value appears more than once, so there is no mode.

Question 3

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in
the original data.
-$$\begin{array} { l l l l l l l l l } 
194 & 283 & 131 & 171 & 196 & 119 & 293 & 132 & 193
\end{array}$$

Accepted Answer

To find the standard deviation, first calculate the mean of the data set. Then, find the squared differences from the mean, average those squared differences, and take the square root. The calculated standard deviation is approximately 62.8.

Question 4

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
-The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. Construct a boxplot for the data set.

$\begin{array} { l l l l l l l l } 310 & 320 & 450 & 460 & 470 & 500 & 520 & 540 \end{array}$
$\begin{array} { l l l l l l l } 580 & 600 & 650 & 700 & 710 & 840 & 870&900 \end{array}$
$\begin{array} { l l l l l l l } 1000&1200&1250&1300&1400&1720&2500&3700 \end{array}$

A)

B)

C)

D)

Accepted Answer

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

Question 5

Find the mode(s) for the given sample data.
-The speeds (in mi/h) of the cars passing a certain checkpoint are measured by radar. The results are shown below. $$\begin{array} { c c c c c } 
42.7 & 41.4 & 44.9 & 41.5 & 46.0 \
46.0 & 41.4 & 40.6 & 47.9 & 41.5 \
42.7 & 40.6 & 41.5 & 39.8 & 41.4 \
44.3 & 44.3 & 44.9 & 49.5 & 42.7
\end{array}$$

Accepted Answer

The mode is the number that appears most frequently in a data set. In this data set, 42.7, 41.5, and 41.4 each appear three times, more frequently than any other numbers.

Question 6

Find the median for the given sample data.
-The distances (in miles) driven in the past week by each of a company's sales representatives are listed below. $$\begin{array} { l l l l l l } 
29 & 99 & 246 & 270 & 379 & 389
\end{array}$$ Find the median distance driven.

Accepted Answer

The answer of Find the median for the given sample...

Question 7

Find the number of standard deviations from the mean. Round your answer to two decimal places.
-The annual snowfall in a town has a mean of 39 inches and a standard deviation of 10 inches. Last year there were 64 inches of snow. How many standard deviations from the mean is that?

Accepted Answer

To find the number of standard deviations from the mean, use the formula: (X - μ) / σ. Here, X = 64, μ = 39, and σ = 10. So, (64 - 39) / 10 = 2.50. Thus, it is 2.50 standard deviations above the mean.

Question 8

Find the midrange for the given sample data.
-$$\begin{array} { l l l l l l l l l l l l l l l l } 
3 & 6 & 9 & 0 & 4 & 1 & 11 & 5 & 9 & 14 & 3 & 8 & 2 & 15 & 0 & 9
\end{array}$$

Accepted Answer

The midrange is calculated by taking the average of the maximum and minimum values in the data set. The maximum value is 15 and the minimum value is 0. The midrange is (15 + 0) / 2 = 7.5.

Question 9

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.
-A distribution of data has a maximum value of 60, a median value of 53, and a minimum of 46.

Accepted Answer

The range rule of thumb estimates the standard deviation as the range divided by 4. The range is 60 - 46 = 14, so the estimated standard deviation is 14 / 4 = 3.5.

Question 10

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place.
-Compare the variation in heights to the variation in weights of thirteen-year old girls. The heights (in inches) and weights (in pounds) of nine randomly selected thirteen-year old girls are listed below.

$\begin{array}{llllllllll}
\text { Heights (inches): } & 59.4 & 61.2 & 62.1 & 64.7 & 60.1 & 58.3 & 64.6 & 63.7 & 66.1 \
\text { Weights (pounds): } &87 & 94 & 93 & 119 & 96 & 90 & 123 & 98 & 139
\end{array}$

Accepted Answer

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

Question 11

Find the midrange for the given sample data.
-$$\begin{array} { l l l l l l l l } 
49 & 52 & 52 & 52 & 74 & 67 & 55 & 55
\end{array}$$

Accepted Answer

The midrange is calculated by taking the average of the maximum and minimum values in the data set. The maximum value is 74 and the minimum value is 49. So, the midrange is (74 + 49) / 2 = 61.5.

Question 12

Find the variance for the given data. Round your answer to one more decimal place than the original data.
-$$\begin{array} { l l l l l } 
19 & 5 & 20 & 6 & 2
\end{array}$$

Accepted Answer

To find the variance, first calculate the mean: (19+5+20+6+2)/5 = 10.4. Then, find the squared differences from the mean: (19-10.4)², (5-10.4)², (20-10.4)², (6-10.4)², (2-10.4)². These are 73.96, 29.16, 92.16, 19.36, and 70.56. The variance is the average of these squared differences: (73.96+29.16+92.16+19.36+70.56)/5 = 71.24, rounded to 71.3.

Question 13

Scores on a test have a mean of 74 and a standard deviation of 12. Michelle has a score of 50. Convert Michelle's score to a z-score.

Accepted Answer

A z-score is calculated by subtracting the mean from the score and then dividing by the standard deviation. For Michelle: (50 - 74) / 12 = -24 / 12 = -2.

Question 14

Find the range for the given sample data.
-The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each employee to record the distance they travel one way from home to work. The six distances (in miles) are listed below: $$\begin{array} { l l l l l l } 
2.8 & 5.3 & 1.4 & 4.8 & 6.6 & 3.3
\end{array}$$

Accepted Answer

The range is calculated by subtracting the smallest value from the largest value in the data set: 6.6 - 1.4 = 5.2 miles.

Question 15

Find the indicated measure.
-The weights (in pounds) of 30 newborn babies are listed below. Find P16. $$\begin{array} { l l l l l l l l l l } 
5.5 & 5.7 & 5.8 & 5.9 & 6.1 & 6.1 & 6.4 & 6.4 & 6.5 & 6.6 \
6.7 & 6.7 & 6.7 & 6.9 & 7.0 & 7.0 & 7.0 & 7.1 & 7.2 & 7.2 \
7.4 & 7.5 & 7.7 & 7.7 & 7.8 & 8.0 & 8.1 & 8.1 & 8.3 & 8.7
\end{array}$$

Accepted Answer

The 16th value in the ordered list is 6.1 lb.

Question 16

Find the number of standard deviations from the mean. Round your answer to two decimal places.
-Mario's weekly poker winnings have a mean of $323 and a standard deviation of $50. Last week he won $177. How many standard deviations from the mean is that?

Accepted Answer

To find the number of standard deviations from the mean, use the formula: (X - μ) / σ. Here, X = $177, μ = $323, and σ = $50. So, (177 - 323) / 50 = -2.92, which means 2.92 standard deviations below the mean.

Question 17

Find the number of standard deviations from the mean. Round your answer to two decimal places.
-The number of assists per match for the setter on your school's volleyball team has a mean of 55 and a standard deviation of 8. How many standard deviations from the mean is an outing with 74 assists?

Accepted Answer

To find the number of standard deviations from the mean, use the formula: (X - μ) / σ. Here, X = 74, μ = 55, and σ = 8. So, (74 - 55) / 8 = 2.38. Therefore, 74 assists is 2.38 standard deviations above the mean.

Question 18

Find the midrange for the given sample data.
-Bill kept track of the number of hours he spent exercising each week. The results for 15 weeks are shown below. Find the midrange.
 $$\begin{array} { l l l l l } 
7.4 & 6.7 & 7.4 & 7.4 & 7.6 \
8.0 & 6.6 & 8.0 & 8.4 & 7.4 \
8.8 & 6.7 & 8.0 & 9.0 & 7.6
\end{array}$$

Accepted Answer

The midrange is calculated by taking the average of the maximum and minimum values in the data set. The minimum value is 6.6 and the maximum value is 9.0. The midrange is (6.6 + 9.0) / 2 = 7.8 hr.

Question 19

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 local Tupperware dealers earned these commissions last month: $$\begin{array} { l l l l l } 
\$ 3120.40 & \$ 2050.85 & \$ 4357.05 & \$ 4632.26 & \$ 3033.20 \
\$ 3150.18 & \$ 1772.68 & \$ 1586.15 & \$ 2269.53 & \$ 3692.16
\end{array}$$ What was the mean commission earned? Round your answer to the nearest cent.

Accepted Answer

The answer of Find the mean for the given sample...

Question 20

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
-The highest temperatures ever recorded (in °F) in 32 different U.S. states are shown below. Construct a boxplot for the data set. 
$\begin{array} { l l l l l l l l } 100 & 100 & 105 & 105 & 106 & 106 & 107 & 107 \ 109 & 110 & 110 & 112 & 112 & 112 & 114 & 114 \ 114 & 115 & 116 & 117 & 118 & 118 & 118 & 118 \ 118 & 119 & 120 & 121 & 122 & 125 & 128 & 134 \end{array}$

A)

B)

C)

D)

Accepted Answer

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

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

In a data set containing n values, the 67th percentile can be found as follows: $\mathrm { P } _ { 67 } = \frac { 67 } { 100 } \cdot \mathrm { n }$ ?

Find the mode(s) for the given sample data. -Listed below are the lengths (in inches) of each snake in the Clarmont Zoo's reptile house. $\begin{array} { l l l l l l l l l l l } 9 & 15 & 99 & 13 & 16 & 101 & 40 & 10 & 14 & 17 & 102\end{array}$

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. - $\begin{array} { l l l l l l l l l } 194 & 283 & 131 & 171 & 196 & 119 & 293 & 132 & 193\end{array}$

Find the median for the given sample data. -The distances (in miles) driven in the past week by each of a company's sales representatives are listed below. $\begin{array} { l l l l l l } 29 & 99 & 246 & 270 & 379 & 389\end{array}$ Find the median distance driven.

Find the number of standard deviations from the mean. Round your answer to two decimal places. -The annual snowfall in a town has a mean of 39 inches and a standard deviation of 10 inches. Last year there were 64 inches of snow. How many standard deviations from the mean is that?

Find the midrange for the given sample data. - $\begin{array} { l l l l l l l l l l l l l l l l } 3 & 6 & 9 & 0 & 4 & 1 & 11 & 5 & 9 & 14 & 3 & 8 & 2 & 15 & 0 & 9\end{array}$

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -A distribution of data has a maximum value of 60, a median value of 53, and a minimum of 46.

Find the midrange for the given sample data. - $\begin{array} { l l l l l l l l } 49 & 52 & 52 & 52 & 74 & 67 & 55 & 55\end{array}$

Find the variance for the given data. Round your answer to one more decimal place than the original data. - $\begin{array} { l l l l l } 19 & 5 & 20 & 6 & 2\end{array}$

Scores on a test have a mean of 74 and a standard deviation of 12. Michelle has a score of 50. Convert Michelle's score to a z-score.

Find the number of standard deviations from the mean. Round your answer to two decimal places. -Mario's weekly poker winnings have a mean of $323 and a standard deviation of $50. Last week he won $177. How many standard deviations from the mean is that?

Find the number of standard deviations from the mean. Round your answer to two decimal places. -The number of assists per match for the setter on your school's volleyball team has a mean of 55 and a standard deviation of 8. How many standard deviations from the mean is an outing with 74 assists?

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

In a data set containing n values, the 67th percentile can be found as follows: P67=67100⋅n\mathrm { P } _ { 67 } = \frac { 67 } { 100 } \cdot \mathrm { n }P67​=10067​⋅n ?

Find the number of standard deviations from the mean. Round your answer to two decimal places. -The annual snowfall in a town has a mean of 39 inches and a standard deviation of 10 inches. Last year there were 64 inches of snow. How many standard deviations from the mean is that?

Find the midrange for the given sample data. - 3690411159143821509\begin{array} { l l l l l l l l l l l l l l l l } 3 & 6 & 9 & 0 & 4 & 1 & 11 & 5 & 9 & 14 & 3 & 8 & 2 & 15 & 0 & 9\end{array}3​6​9​0​4​1​11​5​9​14​3​8​2​15​0​9​

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. -A distribution of data has a maximum value of 60, a median value of 53, and a minimum of 46.

Find the midrange for the given sample data. - 4952525274675555\begin{array} { l l l l l l l l } 49 & 52 & 52 & 52 & 74 & 67 & 55 & 55\end{array}49​52​52​52​74​67​55​55​

Find the variance for the given data. Round your answer to one more decimal place than the original data. - 1952062\begin{array} { l l l l l } 19 & 5 & 20 & 6 & 2\end{array}19​5​20​6​2​

Scores on a test have a mean of 74 and a standard deviation of 12. Michelle has a score of 50. Convert Michelle's score to a z-score.

Find the number of standard deviations from the mean. Round your answer to two decimal places. -Mario's weekly poker winnings have a mean of $323 and a standard deviation of $50. Last week he won $177. How many standard deviations from the mean is that?

Find the number of standard deviations from the mean. Round your answer to two decimal places. -The number of assists per match for the setter on your school's volleyball team has a mean of 55 and a standard deviation of 8. How many standard deviations from the mean is an outing with 74 assists?

In a data set containing n values, the 67th percentile can be found as follows: $\mathrm { P } _ { 67 } = \frac { 67 } { 100 } \cdot \mathrm { n }$ ?

Find the midrange for the given sample data. - $\begin{array} { l l l l l l l l l l l l l l l l } 3 & 6 & 9 & 0 & 4 & 1 & 11 & 5 & 9 & 14 & 3 & 8 & 2 & 15 & 0 & 9\end{array}$

Find the midrange for the given sample data. - $\begin{array} { l l l l l l l l } 49 & 52 & 52 & 52 & 74 & 67 & 55 & 55\end{array}$

Find the variance for the given data. Round your answer to one more decimal place than the original data. - $\begin{array} { l l l l l } 19 & 5 & 20 & 6 & 2\end{array}$