Question 1

A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places.

Accepted Answer

To calculate the GPA, multiply each grade's quality points by the credit hours, sum the results, and divide by the total credit hours: (3*4 + 3*5 + 4*1 + 2*5 + 1*4) / (4+5+1+5+4) = 2.37.

Question 2

If the standard deviation for a set of data is 0, which of the following must be true?

Accepted Answer

When the standard deviation is 0, it means that all of the data values are identical. This is because the standard deviation measures the spread and variability of the data from the mean. If there is no spread or variability, it means that all of the values are the same. The other options are not necessarily true since a set of data could have all positive values and still have a standard deviation of 0 if they are all the same.

Question 3

When finding percentiles, if the locator L is not a whole number, one procedure is to interpolate so that a locator of 23.75, for example, leads to a value that is 3/4 of the way between the 23rd and 24th scores. Use this method
Of interpolation to find P75 for the set of test scores below. $$\begin{array} { l l l l l l } 
51 & 54 & 64 & 68 & 72 & 74 \
76 & 83 & 94 & 94 & 99 &
\end{array}$$

Accepted Answer

To find P75, calculate L = 0.75 * 11 = 8.25. Interpolate between the 8th (83) and 9th (94) scores: 83 + 0.25 * (94 - 83) = 85.75.

Question 4

Find the variance for the given data. Round your answer to one more decimal place than the original data. To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he
Was quoted are listed below: $\begin{array} { l l l l l l } \$ 663 & \$ 273 & \$ 410 & \$ 622 & \$ 174 & \$ 374 \end{array}$

Accepted Answer

The formula for variance is:

$V=\dfrac{\sum(x-\bar{x})^2}{n-1}$

where $x$ is each data point, $\bar{x}$ is the mean, and $n$ is the number of data points.

To find the variance for the given data, we first need to find the mean:

$\bar{x}=\dfrac{\sum x}{n}=\dfrac{663+273+410+622+174+374}{6}=427$

Next, we can calculate the sum of squared deviations from the mean:

$\sum(x-\bar{x})^2=(663-427)^2+(273-427)^2+(410-427)^2+(622-427)^2+(174-427)^2+(374-427)^2=151652$

Finally, we can plug these values into the formula for variance:

$V=\dfrac{\sum(x-\bar{x})^2}{n-1}=\dfrac{151652}{6-1}=36,838.3$ (rounded to one more decimal place than the original data)

Therefore, the best choice is C, with a variance of $36,838.3$ dollars squared.

Question 5

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer?

Accepted Answer

A z score of 2.00 represents a score that is two standard deviations above the mean, indicating a higher performance on the statistics test.

Question 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. $$\begin{array} { l l l l l l } 
22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3
\end{array}$$

Accepted Answer

The formula for sample standard deviation is $\sqrt{\frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n-1}}$. Using this formula, we can find that the sample mean is $\bar{x}=26.5$. Then, we can calculate the deviations from the mean for each data point:
$$\begin{array} { c c } 
x_i & x_i-\bar{x} \ \hline
22.6 & -3.9 \
16.1 & -10.4 \
36.1 & 9.6 \
36.0 & 9.5 \
23.8 & -2.7 \
20.3 & -6.2
\end{array}$$
Using these deviations, we can calculate the sum of squares of deviations:
$$\sum_{i=1}^n (x_i-\bar{x})^2 = (-3.9)^2+(-10.4)^2+9.6^2+9.5^2+(-2.7)^2+(-6.2)^2=442.6$$
Then, we can plug in the values to the formula for sample standard deviation to get: $\sqrt{\frac{442.6}{6-1}}\approx8.35$. Hence, the answer is D.

Question 7

A student earned grades of 84, 78, 84, and 72 on her four regular tests. She earned a grade of 78 on the final exam and 86 on her class projects. Her combined homework grade was 87. The four regular tests count for 40%
Of the course grade, the final exam counts for 30%, the project counts for 10%, and homework counts for 20%.
What is her weighted mean grade? Round to one decimal place.

Accepted Answer

The answer of A student earned grades of 84, 78,...

Question 8

The test scores of 40 students are listed below. Find P56. $$\begin{array} { l l l l l l l l l l } 
30 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \
59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \
72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \
81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98
\end{array}$$

Accepted Answer

P56 is the 56th percentile, which means 56% of the scores are below it and 44% are above it. To find the value at the 56th percentile, we need to arrange the scores in order from lowest to highest, which gives:

$$30, 35, 43, 44, 47, 48, 54, 55, \mathbf{56}, 57, 59, 62, 63, 65, 66, 68, 69, 69, 71, 72, 72, 73, 74, 76, 77, 77, 78, 79, 80, 81, 81, 82, 83, 85, 89, 92, 93, 94, 97, 98$$

There are 40 scores in total, so the 56th percentile corresponds to the score that is $$\frac{56}{100} \times 40 = 22.4$$ positions from the bottom (recall that percentiles can have decimal values). Counting up from the bottom, we see that the 22nd and 23rd scores are both 73, so the 56th percentile score is also \boxed{74}.

Question 9

Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z = -1.5. What is her temperature? Round your answer to the nearest hundredth.

Accepted Answer

The answer of Human body temperatures have a mean of...

Question 10

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $$\begin{array} { l l l l l l } 
22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3
\end{array}$$

Accepted Answer

Using a calculator or statistical software, the sample standard deviation is found to be approximately 8.3499. Rounding to one more decimal place gives 8.4, which is answer choice A. Answer choices B and C are much larger than the actual data, indicating an error in calculation. Answer choice D is one of the original data points and cannot be the standard deviation of the entire set.

Question 11

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. $$\begin{array} { l l l l l } 
7 & 7 & 2 & 5 & 1
\end{array}$$

Accepted Answer

The variance is 7.8. The mean is 4.4. The variance is the average of the squared differences from the mean. The squared differences are 9.68, 9.68, 5.12, 0.64, and 12.96. The average of these is 7.8.

Question 12

Approximately what percentage of apple diameters is greater than the 66th percentile?

Accepted Answer

The answer of Approximately what percentage of apple diameters is...

Question 13

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $$\begin{array} { l l l l l l l l l } 
18 & 18 & 18 & 9 & 15 & 5 & 10 & 5 & 15
\end{array}$$

Accepted Answer

The answer of Find the standard deviation for the given...

Question 14

The customer service department of a phone company is experimenting with two different systems. On Monday they try the first system which is based on an automated menu system. On Tuesday they try the second
System in which each caller is immediately connected with a live agent. A quality control manager selects a
Sample of seven calls each day. He records the time for each customer to have his or her question answered. The
Times (in minutes) are listed below. Find the coefficient of variation for each of the two sets of data, then compare the
Variation. Round results to one decimal place. $\begin{array}{llllllll}
\text { Automated Menu: } & 11.7 & 7.4 & 3.9 & 2.9 & 9.2 & 6.3 & 5.5 \
\text { Live agent: } & 6.2 & 2.9 & 4.4 & 4.1 & 3.4 & 5.2 & 3.7
\end{array}$

Accepted Answer

The coefficient of variation is calculated as the standard deviation divided by the mean, multiplied by 100. For the Automated Menu, the coefficient of variation is 45.4%, and for the Live Agent, it is 26.3%. This indicates that there is substantially more variation in the times for the automated menu system.

Question 15

Listed below are the amounts of time (in months) that the employees of a restaurant have been working at the restaurant. Find the mean for the given sample data. Round your answer to one more decimal place than the original
Data values. $$\begin{array} { l l l l l l l l l l l l l l } 
1 & 5 & 6 & 8 & 11 & 14 & 17 & 46 & 61 & 90 & 99 & 126 & 143 & 167
\end{array}$$

Accepted Answer

To find the mean, we add up all the values and divide by the total number of values. Adding up all the values gives us 559. Dividing by the total number of values, which is 14, gives us 39.92857. Rounding to one more decimal place than the original data values, we get 56.7 months as the mean.

Question 16

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?

Accepted Answer

Since the mean and standard deviation of the two tests are different, we cannot directly compare the scores. We need to use z-scores to compare them. A z-score measures how many standard deviations a value is from the mean.

For SAT score of 1490,

z = (1490-1518)/325 = -0.09

For ACT score of 17.0,

z = (17.0-21.1)/4.8 = -0.854

Therefore, option A and D are true. However, option C is not true since an ACT score of 17.0 has a lower z-score (-0.854) than an SAT score of 1490 (-0.09), indicating that the ACT score is relatively worse than the SAT score. Option B is also true as shown above.

Question 17

The number of vehicles passing through a bank drive -up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a 15-minute period. $$\begin{array} { l l l l } 
25 & 27 & 25 & 28 \
28 & 25 & 30 & 27 \
35 & 31 & 31 & 29 \
24 & 31 & 25 & 20 \
15 & 27 & 27 & 27
\end{array}$$

Accepted Answer

To find the median, we need to first arrange the data in numerical order:

15, 20, 24, 25, 25, 25, 27, 27, 27, 27, 28, 28, 29, 30, 31, 31, 35

There are 17 data points, so the median is the average of the middle two values: 27 and 28. Therefore, the median number of vehicles going through the line in a 15-minute period is 27.

Question 18

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. $$\begin{array} { l l l l l l l } 
81 & 71 & 202 & 113 & 269 & 248 & 242
\end{array}$$ Find the median number of newspapers sold.

Accepted Answer

To find the median, first arrange the numbers in ascending order: 71, 81, 113, 202, 242, 248, 269. The median is the middle number, which is 202.

Question 19

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. The test scores of 40 students are listed below. $\begin{array} { l l l l l l l l l l } 25 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \ 59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \ 72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \ 81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98 \end{array}$

Accepted Answer

The boxplot in A) accurately represents the data with a clear box showing the interquartile range, whiskers showing the smallest and largest non-outlier values, and points representing outliers. The 5-number summary (minimum, lower quartile, median, upper quartile, maximum) is also included. B) and D) do not accurately show the median and quartile values, and C) does not show the outliers.

Question 20

The prices (in dollars) of 12 electric smooth top ranges are listed below. Find the range for the given sample data. $$\begin{array} { l l l l l l } 
865 & 1010 & 655 & 565 & 1465 & 1110 \
710 & 765 & 820 & 1310 & 555 & 1065
\end{array}$$

Accepted Answer

To find the range, we need to subtract the smallest value from the largest value. The largest value in the data set is 1465 and the smallest is 555, so the range is $1465-$555$=$$910. Therefore, the answer is choice letter B.

Quiz 3: Describing, Exploring, and Comparing Data

If the standard deviation for a set of data is 0, which of the following must be true?

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer?

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. $\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}$

Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z = -1.5. What is her temperature? Round your answer to the nearest hundredth.

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}$

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l } 7 & 7 & 2 & 5 & 1\end{array}$

Approximately what percentage of apple diameters is greater than the 66th percentile?

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l l l l } 18 & 18 & 18 & 9 & 15 & 5 & 10 & 5 & 15\end{array}$

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. $\begin{array} { l l l l l l l } 81 & 71 & 202 & 113 & 269 & 248 & 242\end{array}$ Find the median number of newspapers sold.

The prices (in dollars) of 12 electric smooth top ranges are listed below. Find the range for the given sample data. $\begin{array} { l l l l l l } 865 & 1010 & 655 & 565 & 1465 & 1110 \\710 & 765 & 820 & 1310 & 555 & 1065\end{array}$

Quiz 3: Describing, Exploring, and Comparing Data

If the standard deviation for a set of data is 0, which of the following must be true?

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer?

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 22.616.136.136.023.820.3\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}22.6​16.1​36.1​36.0​23.8​20.3​

Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z = -1.5. What is her temperature? Round your answer to the nearest hundredth.

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. 22.616.136.136.023.820.3\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}22.6​16.1​36.1​36.0​23.8​20.3​

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. 77251\begin{array} { l l l l l } 7 & 7 & 2 & 5 & 1\end{array}7​7​2​5​1​

Approximately what percentage of apple diameters is greater than the 66th percentile?

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. 181818915510515\begin{array} { l l l l l l l l l } 18 & 18 & 18 & 9 & 15 & 5 & 10 & 5 & 15\end{array}18​18​18​9​15​5​10​5​15​

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. $\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}$

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l } 22.6 & 16.1 & 36.1 & 36.0 & 23.8 & 20.3\end{array}$

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l } 7 & 7 & 2 & 5 & 1\end{array}$

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l l l l } 18 & 18 & 18 & 9 & 15 & 5 & 10 & 5 & 15\end{array}$