1. The sweater numbers of the 2021-2022 Defensemen on the Carolina Hurricanes are 7, 22, 25, 28, 74, 76, 77. Does it make sense to calculate the average of these numbers? Are these data qualitative or quantitative? Explain.

2. Data: The following are 25 times (measured in hours) until breakage of a certain type of experimental fastener used in airplanes (in order from smallest to largest).

0.74, 0.75, 0.94, 1.02, 1.11, 1.40, 1.47, 1.58, 1.85, 2.12, 2.35, 2.71, 3.2, 3.47, 3.73, 4.09, 4.26, 4.49, 4.97, 5.40, 6.06, 8.41, 9.30, 10.27, 12.30

a. Find the 5-number summary.

b. What are the endpoints that determine possible outliers? (Use the IQR formulas). Identify the possible outliers in the data set (if they exist).

c. Make an outlier box-plot for the data and mark/label all points (Q1, median, Q3, outliers,

minimum, maximum). If the data has outliers, mark them with a * and use the closest non-

outlier value in place of the min or max.

d. Is the distribution symmetric, or skewed right or left?

e. Calculate the mean of the data.

f. If we consider the value of 12.30 to be an outlier (which, by definition, it is), how would

removing it from our data set change the mean? Explain your predication, but you do not need to compute the new mean.

g. What do we expect removing the outlier will do to the standard deviation? Explain your

prediction, but you do not have to compute the standard deviation.

3. The following are 13 observations on burst strength (lb/in2) obtained from a test on a certain type of closure weld: 6200, 7200, 8200, 7600, 6700, 7400, 7200, 7300, 7400, 5900, 8300, 7300, 7300

a. Give the five-number summary of this distribution.

b. What are the endpoints that determine possible outliers? (Use the IQR formulas). Identify the possible outliers in the data set (if they exist).

c. Make an outlier box-plot for the data and mark/label all points (Q1, median, Q3, outliers,

minimum, maximum). If the data has outliers, mark them with a * and use the closest non-

outlier value in place of the min or max.

d. Based on your boxplot, comment on the symmetry and skew of the dataset.

e. What, if anything, can you say about the variation (spread) of the dataset?

4. Given the exams scores of 16 students: 52, 53.5, 55.5, 56, 58, 65, 72, 77, 81, 88, 90.5, 93, 94, 94, 100, 100

a. Find the mean of these data.

b. Find the median of these data (remember to order the data first).

c. How do the mean and median compare to one another (is one bigger than the other)? What does this tell you about the distribution of the data?

d. Find the mode of the data set. Is the mode useful to understand how the students did?

6. Ten students in a college-level mathematics course were asked to estimate the number of hours per week that they spent studying and doing homework. These data are listed below. 3.75, 3.25, 2.50, 1.0, 2.5, 3.25, 1.5, 1.75, 2.75, 3.5

a. Calculate the mean.

b. Find the median.

c. Compute the standard deviation using the Defining Formula.

d. Compute the standard deviation using the Computing Formula.

7. Two friends, Duke and Colby, went bowling. Their scores are given below.

Duke: 225, 212, 238 for a total score of 675 Colby: 221, 221, 225 for a total score of 667

a. Calculate both the mean and standard deviation of Duke's scores.

b. Calculate both the mean and standard deviation of Colby's scores.

c. Which of the two is the better bowler? Explain your answer.

d. Which of the two is the more consistent bowler? Explain your answer.