3. Describing Data Numerically

The Federal Reserve Bank of St. Louis reported two average personal incomes for 2018: \$33,706 and \$50,731. One of these averages is the mean and the other is the median. Which is the mean? Support your answer.

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.

Travel Time to Work The frequency distribution listed in the table represents the travel time to work (in minutes) for a random sample of 895 U.S. adults.

a. Approximate the mean travel time to work for U.S. adults.

Which Car Would You Buy? Suppose that you are in the market to purchase a car. You have narrowed it down to two choices and will let gas mileage be the deciding factor. You decide to conduct a little experiment in which you put 10 gallons of gas in the car and drive it on a closed track until it runs out gas. You conduct this experiment 15 times on each car and record the number of miles driven. Describe each data set. That is, determine the shape, center, and spread. Which car would you buy and why?

Yolanda wishes to develop a new type of meatloaf to sell at her restaurant. She decides to combine 2 pounds of ground sirloin (cost \$2.70 per pound), 1 pound of ground turkey (cost \$1.30 per pound), and 12\(\frac{1}{2}\)21 pound of ground pork (cost \$1.80 per pound). What is the cost per pound of the meatloaf?

Weighted Mean A student of the author earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned grades of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60% of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.

In Exercises 29–32, compute the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (29) 31.4 minutes; (Exercise 30) 140.6 minutes; (Exercise 31) 55.2 years; (Exercise 32) 240.2 seconds.

Suppose the following data represent the amount of time (in hours) a random sample of students enrolled in College Algebra spent working on a homework assignment: 3.2, 4.1, 1.2, 0.6, and 2.5. Below are three bootstrap samples. For each bootstrap sample, determine the bootstrap sample mean.

Bootstrap Sample 1: 1.2, 0.6, 3.2, 3.2, 1.2

Bootstrap Sample 2: 0.6, 4.1, 4.1, 0.6, 4.1

Bootstrap Sample 3: 4.1, 3.2, 3.2, 0.6, 1.2

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).

35 35 20 50 95 75 45 50 30 35 30 30

a. Find the mean xbar.

According to data from the city of Toronto, Ontario, Canada, there were nearly 112,000 parking infractions in the city for December 2020, with fines totaling over 5,500,000 Canadian dollars. The fines (in Canadian dollars) for a random sample of 105 parking infractions in Toronto, Ontario, Canada, for December 2020 are listed below. (Source: City of Toronto)

In Exercises 1–5, use technology. If possible, print your results.

Find the sample mean of the data.

Missing Exam Grade A professor has recorded exam grades for 20 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 82 and the mean of the 19 readable scores is 84, what is the value of the unreadable score?

"Birth Weights Suppose birth weights of babies are approximately normal with a mean of 3570 grams and a standard deviation of 495 grams. In a random sample of 15 mothers who were smokers during pregnancy, the mean birth weight of the babies was 3481.6 grams.

b. Simulate obtaining 2000 simple random samples for size n=15 babies from a population that is normally distributed with mean 3570 and standard deviation 495. For each sample, determine the sample mean. Draw a histogram of the 2000 sample means. Explain what each sample mean represents."

Constructing a Confidence Interval In Exercises 25–28, use the data set to (a) find the sample mean. Assume the population is normally distributed.

SAT Scores The SAT scores of 12 randomly selected high school seniors

Extending Concepts

Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.

c. What is the benefit of using a trimmed mean versus using a mean found using all data entries? Explain your reasoning.