3. Describing Data Numerically

Sampling Distributions The following data represent the ages of the winners of the Academy Award for Best Actor for the years 2012–2017.

a. Compute the population mean, mu.

Putting It Together: Bike Sharing Bicycle sharing exists in a variety of cities around the country. Los Angeles has the Metro Bike Share system. Users pick up a bike from one station, go for a ride, and return the bike to any station. Go to www.pearsonhighered.com/sullivanstats and download the file 8_1_34. The data represent the duration (in minutes) of all rides in the fourth quarter (October through December) of 2018.

e. The column “Sample1” represents the duration (in minutes) of a simple random sample of 40 bike rides where the ride was a “Round Trip” (that is, return the bike to the same location it was rented from). What is the sample mean?

In Problems 7– 10, find the population mean or sample mean as indicated.

Sample: 83, 65, 91, 87, 84

Flight Time The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on United Airlines. Compute the mean, median, and mode flight time.

282, 270, 260, 266, 257, 260, 267

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?

A researcher with the Department of Energy wants to determine the mean natural gas bill of households throughout the United States. He knows the mean natural gas bill of households for each state, so he adds together these 50 values and divides by 50 to arrive at his estimate. Is this a valid approach? Why or why not?

Grade-Point Average Marissa has just completed her second semester in college. She earned a B in her five-hour calculus course, an A in her three-hour social work course, an A in her four-hour biology course, and a C in her three-hour American literature course. Assuming that an A equals 4 points, a B equals 3 points, and a C equals 2 points, determine Marissa’s grade-point average for the semester.

Nut Mix Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can’t decide among peanuts, cashews, or almonds. They again agree to create a mix. They bought 2.5 pounds of peanuts for \$1.30 per pound, 4 pounds of cashews for \$4.50 per pound, and 2 pounds of almonds for \$3.75 per pound. Determine the price per pound of the mix.

Weighted Mean Michael has just completed his first semester in college. He earned an A in his five-hour calculus course, a B in his four-hour chemistry course, an A in his three-hour speech course, and a C in his three-hour psychology course. Assuming an A equals 4 points, a B equals 3 points, and a C equals 2 points, determine Michael’s grade-point average if grades are weighted by class hours.

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?

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

Download Time A histogram of the download time of a movie, in minutes, for 30 randomly selected movies is shown. The mean download time is 39.007 minutes and the median download time is 39.065 minutes. Identify the shape of the distribution. Which measure of central tendency better describes the “center” of the distribution?

Chicago Taxis Open the data file “ChicagoTaxi”, which is available in StatCrunch. The data file ChicagoTaxi is also available at www.pearsonhighered.com/sullivanstats. This data set represents the trip time, fare, and payment method for all taxi rides on July 25, 2017.

a. Determine the population mean fare of all taxi rides on July 25, 2017.

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?