3. Describing Data Numerically

Extending Concepts

Golf The distances (in yards) for nine holes of a golf course are listed.

336 393 408 522 147 504 177 375 360

a. Find the mean and the median of the data.

Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.

Weights Use the weights of the males listed in Data Set 2 “ANSUR I 1988,” which were measured in 1988 and use the weights of the males listed in Data Set 3 “ANSUR II 2012,” which were measured in 2012. Does it appear that males have become heavier?

Find the median of the sample data below.

U.S. Trade Deficits The table at the left shows the U.S. trade deficits (in billions of dollars) with 18 countries in 2020. (Source: U.S. Department of Commerce)

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a. Find the mean and the median of the trade deficits.

Resistant Measures Listed below are 10 wait times (minutes) for “Rock ‘n’ Roller Coaster” at 10 AM (from Data Set 33 “Disney World Wait Times”). The data are listed in order from lowest to highest. Find the mean and median of these ten values. Then find the mean and median after excluding the value of 180, which appears to be an outlier. Compare the two sets of results. How much was the mean affected by the inclusion of the outlier? How much is the median affected by the inclusion of the outlier?

15 20 25 30 30 35 45 50 50 180 

Using and Interpreting Concepts

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.

Prices (in dollars) of Flights from Chicago to Alanta

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Wait Time The following data represent the wait time (in minutes) for a random sample of 40 visitors to Disney’s Dinosaur Ride in Animal Kingdom. Determine the shape of the distribution of wait time by drawing a frequency histogram. Find the mean and median wait time. Which measure of central tendency better describes wait time?

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 

b. Find the median.

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.

0 0 1 2 17 28 21 8

a. Find the mean.

b. Find the median.

Problems 17 and 18 use the following definition of the modal class. The modal class of a variable can be obtained from data in a frequency distribution by determining the class that has the largest frequency. Determine the modal class of the frequency distribution in Problem 2.

Problems 15 and 16 use the following steps to approximate the median from grouped data.

Approximate the median of the frequency distribution in Problem 4.