3. Describing Data Numerically

Building Basic Skills and Vocabulary

True or False? In Exercises 1–4, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A data set can have the same mean, median, and mode.

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.

Cholesterol The cholesterol levels of a sample of 10 female employees

154 240 171 188 235 203 184 173 181 275

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.

Judicial System The responses of a sample of 34 young adult United Kingdom males in custodial sentences who were asked what is affected by such sentences (Adapted from User Voice)

Mental health: 8

Trust: 3

Education: 8

Personal development: 5

Family: 3

Future opportunities: 3

Other: 4

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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Protein Powder During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1525, 1526, 1502, 1516, 1529, and 1511.

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

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.

The overall averages of 12 students in a statistics class prior to taking the final exam are listed.

67 72 88 73 99 85 81 87 63 94 68 87

a. Find the mean, median, and mode of the data set. Which best represents the center of the data?

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.

Extending Concepts

Data Analysis Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown in the table at the left.

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

In Exercises 13 and 14, 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.

The responses of 1019 adults who were asked how much money they think they will spend on Christmas gifts in a recent year (Adapted from Gallup)

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M&Ms The following data represent the weights (in grams) of a simple random sample of 50 M&M plain candies. Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M&M?

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.

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?

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?

The median for the given set of six ordered data values is 26.5. What is the missing value? 7 12 21 ______ 41 50