Interpreting Percentiles In Exercises 29–32, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What score represents the 65th percentile? How should you interpret this?

Finding and Interpreting Percentiles In Exercises 37– 40, use the data set, which represents wait times (in minutes) for various services at a state’s Department of Motor Vehicles locations.

6 10 1 22 23 10 6 7 2 1 6 6 2 4 14 15 16 4

19 3 19 26 5 3 4 7 6 10 9 10 20 18 3 20 10 13

14 11 14 17 4 27 4 8 4 3 26 18 21 1 3 3 5 5

Which wait time represents the 50th percentile? How would you interpret this?

Extending Concepts

Midquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below.

Midquartile = (Q₁ + Q₃) / 2

In Exercises 55 and 56, find the midquartile of the data set.

5 7 1 2 3 10 8 7 5 3

Using Technology to Find Quartiles and Draw Graphs In Exercises 23–26, use technology to draw a box-and-whisker plot that represents the data set.

Vacation Days The number of vacation days used by a sample of 20 employees in a recent year

3 9 2 1 7 5 3 2 2 6

4 0 10 0 3 5 7 8 6 5

Using Technology to Find Quartiles and Draw Graphs In Exercises 23–26, use technology to draw a box-and-whisker plot that represents the data set.

Hourly Earnings The hourly earnings (in dollars) of a sample of 21 employees at a consulting firm

25.89 27.09 31.76 28.28 26.19 27.43 24.06

25.61 22.56 29.76 18.01 23.66 38.24 37.27

32.70 31.12 25.87 15.06 23.12 30.62 19.85

Studying Refer to the data set in Exercise 23 and the box-and-whisker plot you drew that represents the data set.

c. You randomly select one student from the sample. What is the likelihood that the student studied less than 2 hours per day? Write your answer as a percent.

Hourly Earnings Refer to the data set in Exercise 26 and the box-and-whisker plot you drew that represents the data set.

b. What percent of the employees made more than $23.39 per hour?

Building Basic Skills and Vocabulary

A student’s grade on the Fundamentals of Engineering exam has a z-score of −0.5. Make an observation about the student’s grade.

True or False? In Exercises 7–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

It is impossible to have a z-score of 0.

Graphical Analysis In Exercises 41 and 42, the midpoints A, B, and C are marked on the histograms at the left. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?

z = 0, z = 2.14, z = −1.43

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2020 is approximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.4 years. In Exercises 43–48, use the corresponding z-score to determine whether the age is unusual. Explain your reasoning. (Source: Le Tour de France)

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2020 is approximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.4 years. In Exercises 43–48, use the corresponding z-score to determine whether the age is unusual. Explain your reasoning. (Source: Le Tour de France)

Life Spans of Tires A brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.

b. The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

Life Spans of Fruit Flies The life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 33 days and a standard deviation of 4 days.

b. The life spans of three randomly selected fruit flies are 29 days, 41 days, and 25 days. Using the Empirical Rule, find the percentile that corresponds to each life span.

Comparing z-Scores from Different Data Sets The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2020. The distributions of the ages are approximately bell-shaped. In Exercises 51–54, compare the z-scores for the actors.

Best Actor 1970: John Wayne, Age: 62

Best Supporting Actor 1970: Gig Young, Age: 56

Graphical Analysis In Exercises 19–22, use the box-and-whisker plot to determine whether the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Justify your answer.

Graphical Analysis In Exercises 19–22, use the box-and-whisker plot to determine whether the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Justify your answer.

Project Find a real-life data set and use the techniques of Chapter 2, including graphs and numerical quantities, to discuss the center, variation, and shape of the data set. Describe any patterns.