Answer: Using Technology to Find Quartiles and Draw Graphs

Problem 1E A movie’s length represents the first quartile for movies showing at a theater. Make an observation about the movie’s length.

Problem 1UAE Use the Internet or some other resource to find an example of a graph that might lead to incorrect conclusions.

Problem 2E A car’s fuel efficiency represents the ninth decile of cars in its class. Make an observation about the car’s fuel efficiency.

Problem 2UAE You are publishing an article that discusses how eating oatmeal can help lower cholesterol. Because eating oatmeal might help people with high cholesterol, you include a graph that exaggerates the effects of eating oatmeal on lowering cholesterol. Do you think it is ethical to publish this graph? Explain

Problem 3E A student’s score on an actuarial exam is in the 83rd percentile. Make an observation about the student’s exam score.

Problem 4E A child’s IQ is in the 93rd percentile for the child’s age group. Make an observation about the child’s IQ.

Problem 58EC Modified Boxplot A modified boxplot is a boxplot that uses symbols to identify outliers. The horizontal line of a modified boxplot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. In Exercise, (a) identify any outliers and (b) draw a modified boxplot that represents the data set. Use asterisks (*) to identify outliers. 75 78 80 75 62 72 74 75 80 95 76 72

Problem 5E Explain how to identify outliers using the interquartile range.

Problem 6E Describe the relationship between quartiles and percentiles.

Problem 8E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. The second quartile is the mean of an ordered data set.

Problem 9E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. An outlier is any number above Q3 or below Q1.

Problem 7E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. About one-quarter of a data set falls below Q1.

Problem 11E Finding Quartiles In Exercise, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers. 56 63 51 60 57 60 60 54 63 59 80 63 60 62 65

Problem 10E True or False? In Exercise, 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.

Problem 13E Finding Quartiles In Exercise, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers. 42 53 36 28 26 41 37 40 48 45 19 38 36 56 43 34 52 38 50 43

Problem 14E Finding Quartiles In Exercise, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers. 22 25 22 24 20 24 19 22 29 21 21 20 23 25 23 23 21 25 23 22

Graphical Analysis In Exercises 15 and 16, use the box-and-whisker plot to identify the five-number summary.

Graphical Analysis In Exercises 15 and 16, use the box-and-whisker plot to identify the five-number summary.

Problem 12E Finding Quartiles In Exercise, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers. 36 41 39 47 15 48 34 28 25 28 19 18 50 27 53

Problem 17E Drawing a Box-and-Whisker Plot In Exercise, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set. 39 36 30 27 26 24 28 35 39 60 50 41 35 32 51

Problem 20E Drawing a Box-and-Whisker Plot In Exercise, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set. 2 7 1 3 1 2 8 9 9 2 5 4 7 3 7 5 4 7 2 3 5 9 5 6 3 9 3 4 9 8 8 2 3 9 5

Problem 18E Drawing a Box-and-Whisker Plot In Exercise, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set. 171 176 182 150 178 180 173 170 174 178 181 180

Graphical Analysis In Exercises 21–24, 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.

Problem 19E Drawing a Box-and-Whisker Plot In Exercise, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set. 4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9

Graphical Analysis In Exercises 21–24, 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 21–24, 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 21–24, 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.

Problem 25E Using Technology to Find Quartiles and Draw Graphs In Exercise, use technology to (a) find the data set’s first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set. TV Viewing The numbers of hours of television watched per day by a sample of 28 people 2 4 1 5 7 2 5 4 4 2 3 6 4 3 5 2 0 3 5 9 4 5 2 1 3 6 7 2

Problem 27E Using Technology to Find Quartiles and Draw Graphs In Exercise, use technology to (a) find the data set’s first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set. Airplane Distances The distances (in miles) from an airport of a sample of 22 inbound and outbound airplanes 2.8 2.0 3.0 3.0 3.2 5.9 3.5 3.6 1.8 5.5 3.7 5.2 3.8 3.9 6.0 2.5 4.0 4.1 4.6 5.0 5.5 6.0

Problem 29E TV Viewing Refer to the data set In Exercise 25, and the box-and-whisker plot you drew that represents the data set. (a) About 75% of the people watched no more than how many hours of television per day? (b) What percent of the people watched more than 4 hours of television per day? (c) You randomly select one person from the sample. What is the likelihood that the person watched less than 2 hours of television per day? Write your answer as a percent. Exercise 25 : Using Technology to Find Quartiles and Draw Graphs Use technology to (a) find the data set’s first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set. TV Viewing The numbers of hours of television watched per day by a sample of 28 people 2 4 1 5 7 2 5 4 4 2 3 6 4 3 5 2 0 3 5 9 4 5 2 1 3 6 7 2

Problem 28E Using Technology to Find Quartiles and Draw Graphs In Exercise, use technology to (a) find the data set’s first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set. Hourly Earnings The hourly earnings (in dollars) of a sample of 25 railroad equipment manufacturers 15.60 18.75 14.60 15.80 14.35 13.90 17.50 17.55 13.80 14.20 19.05 15.35 15.20 19.45 15.95 16.50 16.30 15.25 15.05 19.10 15.20 16.22 17.75 18.40 15.25

Problem 26E Using Technology to Find Quartiles and Draw Graphs In Exercise, use technology to (a) find the data set’s first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set. Vacation Days The numbers 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

Problem 30E Manufacturer Earnings Refer to the data set In Exercise 28, and the box-and-whisker plot you drew that represents the data set. (a) About 75% of the manufacturers made less than what amount per hour? (b) What percent of the manufacturers made more than $15.80 per hour? (c) You randomly select one manufacturer from the sample. What is the likelihood that the manufacturer made less than $15.80 per hour? Write your answer as a percent. Exercise 28: Using Technology to Find Quartiles and Draw Graphs In Exercise, use technology to (a) find the data set’s first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set. Hourly Earnings The hourly earnings (in dollars) of a sample of 25 railroad equipment manufacturers 15.60 18.75 14.60 15.80 14.35 13.90 17.50 17.55 13.80 14.20 19.05 15.35 15.20 19.45 15.95 16.50 16.30 15.25 15.05 19.10 15.20 16.22 17.75 18.40 15.25

Interpreting Percentiles In Exercises 31–34, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 20–29 age group. (Adapted from National Center for Health Statistics) Adult Males Ages 20–29 What height represents the 60th percentile? How should you interpret this?

Interpreting Percentiles In Exercises 31–34, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 20–29 age group. (Adapted from National Center for Health Statistics) Adult Males Ages 20–29 What percentile is a height of 73 inches? How should you interpret this?

Interpreting Percentiles In Exercises 31–34, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 20–29 age group. (Adapted from National Center for Health Statistics) Which height represents the 80th percentile? How should you interpret this?

Problem 35E Finding a Percentile In Exercise, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Find the percentile that corresponds to an age of 40 years old.

Problem 36E Finding a Percentile In Exercise, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Find the percentile that corresponds to an age of 56 years old.

Interpreting Percentiles In Exercises 31–34, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 20–29 age group. (Adapted from National Center for Health Statistics) What percentile is a height of 67 inches? How should you interpret this?

Problem 37E Finding a Percentile In Exercise, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Which ages are above the 75th percentile?

Problem 38E Finding a Percentile In Exercise, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Which ages are below the 25th percentile?

Graphical Analysis In Exercises 39 and 40, the midpoints A, B, and C are marked on the histogram. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual? \(z=0\) \(z=2.14\) \(z=-1.43\) Equation Transcription: Text Transcription: z=0 z=2.14 z=-1.43

Problem 41E Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercise, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France) Winner Year Age Bradley Wiggins 2012 32

Problem 42E Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercise, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France) Winner Year Age Jan Ullrich 1997 24

Graphical Analysis In Exercises 39 and 40, the midpoints A, B, and C are marked on the histogram. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual? \(z=0.77\) \(z=1.54\) \(z=-1.54\) Equation Transcription: Text Transcription: z=0.77 z=1.54 z=-1.54

Problem 43E Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercise, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France) Winner Year Age Cadel Evans 2011 34

Problem 44E Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercise, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France) Winner Year Age Henri Cornet 1904 20

Problem 45E Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercise, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France) Winner Year Age Firmin Lambot 1922 36

Problem 48E 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. (a) The life spans of three randomly selected fruit flies are 34 days, 30 days, and 42 days. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual. ________________ (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.

Problem 49E Comparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 49, compare the z-scores for the actors. Best actor Best supporting actor ? ? 44.0 yr ? ? 8.8 yr ? ? 50.0 yr ? ? 14.1 yr Best Actor 1984: Robert Duvall, Age: 53 Best Supporting Actor 1984: Jack Nicholson, Age: 46

Comparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 50, compare the z-scores for the actors. Best Actor 2005: Jamie Foxx, Age: 37 Best Supporting Actor 2005: Morgan Freeman, Age: 67

Problem 51E Comparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 51, compare the z-scores for the actors. Best actor Best supporting actor ? ? 44.0 yr ? ? 8.8 yr ? ? 50.0 yr ? ? 14.1 yr Best Actor 1970: John Wayne, Age: 62 Best Supporting Actor 1970: Gig Young, Age: 56

Problem 46E Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercise, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France) Winner Year Age Philippe Thys 1913 23

Problem 47E Life Spans of Tires A certain 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. (a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual. ________________ (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.

Problem 52E Comparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 52, compare the z-scores for the actors. Best actor Best supporting actor ? ? 44.0 yr ? ? 8.8 yr ? ? 50.0 yr ? ? 14.1 yr Best Actor 1982: Henry Fonda, Age: 76 Best Supporting Actor 1982: John Gielgud, Age: 77

Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown. (a) Describe the shape of each distribution. Which concert has less variation in song lengths? (b) Which distribution is more likely to have outliers? Explain your reasoning. (c) Which concert do you think has a standard deviation of 16.3? Explain your reasoning. (d) Can you determine which concert lasted longer? Explain.

In Exercises 53 and 54, find the midquartile of the data set. \(\text { Midquartile }=\frac{Q_{1}+Q_{3}}{2}\) 23 36 47 33 34 40 39 24 32 22 38 41 Equation Transcription: Text Transcription: Midquartile =\frac{Q_{1}+Q_{3}}{2}

Problem 56EC Credit Card Purchases The credit card purchases (rounded to the nearest dollar) over the last three months for you and a friend are listed. You 60 95 102 110 130 130 162 200 215 120 124 28 58 40 102 105 141 160 130 210 145 90 46 76 Friend 100 125 132 90 85 75 140 160 180 190 160 105 145 150 151 82 78 115 170 158 140 130 165 125 Use technology to draw side-by-side box-and-whisker plots that represent the data sets. Then describe the shapes of the distributions.

In Exercises 53 and 54, find the midquartile of the data set. \(\text{Midquartile}=\frac{Q_1+Q_3}{2}\) 5 7 1 2 3 10 8 7 5 3 ________________ Equation Transcription: Text Transcription: Midquartile=frac{Q_1+Q_3}{2}

Problem 57EC Modified Boxplot A modified boxplot is a boxplot that uses symbols to identify outliers. The horizontal line of a modified boxplot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. In Exercise, (a) identify any outliers and (b) draw a modified boxplot that represents the data set. Use asterisks (*) to identify outliers. 16 9 11 12 8 10 12 13 11 10 24 9 2 15 7

A movies length represents the first quartile for movies showing at a theater. Make an observation about the movies length.

A cars fuel efficiency represents the ninth decile of cars in its class. Make an observation about the cars fuel efficiency.

. A students score on an actuarial exam is in the 83rd percentile. Make an observation about the students exam score.

A childs IQ is in the 93rd percentile for the childs age group. Make an observation about the childs IQ.

Explain how to identify outliers using the interquartile range.

Describe the relationship between quartiles and percentiles.

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.About one-quarter of a data set falls below Q

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.. The second quartile is the mean of an ordered data set.

True or False? In Exercises 710, 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.

Finding Quartiles In Exercises 1114, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers.56 63 51 60 57 60 60 54 63 59 80 63 60 62 65

Finding Quartiles In Exercises 1114, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers.. 36 41 39 47 15 48 34 28 25 28 19 18 50 27 53

Finding Quartiles In Exercises 1114, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers.42 53 36 28 26 41 37 40 48 45 19 38 36 56 43 34 52 38 50 43

Finding Quartiles In Exercises 1114, (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers.22 25 22 24 20 24 19 22 29 21 21 20 23 25 23 23 21 25 23 22

Graphical Analysis In Exercises 15 and 16, use the box-and-whisker plot to identify the five-number summary0 13 15 17 20

Graphical Analysis In Exercises 15 and 16, use the box-and-whisker plot to identify the five-number summary100 130 205 270 320

Drawing a Box-and-Whisker Plot In Exercises 1720, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set.39 36 30 27 26 24 28 35 39 60 50 41 35 32 51

Drawing a Box-and-Whisker Plot In Exercises 1720, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set.. 171 176 182 150 178 180 173 170 174 178 181 180

Drawing a Box-and-Whisker Plot In Exercises 1720, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set.4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9

Drawing a Box-and-Whisker Plot In Exercises 1720, (a) find the five-number summary, and (b) draw a box-and-whisker plot that represents the data set.2 7 1 3 1 2 8 9 9 2 5 4 7 3 7 5 4 7 2 3 5 9 5 6 3 9 3 4 9 8 8 2 3 9 5

Graphical Analysis In Exercises 2124, 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.0 40 80 120 160 200

Graphical Analysis In Exercises 2124, 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.20 30 40 50 60 70 80 9

Graphical Analysis In Exercises 2124, 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.30 40 50 60 70 80 90 100 110

Graphical Analysis In Exercises 2124, 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.100 200 300 400 500 600

Using Technology to Find Quartiles and Draw Graphs In Exercises 2528, use technology to (a) find the data sets first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set.TV Viewing The numbers of hours of television watched per day by a sample of 28 people 2 4 1 5 7 2 5 4 4 2 3 6 4 3 5 2 0 3 5 9 4 5 2 1 3 6 7 2

Using Technology to Find Quartiles and Draw Graphs In Exercises 2528, use technology to (a) find the data sets first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set.Vacation Days The numbers 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 2528, use technology to (a) find the data sets first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set.Airplane Distances The distances (in miles) from an airport of a sample of 22 inbound and outbound airplanes 2.8 2.0 3.0 3.0 3.2 5.9 3.5 3.6 1.8 5.5 3.7 5.2 3.8 3.9 6.0 2.5 4.0 4.1 4.6 5.0 5.5 6.0

Using Technology to Find Quartiles and Draw Graphs In Exercises 2528, use technology to (a) find the data sets first, second, and third quartiles, and (b) draw a box-and-whisker plot that represents the data set.. Hourly Earnings The hourly earnings (in dollars) of a sample of 25 railroad equipment manufacturers 15.60 18.75 14.60 15.80 14.35 13.90 17.50 17.55 13.80 14.20 19.05 15.35 15.20 19.45 15.95 16.50 16.30 15.25 15.05 19.10 15.20 16.22 17.75 18.40 15.25

TV Viewing Refer to the data set in Exercise 25 and the box-and-whisker plot you drew that represents the data set. (a) About 75% of the people watched no more than how many hours of television per day? (b) What percent of the people watched more than 4 hours of television per day? (c) You randomly select one person from the sample. What is the likelihood that the person watched less than 2 hours of television per day? Write your answer as a percent.

Manufacturer Earnings Refer to the data set in Exercise 28 and the box-and-whisker plot you drew that represents the data set. (a) About 75% of the manufacturers made less than what amount per hour? (b) What percent of the manufacturers made more than $15.80 per hour? (c) You randomly select one manufacturer from the sample. What is the likelihood that the manufacturer made less than $15.80 per hour? Write your answer as a percent.

Interpreting Percentiles In Exercises 3134, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 2029 age group. (Adapted from National Center for Health Statistics). What height represents the 60th percentile? How should you interpret this?

Interpreting Percentiles In Exercises 3134, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 2029 age group. (Adapted from National Center for Health Statistics). Which height represents the 80th percentile? How should you interpret this?

Interpreting Percentiles In Exercises 3134, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 2029 age group. (Adapted from National Center for Health Statistics)What percentile is a height of 73 inches? How should you interpret this?

Interpreting Percentiles In Exercises 3134, use the ogive to answer the questions. The ogive represents the heights of males in the United States in the 2029 age group. (Adapted from National Center for Health Statistics)What percentile is a height of 67 inches? How should you interpret this?

Finding a Percentile In Exercises 3538, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Find the percentile that corresponds to an age of 40 years old.

Finding a Percentile In Exercises 3538, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Find the percentile that corresponds to an age of 56 years old.

Finding a Percentile In Exercises 3538, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Which ages are above the 75th percentile?

Finding a Percentile In Exercises 3538, use the data set, which represents the ages of 30 executives. 43 57 65 47 57 41 56 53 61 54 56 50 66 56 50 61 47 40 50 43 54 41 48 45 28 35 38 43 42 44 Which ages are below the 25th percentile?

Graphical Analysis In Exercises 39 and 40, the midpoints A, B, and C are marked on the histogram. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual?. z = 0

Graphical Analysis In Exercises 39 and 40, the midpoints A, B, and C are marked on the histogram. Match them with the indicated z-scores. Which z-scores, if any, would be considered unusual? = 0.77

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercises 4146, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France)Bradley Wiggins 2012 32

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercises 4146, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France). Jan Ullrich 1997 24

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercises 4146, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France)Cadel Evans 2011 34

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercises 4146, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France)Henri Cornet 1904 20

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercises 4146, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France)Firmin Lambot 1922 36

Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped. The mean age is 28.1 years, with a standard deviation of 3.4 years. In Exercises 4146, (a) transform the age to a z-score, (b) interpret the results, and (c) determine whether the age is unusual. (Source: Le Tour de France). Philippe Thys 1913 23

. Life Spans of Tires A certain 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. (a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual. (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. (a) The life spans of three randomly selected fruit flies are 34 days, 30 days, and 42 days. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual. (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.

omparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 4952, compare the z-scores for the actors. Best actor Best supporting actorBest Actor 1984: Robert Duvall, Age: 53 Best Supporting Actor 1984: Jack Nicholson, Age: 46

omparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 4952, compare the z-scores for the actors. Best actor Best supporting actorBest Actor 2005: Jamie Foxx, Age: 37 Best Supporting Actor 2005: Morgan Freeman, Age: 67

omparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 4952, compare the z-scores for the actors. Best actor Best supporting actorBest Actor 1970: John Wayne, Age: 62 Best Supporting Actor 1970: Gig Young, Age: 56

omparing z-Scores The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at the Academy Awards from 1929 to 2013. The distributions of the ages are approximately bell-shaped. In Exercises 4952, compare the z-scores for the actors. Best actor Best supporting actorBest Actor 1982: Henry Fonda, Age: 76 Best Supporting Actor 1982: John Gielgud, Age: 77

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 53 and 54, find the midquartile of the data set.

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 53 and 54, find the midquartile of the data set.

23 36 47 33 34 40 39 24 32 22 38 41

Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown. 125 150 175 200 225 250 275 300 325 350 375 400 200 224 275 288 390 177 200 210 220 240 Concert 1 Concert 2 Song length (in seconds) (a) Describe the shape of each distribution. Which concert has less variation in song lengths? (b) Which distribution is more likely to have outliers? Explain your reasoning. (c) Which concert do you think has a standard deviation of 16.3? Explain your reasoning. (d) Can you determine which concert lasted longer? Explain.

Credit Card Purchases The credit card purchases (rounded to the nearest dollar) over the last three months for you and a friend are listed. You 60 95 102 110 130 130 162 200 215 120 124 28 58 40 102 105 141 160 130 210 145 90 46 76 Friend 100 125 132 90 85 75 140 160 180 190 160 105 145 150 151 82 78 115 170 158 140 130 165 125 Use technology to draw side-by-side box-and-whisker plots that represent the data sets. Then describe the shapes of the distributions.

Modified Boxplot A modified boxplot is a boxplot that uses symbols to identify outliers. The horizontal line of a modified boxplot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. In Exercises 57 and 58, (a) identify any outliers and (b) draw a modified boxplot that represents the data set. Use asterisks (*) to identify outliers. . 75 78 80 75 62 72 74 75 80 95 76 72

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.