Marijuana and traffic accidents. Researchers in New Zealand interviewed 907drivers at

Fuel economy. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles: (a) What are the individuals in this data set? (b) For each individual, what variables are given? Which of these variables are categorical and which are quantitative?

Students and TV. You are preparing to study the television-viewing habits of college students. Describe two categorical variables and two quantitative variables that you might measure for each student. Give the units of measurement for the quantitative variables.

The color of your car. News from the auto color front: fewer luxury car buyers are choosing neutral colors (silver, white, black). Here is the distribution of the most popular colors for 2005 model luxury cars made in North America:3 (a) What percent of vehicles are some other color? (b) Make a bar graph of the color data. Would it be correct to make a pie chart if you added an Other category?

Never on Sunday? Births are not, as you might think, evenly distributed across the days of the week. Here are the average numbers of babies born on each day of the week in 2003:4 Present these data in a well-labeled bar graph. Would it also be correct to make a pie chart? Suggest some possible reasons why there are fewer births on weekends.

Do the data tell you what you want to know? To help you plan advertising for a Web site for downloading MP3 music files, you want to know what percent of owners of portable MP3 players are 18 to 24 years old. The data in Example 1.3 do not tell you what you want to know. Why not?

Traveling to work. How long must you travel each day to get to work or school? Table 1.2 gives the average travel time to work for workers in each state who are at least 16 years old and dont work at home.7 Make a histogram of the travel times using classes of width 2 minutes starting at 15 minutes. (Make this histogram by hand even if you have software, to be sure you understand the process. You may then want to compare your histogram with your softwares choice.)

Choosing classes in a histogram. The data set menu that accompanies the One APPLET Variable Statistical Calculator applet includes the data on college graduates in the states from Table 1.1. Choose these data, then click on the Histogram tab to see a histogram. (a) How many classes does the applet choose to use? (You can click on the graph outside the bars to get a count of classes.) (b) Click on the graph and drag to the left. What is the smallest number of classes you can get? What are the lower and upper bounds of each class? (Click on the bar to find out.) Make a rough sketch of this histogram. (c) Click and drag to the right. What is the greatest number of classes you can get? How many observations does the largest class have? (d) You see that the choice of classes changes the appearance of a histogram. Drag back and forth until you get the histogram you think best displays the distribution. How many classes did you use?

Traveling to work. In Exercise 1.6, you made a histogram of the average travel times to work in Table 1.2. The shape of the distribution is a bit irregular. Is it closer to symmetric or skewed? About where is the center (midpoint) of the data? What is the spread in terms of the smallest and largest values?

Foreign-born residents. The states differ greatly in the percent of their residents who were born outside the United States. California leads with 26.5% foreign-born. Figure 1.8 is a histogram of the distribution of percent foreign-born residents in the states.9 Describe the shape of this distribution. Within which class does the midpoint of the distribution lie?

Traveling to work. Make a stemplot of the average travel times to work in Table 1.2. Use whole minutes as your stems. Because the stemplot preserves the actual value of the observations, it is easy to find the midpoint (26th of the 51 observations in order) and the spread. What are they?

Glucose levels. People with diabetes must monitor and control their blood glucose level. The goal is to maintain fasting plasma glucose between about 90 and 130 milligrams per deciliter (mg/dl). The following are the fasting plasma glucose levels for 18 diabetics enrolled in a diabetes control class, five months after the end of the class:10 141 158 112 153 134 95 96 78 148 172 200 271 103 172 359 145 147 255 Make a stemplot of these data and describe the main features of the distribution. (You will want to round and also split stems.) Are there outliers? How well is the group as a whole achieving the goal for controlling glucose levels?

The cost of college. Here are data on the average tuition and fees charged by public four-year colleges and universities for the 1976 to 2005 academic years. Because almost any variable measured in dollars increases over time due to inflation (the falling buying power of a dollar), the values are given in constant dollars, adjusted to have the same buying power that a dollar had in 2005.12 Year Tuition Year Tuition Year Tuition Year Tuition 1976 $2,059 1984 $2,274 1992 $3,208 2000 $3,925 1977 $2,049 1985 $2,373 1993 $3,396 2001 $4,140 1978 $1,968 1986 $2,490 1994 $3,523 2002 $4,408 1979 $1,862 1987 $2,511 1995 $3,564 2003 $4,890 1980 $1,818 1988 $2,551 1996 $3,668 2004 $5,239 1981 $1,892 1989 $2,617 1997 $3,768 2005 $5,491 1982 $2,058 1990 $2,791 1998 $3,869 1983 $2,210 1991 $2,987 1999 $3,894 (a) Make a time plot of average tuition and fees. (b) What overall pattern does your plot show? (c) Some possible deviations from the overall pattern are outliers, periods of decreasing charges (in 2005 dollars), and periods of particularly rapid increase. Which are present in your plot, and during which years?

Here are the first lines of a professors data set at the end of a statistics course: Name Major Points Grade ADVANI, SURA COMM 397 B BARTON, DAVID HIST 323 C BROWN, ANNETTE BIOL 446 A CHIU, SUN PSYC 405 B CORTEZ, MARIA PSYC 461 A The individuals in these data are (a) the students. (b) the total points. (c) the course grades.

To display the distribution of grades (A, B, C, D, F) in a course, it would be correct to use (a) a pie chart but not a bar graph. (b) a bar graph but not a pie chart. (c) either a pie chart or a bar graph.

A study of recent college graduates records the sex and total college debt in dollars for 10,000 people a year after they graduate from college. (a) Sex and college debt are both categorical variables. (b) Sex and college debt are both quantitative variables. (c) Sex is a categorical variable and college debt is a quantitative variable. Figure 1.7 (page 17) is a histogram of the tuition and fee charges for the 20042005 academic year for 59 four-year colleges in Massachusetts. The following two exercises are based on this histogram.

The number of colleges with tuition and fee charges covered by the leftmost bar in the histogram is (a) 4000. (b) 6. (c) 7.

The leftmost bar in the histogram covers tuition and fee charges ranging from about (a) $3500 to $7500. (b) $4000 to $7000. (c) $4500 to $7500.

Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you would use as stems (a) 0 and 1. (b) 09, 10, 11, 12, 13, and 14. (c) 96, 110, 118, 122, 125, 126, 130, 139, and 145.

The population of the United States is aging, though less rapidly than in other developed countries. Here is a stemplot of the percents of residents aged 65 and older in the 50 states, according to the 2000 census. The stems are whole percents and the leaves are tenths of a percent. There are two outliers: Alaska has the lowest percent of older residents, and Florida has the highest. What is the percent for Florida? (a) 5.7% (b) 17.6% (c) 176%

Ignoring the outliers, the shape of the distribution in Exercise 1.19 is (a) somewhat skewed to the right. (b) close to symmetric. (c) somewhat skewed to the left.

The center of the distribution in Exercise 1.19 is close to (a) 12.7%. (b) 13.5%. (c) 5.7% to 17.6%.

You look at real estate ads for houses in Sarasota, Florida. There are many houses ranging from $200,000 to $400,000 in price. The few houses on the water, however, have prices up to $15 million. The distribution of house prices will be (a) skewed to the left. (b) roughly symmetric. (c) skewed to the right.

How can we help wood surfaces resist weathering, especially when restoring historic wooden buildings? In a study of this question, researchers prepared wooden panels and then exposed them to the weather. Here are some of the variables recorded. Which of these variables are categorical and which are quantitative? (a) Type of wood (yellow poplar, pine, cedar) (b) Type of water repellent (solvent-based, water-based) (c) Paint thickness (millimeters) (d) Paint color (white, gray, light blue) (e) Weathering time (months)

Baseball players. Here is a small part of a data set that describes Major League Baseball players as of opening day of the 2005 season: Player Team Position Age Height Weight Salary Ortiz, David Red Sox Outfielder 29 6-4 230 5,250,000 Nix, Laynce Rangers Outfielder 24 6-0 200 316,000 Perez, Antonio Dodgers Infielder 25 5-11 175 320,500 Piazza, Mike Mets Catcher 36 6-3 215 16,071,429 Rolen, Scott Cardinals Infielder 30 6-4 240 10,715,509 (a) What individuals does this data set describe? (b) In addition to the players name, how many variables does the data set contain? Which of these variables are categorical and which are quantitative? (c) Based on the data in the table, what do you think are the units of measurement for each of the quantitative variables?

Car colors in Europe. Exercise 1.3 (page 10) gives data on the most popular colors for luxury cars made in North America. Here are similar data for luxury cars made in Europe:13 Color Percent Black 30 Silver 24 Gray 19 Blue 14 Green 3 White, pearl 3 What percent of European luxury cars have other colors? Make a graph of these data. What are the most important differences between color preferences in Europe and North America?

Deaths among young people. The number of deaths among persons aged 15 to 24 years in the United States in 2003 due to the leading causes of death for this age group were accidents, 14,966; homicide, 5148; suicide, 3921; cancer, 1628; heart disease, 1083; congenital defects, 425.14 (a) Make a bar graph to display these data. (b) What additional information do you need to make a pie chart?

Hispanic origins. Figure 1.12 is a pie chart prepared by the Census Bureau to show the origin of the 35.3 million Hispanics in the United States, according to the 2000 census.15 About what percent of Hispanics are Mexican? Puerto Rican? You see that it is hard to determine numbers from a pie chart. Bar graphs are much easier to use.

The audience for movies. Here are data on the percent of people in several age groups who attended a movie in the past 12 months:16 Age group Movie attendance 18 to 24 years 83% 25 to 34 years 73% 35 to 44 years 68% 45 to 54 years 60% 55 to 64 years 47% 65 to 74 years 32% 75 years and over 20% (a) Display these data in a bar graph. What is the main feature of the data? (b) Would it be correct to make a pie chart of these data? Why? (c) A movie studio wants to know what percent of the total audience for movies is 18 to 24 years old. Explain why these data do not answer this question.

Spam. Email spam is the curse of the Internet. Here is a compilation of the most common types of spam:17 Type of spam Percent Adult 14.5 Financial 16.2 Health 7.3 Leisure 7.8 Products 21.0 Scams 14.2 Make two bar graphs of these percents, one with bars ordered as in the table (alphabetically) and the other with bars in order from tallest to shortest. Comparisons are easier if you order the bars by height. A bar graph ordered from tallest to shortest bar is sometimes called a Pareto chart, after the Italian economist who recommended this procedure.

Returns on common stocks. The return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. Figure 1.14 is a histogram of the distribution of the monthly returns for all stocks listed on U.S. markets from January 1980 to March 2005 (243 months).19 The extreme low outlier is the market crash of October 1987, when stocks lost 23% of their value in one month. (a) Ignoring the outliers, describe the overall shape of the distribution of monthly returns. (b) What is the approximate center of this distribution? (For now, take the center to be the value with roughly half the months having lower returns and half having higher returns.) (c) Approximately what were the smallest and largest monthly returns, leaving out the outliers? (This is one way to describe the spread of the distribution.) (d) A return less than zero means that stocks lost value in that month. About what percent of all months had returns less than zero?

Name that variable. A survey of a large college class asked the following questions: 1. Are you female or male? (In the data, male = 0, female = 1.) 2. Are you right-handed or left-handed? (In the data, right = 0, left = 1.) 3. What is your height in inches? 4. How many minutes do you study on a typical weeknight? Figure 1.15 shows histograms of the student responses, in scrambled order and without scale markings. Which histogram goes with each variable? Explain your reasoning.

Tornado damage. The states differ greatly in the kinds of severe weather that afflict them. Table 1.3 shows the average property damage caused by tornadoes per year over the period from 1950 to 1999 in each of the 50 states and Puerto Rico.20 (To adjust for the changing buying power of the dollar over time, all damages were restated in 1999 dollars.) (a) What are the top five states for tornado damage? The bottom five? (Include Puerto Rico, though it is not a state.) (b) Make a histogram of the data, by hand or using software, with classes 0 damage < 10, 10 damage < 20, and so on. Describe the shape, center, and spread of the distribution. Which states may be outliers? (To understand the outliers, note that most tornadoes in largely rural states such as Kansas cause little property damage. Damage to crops is not counted as property damage.) (c) If you are using software, also display the default histogram that your software makes when you give it no instructions. How does this compare with your graph in (b)?

Where are the doctors? Table 1.4 gives the number of active medical doctors per 100,000 people in each state.21 (a) Why is the number of doctors per 100,000 people a better measure of the availability of health care than a simple count of the number of doctors in a state? (b) Make a histogram that displays the distribution of doctors per 100,000 people. Write a brief description of the distribution. Are there any outliers? If so, can you explain them?

Carbon dioxide emissions. Burning fuels in power plants or motor vehicles emits carbon dioxide (CO2), which contributes to global warming. Table 1.5 displays CO2 emissions per person from countries with populations of at least 20 million.22 (a) Why do you think we choose to measure emissions per person rather than total CO2 emissions for each country? (b) Make a stemplot to display the data of Table 1.5. Describe the shape, center, and spread of the distribution. Which countries are outliers?

Recruitment, the addition of new members to a fish population, is an important measure of the health of ocean ecosystems. Here are data on the recruitment of rock sole in the Bering Sea from 1973 to 2000:23 Sarkis Images/Alamy Recruitment Recruitment Recruitment Recruitment Year (millions) Year (millions) Year (millions) Year (millions) 1973 173 1980 1411 1987 4700 1994 505 1974 234 1981 1431 1988 1702 1995 304 1975 616 1982 1250 1989 1119 1996 425 1976 344 1983 2246 1990 2407 1997 214 1977 515 1984 1793 1991 1049 1998 385 1978 576 1985 1793 1992 505 1999 445 1979 727 1986 2809 1993 998 2000 676 Make a stemplot to display the distribution of yearly rock sole recruitment. (Round to the nearest hundred and split the stems.) Describe the shape, center, and spread of the distribution and any striking deviations that you see.

Do women study more than men? We asked the students in a large first-year college class how many minutes they studied on a typical weeknight. Here are the responses of random samples of 30 women and 30 men from the class: Women Men 180 120 180 360 240 90 120 30 90 200 120 180 120 240 170 90 45 30 120 75 150 120 180 180 150 150 120 60 240 300 200 150 180 150 180 240 60 120 60 30 120 60 120 180 180 30 230 120 95 150 90 240 180 115 120 0 200 120 120 180 (a) Examine the data. Why are you not surprised that most responses are multiples of 10 minutes? We eliminated one student who claimed to study 30,000 minutes per night. Are there any other responses you consider suspicious? (b) Make a back-to-back stemplot to compare the two samples. That is, use one set of stems with two sets of leaves, one to the right and one to the left of the stems. (Draw a line on either side of the stems to separate stems and leaves.) Order both sets of leaves from smallest at the stem to largest away from the stem. Report the approximate midpoints of both groups. Does it appear that women study more than men (or at least claim that they do)?

Rock sole in the Bering Sea. Make a time plot of the rock sole recruitment data in Exercise 1.36. What does the time plot show that your stemplot in Exercise 1.36 did not show? When you have time series data, a time plot is often needed to understand what is happening.

Marijuana and traffic accidents. Researchers in New Zealand interviewed 907 drivers at age 21. They had data on traffic accidents and they asked their subjects about marijuana use. Here are data on the numbers of accidents caused by these drivers at age 19, broken down by marijuana use at the same age:24 Marijuana Use per Year Never 110 times 1150 times 51+ times Drivers 452 229 70 156 Accidents caused 59 36 15 50 (a) Explain carefully why a useful graph must compare rates (accidents per driver) rather than counts of accidents in the four marijuana use classes. (b) Make a graph that displays the accident rate for each class. What do you conclude? (You cant conclude that marijuana use causes accidents, because risk takers are more likely both to drive aggressively and to use marijuana.)

General Motors versus Toyota. The J. D. Power Initial Quality Study polls more than 50,000 buyers of new motor vehicles 90 days after their purchase. A two-page questionnaire asks about things gone wrong. Here are data on problems per 100 vehicles for vehicles made by Toyota and by General Motors in recent years. Make two time plots in the same graph to compare Toyota and GM. What are the most important conclusions you can draw from your graph?

Watch those scales! The impression that a time plot gives depends on the scales you use on the two axes. If you stretch the vertical axis and compress the time axis, change appears to be more rapid. Compressing the vertical axis and stretching the time axis make change appear slower. Make two more time plots of the college tuition data in Exercise 1.12 (page 23), one that makes tuition appear to increase very rapidly and one that shows only a gentle increase. The moral of this exercise is: pay close attention to the scales when you look at a time plot.

Orange prices. Figure 1.16 is a time plot of the average price of fresh oranges each month from March 1995 to March 2005.25 The prices are index numbers given as percents of the average price during 1982 to 1984. (a) The most notable pattern in this time plot is yearly cycles. At what season of the year are orange prices highest? Lowest? (To read the graph, note that the tick mark for each year is at the beginning of the year.) The cycles are explained by the time of the orange harvest in Florida. (b) Is there a longer-term trend visible in addition to the cycles? If so, describe it.

Alligator attacks. Here are data on the number of unprovoked attacks by alligators on people in Florida over a 33-year period:26 Year Attacks Year Attacks Year Attacks Year Attacks 1972 5 1981 5 1990 18 1999 15 1973 3 1982 6 1991 18 2000 23 1974 4 1983 6 1992 10 2001 17 1975 5 1984 5 1993 18 2002 14 1976 2 1985 3 1994 22 2003 6 1977 14 1986 13 1995 19 2004 11 1978 5 1987 9 1996 13 1979 2 1988 9 1997 11 1980 4 1989 13 1998 9 Make two graphs of these data to illustrate why you should always make a time plot for data collected over time. (a) Make a histogram of the counts of attacks. What is the overall shape of the distribution? What is the midpoint of the yearly counts of alligator attacks? (b) Make a time plot. What overall pattern does your plot show? Why is the typical number of attacks from 1972 to 2004 not very useful in (say) 2006? (The main reason for the time trend is the continuing increase in Floridas population.)

To split or not to split. The data sets in the One Variable Statistical Calculator APPLET applet on the text CD and Web site include the pulling wood apart data from Example 1.10. The applet rounds the data in the same way as Figure 1.10 (page 21). Use the applet to make a stemplot with split stems. Do you prefer this stemplot or that in Figure 1.10? Explain your choice.