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How — The information is collected and stored as part of school records. Variables — There are seven variables. Number of absences, age, reading test score, and math test score are quantitative variables. Concerns — What tests are used to measure reading and math ability, and what are the units of measure for the tests? What — type of meat, number of calories in calories , and serving size in ounces. Why — These data might be used to assess the nutritional value of the different sandwiches. Variables — There are three variables. Number of calories and serving size are quantitative variables, and type of meat is a categorical variable. Age and party. Who — Americans. What — Region, age in years , political affiliation, and whether or not the person voted in the midterm Congressional election.

When — First quarter of Where — United States. Why — The information was gathered for presentation in a Gallup public opinion poll. How — Phone Survey. Variables — There are four variables. Region, political affiliation, and whether or not the person voted in are categorical variables, and age is a quantitative variable. Who — births. When — Where — Large city hospital. Why — Researchers were investigating the impact of prenatal care on newborn health. How — It appears that they kept track of all births in the form of hospital records, although it is not specifically stated. Who — species of flowers. What — Date of first flowering in days.

Where — Southern England. Why — The researchers believe that this indicates a warming of the overall climate. How — Not specified. Variables — Date of first flowering is a quantitative variable. Concerns - Hopefully, date of first flowering was measured in days from January 1, or some other convention, to avoid problems with leap years. Herbal medicine. Who — experiment volunteers. What — herbal cold remedy or sugar solution, and cold severity. Where — Major pharmaceutical firm. Why — Scientists were testing the efficacy of an herbal compound on the severity of the common cold. How — The scientists set up a controlled experiment. Variables — There are two variables. Type of treatment herbal or sugar solution is categorical, and severity rating is quantitative. Concerns — The severity of a cold seems subjective and difficult to quantify.

Also, the scientists may feel pressure to report negative findings about the herbal product. Who — American Vineyards. What — Size of vineyard in acres , number of years in existence, state, varieties of grapes grown, average case price in dollars , gross sales probably in dollars , and percent profit. Why — Business analysts hoped to provide information that would be helpful to producers of American wines. Variables — There are five quantitative variables and two categorical variables. Size of vineyard, number of years in existence, average case price, gross sales, and percent profit are quantitative variables. State and variety of grapes grown are categorical variables. Who — Streams. What — Name of stream, substrate of the stream limestone, shale, or mixed , acidity of the water measured in pH , temperature in degrees Celsius , and BCI unknown units.

Where — Upstate New York. Why — Research was conducted for an Ecology class. Variables — There are five variables. Name and substrate of the stream are categorical variables, and acidity, temperature, and BCI are quantitative variables. Fuel economy. Who — Every model of automobile in the United States. What — Vehicle manufacturer, vehicle type, weight probably in pounds , horsepower in horsepower , and gas mileage in miles per gallon for city and highway driving. When — This information is collected currently. Why — The Environmental Protection Agency uses the information to track fuel economy of vehicles. How — The data is collected from the manufacturer of each model. Variables — There are six variables. City mileage, highway mileage, weight, and horsepower are quantitative variables. Manufacturer and type of car are categorical variables. Who — refrigerators. What — Brand, cost probably in dollars , size in cu. Why — The information was compiled to provide information to the readers of Consumer Reports.

Variables — There are 7 variables. Brand, type, and overall rating are categorical variables. Cost, size, estimated energy cost, and repair history are quantitative variables. Walking in circles. Who — 32 volunteers. What — Sex, height, handedness, the number of yards walked before going out of bounds, and the side of the field on which the person walked out of bounds. Why — The researcher was interested in whether people walk in circles when lost. How — Data were collected by observing the people on the field, as well as by measuring and asking the participants. Variables — There are 5 variables. Sex, handedness, and side of the field are categorical variables. Height and number of yards walked are quantitative variables. Kentucky Derby Who — Kentucky Derby races.

What — Year, winner, jockey, trainer, owner, and time in minutes, seconds, and hundredths of a second. When — — Where — Churchill Downs, Louisville, Kentucky. Why — It is interesting to examine the trends in the Kentucky Derby. How — Official statistics are kept for the race each year. Variables — There are 6 variables. Winner, jockey, trainer and owner are categorical variables. Date and duration are quantitative variables. Indianapolis Who — Indy races. What — Year, driver, time in minutes, seconds, and hundredths of a second , and speed in miles per hour. Where — Indianapolis, Indiana. Why — It is interesting to examine the trends in Indy races. How — Official statistics are kept for the race every year.

Variables — There are 4 variables. Driver is a categorical variable. Year, time, and speed are quantitative variables. Chapter 2 — Displaying and Describing Categorical Data Section 2. Automobile fatalities. Subcompact and Mini Compact Intermediate Full Unknown. Marriage in decline. Movies again. Labor force. Chapter Exercises 7. Graphs in the news. Graphs in the news II. Tables in the news. Tables in the news II. Movie genres. a A pie chart seems appropriate from the movie genre data. It has the smallest region in the chart. Movie ratings.

a A pie chart seems appropriate for the movie rating data. The percentages of each rating are different enough that the pie chart is easy to read. b The most common rating is PG It has the largest region on the chart. Genres, again. b This is easier to see on the bar chart. The percentages are so close that the difference is nearly indistinguishable in the pie chart. Ratings, again. a The least common rating was G. It has the shortest bar. b The bar chart does not support this claim. These data are for a single year only. We have no idea if the percentages of G and PG movies changed from year to year. Magnet Schools. Magnet schools again. Causes of death a Yes, it is reasonable to assume that heart and respiratory disease caused approximately deaths in , since there is no possibility for overlap. Each person could Cause of Death only have one cause of 40 death.

b Since the percentages listed add up to Since causes of US deaths represent parts of a whole, a pie chart would also be a good display. Plane crashes. c A relative frequency bar chart is a good choice. A pie chart would also be a good display, as long as each plane crash has only one cause. Oil spills as of a Grounding, accounting for approximately spills, is the most frequent cause of oil spillage for these spills. A substantial number of spills, approximately , were caused by Collision. b A pie chart is an appropriate display of the data, since there is only a single cause attributed to each spill, and all spills are represented in some category.

c There were more spills due to Grounding than Collisions. This is much easier to see on the bar chart. Winter Olympics a There are too many categories to construct an appropriate display. In a bar chart, there are too many bars. In a pie chart, there are too many slices. b Perhaps we are primarily interested in countries that won many medals. We might choose to combine all countries that won fewer than 6 medals into a single category. This will make our chart easier to read. A bar chart is also better for comparisons. Global warming. Furthermore, the threedimensional perspective view distorts the regions in the graph, violating the area principle.

Always use simple, two-dimensional graphs. Additionally, the graph does not include a title. a The bars have false depth, which can be misleading. This is a bar chart, so the bars should have space between them. Running the labels on the bars from top to bottom and the vertical axis labels from bottom to top is confusing. Normally, we would take this as a sign that all of the observations had been correctly accounted for. But in this case, it is extremely unlikely. Each of the respondents was asked to list three modalities. Teen smokers. According to the Monitoring the Future study, teen smoking brand preferences differ somewhat by region.

Camels are more popular in the West, with 9. Teen smokers in the West are also more likely to have no particular brand than teen smokers in the South. Along the same lines, only A similar disparity is seen in large caliber handguns. Only 2. Finally, 2. Generally, the handguns that are involved in buyback programs are not the same caliber as handguns used in homicides in Milwaukee. Movies by genre and rating. ii You cannot determine this from the table. iv You cannot determine this from the table. The last picture show. d A total of 2. So patrons under 13 can see only This supports the assertion that approximately three-quarters of movies can only be seen by patrons 13 years old or older.

a A table with marginal totals is to the right. There are White graduates and total graduates. b There are 42 graduates planning to attend 2-year colleges. a There are students taking Intro Stats. Of those, , or about b There are students taking Intro Stats. Of those, 27, or about c There are males taking Intro Stats. Of those, 21, or about d There are students taking Intro Stats. More about seniors. a For white students, c A segmented bar chart is a good display of these data. Caution should be used with the percentages for Minority graduates, because the total is so small.

Still, the conditional distributions of plans are essentially the same for the two groups. There is little evidence of an association between race and plans for after graduation. Politics revisited. a The females in this course were Female Male d Politics and sex do not appear to be independent in this course. Although the percentage of liberals was roughly the same for each sex, females had a greater percentage of moderates and a lower percentage of conservatives than males. Magnet schools revisited. b There were students accepted to the magnet schools program. c There were Asian applicants. d There were total applicants. More politics. b The percentage of males and females varies across political categories. The percentage of self-identified Liberals and Moderates who are female is about twice the percentage of Conservatives who are female. This suggests that sex and politics are not independent. Back to school. There were 1, qualified applicants for admission to the magnet schools program.

Overall, Asians accounted for Parking lots. a In order to get percentages, first we need totals. Here is the same table, with row and column totals. Foreign cars are defined as non-American. The conditional distribution of Origin for Staff is: f The percentages in the conditional distributions of Origin by Driver students and staff seem slightly different. Driver Although students appear to own a higher percentage of European cars and a smaller percentage of American cars than the staff, the two groups own nearly the same percentage of Asian cars. However, because of the differences, there is evidence of an association between Driver and Origin of the car. b Rain was predicted on 90 of days. So, the forecast was correct a total of times. d On rainy days, rain had been predicted 27 out of 34 times On days when it did not rain, forecasters were correct in their predictions out of times These two percentages are very close.

There is no evidence of an association between the type of weather and the ability of the forecasters to make an accurate prediction. Twin births. Twin Births in thousands a Of the , Preterm Preterm mothers who Induced or Level of without Term or had twins in Caesarean Prenatal Care procedures Postterm Intensive 18 15 28 , Adequate 46 43 65 63, had Inadequate 12 13 38 inadequate Total 76 71 health care during their pregnancies. b There were 76, induced or Caesarean births and 71, preterm births without these procedures. This is evidence of an association between level of prenatal care and twin birth outcome. If these variables were independent, we would expect the percentages to be roughly the same. Generally, those mothers who received adequate medical care were more likely to have preterm births than mothers who received intensive medical care, who were in turn more likely to have preterm births than mothers who received inadequate health care.

This does not imply that mothers should receive inadequate health care do decrease their chances of having a preterm birth, since it is likely that women that have some complication during their pregnancy that might lead to a preterm birth , would seek intensive or adequate prenatal care. Blood pressure. a The marginal distribution of blood pressure for the employees of the company is the total column of the Total 98 table, converted to percentages. c A segmented bar chart of the conditional distributions of blood pressure by age category is at the right. d In this company, as age increases, the percentage of employees with low blood pressure decreases, and the percentage of employees with high blood pressure increases. Generally, an association between two variables does not imply a cause-andeffect relationship. Specifically, these data come from only one company and cannot be applied to all people.

Furthermore, there may be some other variable that is linked to both age and blood pressure. Only a controlled experiment can isolate the relationship between age and blood pressure. Obesity and exercise. a Participants were categorized as Normal, Overweight or Obese, according to their Body Mass Index. Within each classification of BMI column , participants self reported exercise levels. Therefore, these are column percentages. b A segmented bar chart of the conditional distributions of level of physical activity by Body Mass Index category is at the right.

While it may seem logical that lack of exercise causes obesity, association between variables does not imply a cause-and-effect relationship. both BMI and level of physical activity, or perhaps lack of exercise is caused by obesity. Only a controlled experiment could isolate the relationship between BMI and level of physically activity. These data provide no evidence that Prozac might be helpful in treating anorexia. Even though the percentage was higher for the placebo patients, this does not mean that Prozac is hurting patients. Antidepressants and bone fractures. These data provide evidence that taking a certain class of antidepressants SSRI might be associated with a greater risk of bone fractures. At younger ages, males form the slight majority of drivers.

The percentage of male drivers continues to shrink until, at around age 45, female drivers hold a slight majority. This continues into the 85 and over category. d There appears to be a slight association between age and gender of U. Younger drivers are slightly more likely to be male, and older drivers are slightly more likely to be female. If having a tattoo and having hepatitis C were independent, we would have expected these percentages to be roughly the same. Discharge delayed Large Small Total Hospital Hospital of 10 of 50 of 10 of 20 of 30 of of 30 of of b Yes. Major surgery patients were delayed of times, or about Minor Surgery patients were delayed 30 of times, or about 6. The small hospital has the lower overall rate of delayed discharge. Even though small hospital had the lower overall rate of delayed discharge, the large hospital had a lower rate of delayed discharge for each type of surgery.

While the overall rate of delayed discharge is lower for the small hospital, the large hospital did better with both major surgery and minor surgery. f The small hospital performs a higher percentage of minor surgeries than major surgeries. Minor surgery had a lower delay rate than major surgery 6. Simply put, it is a mistake to look at the overall percentages. The real truth is found by looking at the rates after the information is broken down by type of surgery, since the delay rates for each type of surgery are so different. The larger hospital is the better hospital when comparing discharge delay rates. Delivery service. b The company should have hired Boxes R Us instead of Pack Rats. Boxes R Us is better at delivering Regular and Overnight packages.

Boxes R Us delivers a greater percentage of its packages Overnight, where it is comparatively harder to deliver on time. Pack Rats delivers many Regular packages, where it is easier to make an on-time delivery. Graduate admissions. a applicants were admitted out of a total of applicants. Total of of b of c Since there are four comparisons to make, the table at the right organizes the percentages of males and females accepted in each program. Females are accepted at a higher rate in every program. d The comparison of acceptance rate within each program is most valid. The overall percentage is an unfair average. It fails to take the different numbers of applicants and different acceptance rates of each program. Women tended to apply to the programs in which gaining acceptance was difficult for everyone. Be a Simpson!

The three-way table below shows one possibility. The number of local hires out of new hires is shown in each cell. Chapter 3 — Displaying and Summarizing Quantitative Data Section 3. The given boxplot could be displaying a distribution that has multiple modes the first histogram , is reasonably unimodal the second histogram , has gaps and clusters the third histogram , or has outliers the fourth histogram. a The tallest bars on the histogram are where the vertical lines on the boxplot are closest together. b The boxplot indicates a skewed distribution when the vertical lines on one side of the median are closer together than the vertical lines on the other side.

The histogram indicates a skewed distribution when the bars on one side of the histogram are generally taller than the bars on the other side of the histogram. c The histogram shows a second mode in the distribution, as well as clusters and gaps. The boxplot does not show this. d The boxplot shows the quartiles and the median, as well as showing outliers. These cannot be determined from the histogram. Section 3. Using the Outlier Rule 1. Since the maximum, minutes, is above the upper fence, there is at least one high outlier. Lower Fence:. Since the mean age at adoption is higher than the median age at adoption, the distribution of adoption ages is likely to be skewed to the right, with many adoptions happening when children are relatively young, with fewer adoptions of older children.

Adoptions II. The mean number of adoptions is expected to by higher than the median number of adoptions, since the distribution of the number of adoptions is skewed to the right. Test score centers. The median test score will not be affected, but the mean test score will increase by 0. Test score spreads. The IQR of the test scores will not be affected, but the standard deviation of the test scores will increase. If the outlier is removed, the standard deviation will decrease. The IQR will not change substantially. It may change slightly, since removing one value from the data set may change the quartiles, which would change the IQR.

Chapter Exercises 9. Not a histogram. In the news. In the news II. Thinking about shape. a The distribution of the number of speeding tickets each student in the senior class of a college has ever had is likely to be unimodal and skewed to the right. Most students will have very few speeding tickets maybe 0 or 1 , but a small percentage of students will likely have comparatively many 3 or more? Open Golf Tournament would most likely be unimodal and slightly skewed to the right. The best golf players in the game will likely have around the same average score, but some golfers might be off their game and score 15 strokes above the mean.

Remember that high scores are undesirable in the game of golf! c The weights of female babies in a particular hospital over the course of a year will likely have a distribution that is unimodal and symmetric. Most newborns have about the same weight, with some babies weighing more and less than this average. There may be slight skew to the left, since there seems to be a greater likelihood of premature birth and low birth weight than post-term birth and high birth weight. d The distribution of the length of the average hair on the heads of students in a large class would likely be bimodal and skewed to the right. The average hair length of the males would be at one mode, and the average hair length of the females would be at the other mode, since women typically have longer hair than men.

The distribution would be skewed to the right, since it is not possible to have hair length less than zero, but it is possible to have a variety of lengths of longer hair. More shapes. a The distribution of the ages of people at a Little League game would likely be bimodal and skewed to the right. The average age of the players would be at one mode and the average age of the spectators probably mostly parents would be at the other mode. The distribution would be skewed to the right, since it is possible to have a greater variety of ages among the older people, while there is a natural left endpoint to the distribution at zero years of age. b The distribution of the number of siblings of people in your class is likely to be unimodal and skewed to the right. Most people would have 0, 1, or 2 siblings, with some people having more siblings.

c The distribution of pulse rate of college-age males would likely be unimodal and symmetric. d The distribution of the number of times each face of a die shows in tosses would likely be uniform, with around 16 or 17 occurrences of each face assuming the die had six sides. Sugar in cereals. The lower cluster shows a bit of skew to the right. b There are two different types of breakfast cereals, those for children and those for adults. Adult cereals often advertise low sugar content. a The distribution of the heights of singers in the chorus is bimodal, with a mode at around 65 inches and another mode around 71 inches. No chorus member has height below 60 inches or above 76 inches. b The two modes probably represent the mean heights of the male and female members of the chorus. a There is information displayed about 36 vineyards and it appears that 28 of the vineyards are smaller than 90 acres.

b The distribution of the size of 36 Finger Lakes vineyards is skewed to the right. Most vineyards are smaller than 90 acres, with a few larger ones, from 90 to acres. One vineyard was larger than all the rest, over acres. The mode of the distribution is between 0 and 30 acres. Run times. The distribution of runtimes is skewed to the right. The shortest runtime was around

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To learn more about how MyStatLab combines proven learning applications with powerful assessment, visit www. Access Code Card. Richard D. DeVeaux is an internationally known educator and consultant. His research focuses on the analysis of large data sets and data mining in science and industry. In his spare time, he is an avid cyclist and swimmer. Dick is the father of four children. Paul F. Velleman has an international reputation for innovative Statistics education. Paul has taught Statistics at Cornell University since He holds an A. His research often deals with statistical graphics and data analysis methods. Paul is the father of two boys. David E. Bock taught mathematics at Ithaca High School for 35 years.

Dave holds degrees from the University at Albany in Mathematics B. Dave has been a reader and table leader for the AP Statistics exam, serves as a Statistics consultant to the College Board, and leads workshops and institutes for AP Statistics teachers. Dave and his wife relax by biking or hiking, spending much of their free time in Canada, the Rockies, or the Blue Ridge Mountains. They have a son, a daughter, and four grandchildren. We're sorry! We don't recognize your username or password. Please try again. The work is protected by local and international copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. You have successfully signed out and will be required to sign back in should you need to download more resources.

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