Expanded and Condensed Stemplotsa. A stemplot can be

Back­-to­-Back Relative Frequency Histograms When using histograms to compare two data sets, it is sometimes difficult to make comparisons by looking back and forth between the two histograms. A back­to­back relative frequency histogram has a format that makes the comparison much easier. Instead of frequencies, we should use relative frequencies (percentages or proportions) so that the comparisons are not difficult when there are different sample sizes. Use the relative frequency distributions of the ages of Oscar­-winning actresses and actors from Exercise 15 in Section 2­2, and complete the back­to­back relative frequency histograms shown below. Then use the result to compare the two data sets.

Interpreting a Histogram Refer to the histogram given for Exercises 5–8 and answer the following questions: a. What are the possible values (rounded to the nearest inch) of the largest height included in the histogram? What are those values expressed in feet and inches? b. Why is it wrong to say that the people with heights between 43 in. and 55 in. are the tallest people because they have the tallest bars in the histogram? Interpreting a Histogram. In Exercises 5–8, answer the questions by referring to the following Minitab-­generated histogram, which represents the heights (inches) of people randomly selected from those who entered New York City's Museum of Natural History during a recent Friday morning. MINITAB

Deceptive Graphs. In Exercises 21–24, identify the characteristic that causes the graph to be deceptive. Election Results The accompanying graph depicts the numbers of votes (in millions) in the 2008 U.S. presidential election.

Deceptive Graphs. In Exercises 21–24, identify the characteristic that causes the graph to be deceptive. Subway Fare In 1986, the New York City subway fare cost $1, and as of this writing, it now costs $2, so the price doubled. In the accompanying graph, the $2 bill is twice as long and twice as tall as the $1 bill.

Deceptive Graphs. In Exercises 21–24, identify the characteristic that causes the graph to be deceptive. Oil Consumption China currently consumes 7.6 million barrels of oil per day, compared to the United States oil consumption of 20.7 million barrels of oil per day. In the accompanying illustration, the larger barrel is about three times as wide and three times as tall as the smaller barrel.

Deceptive Graphs. In Exercises 21–24, identify the characteristic that causes the graph to be deceptive. Braking Distance Data Set 14 in Appendix B lists braking distances (ft) of different cars, and the braking distances of three of those cars are shown in the accompanying illustration.

Back-­to-­Back Stemplots Exercise 19 in Section 2­3 used back-­to-­back relative frequency histograms for the ages of actresses and actors that are listed in Data Set 11 of Appendix B. Use the same method to construct back-­to­-back stemplots of the ages of actresses and actors, and then use the results to compare the two data sets. Exercise Earthquake Magnitudes Use the frequency distribution from Exercise 23 in Section 2­2 to construct a frequency polygon. Applying a loose interpretation of the requirements for a normal distribution, do the magnitudes appear to be normally distributed? Why or why not?

Expanded and Condensed Stemplots a. A stemplot can be expanded by subdividing rows into those with leaves having digits of 0 through 4 and those with leaves having digits 5 through 9. Using the body temperatures from 12 am on Day 2 listed in Data Set 3 of Appendix B, the first three rows of an expanded stemplot have stems of 96 (for leaves between 5 and 9 inclusive), 97 (for leaves between 0 and 4 inclusive), and 97 (for leaves between 5 and 9 inclusive). Construct the complete expanded stemplot for the body temperatures from 12 am on Day 2 listed in Data Set 3 of Appendix B. b. A stemplot can be condensed by combining adjacent rows. Using the LDL cholesterol measurements from males in Data Set 1 of Appendix B, we obtain the first two rows of the condensed stemplot as shown below. Note that we insert an asterisk to separate digits in the leaves associated with the numbers in each stem. Every row in the condensed plot must include exactly one asterisk so that the shape of the condensed stemplot is not distorted. Complete the condensed stemplot. What is an advantage of using a condensed stemplot instead of one that is not condensed? \(6-779 * 7788-945678 * 049\) Equation Transcription: Text Transcription: 6-779 * 7788-945678 * 049

Problem 1BSC Bar Chart and Pareto Chart A bar chart and a Pareto chart both use bars to show frequencies of categories of categorical data. What characteristic distinguishes a Pareto chart from a bar chart, and how does that characteristic help us in understanding the data?

Problem 1CRE In Exercises, refer to the below table, which summarizes results from 641 people who responded to a USA Today survey. Participants responded to this question: “Who do you most like to get compliments from at work?” Response Frequency Co-workers 260 Boss 241 Strangers 82 People who report to me 58 Graph Which of the following graphs would be best for visually illustrating the data in the table: histogram; dotplot; scatterplot; Pareto chart; stemplot?

Frequency Distribution of Brain Volumes Construct a frequency distribution of the 20 brain volumes \((\mathrm{cm} 3)) listed below. (These volumes are from Data Set 6 of Appendix B.) Use the classes 900–999, 1000–1099, and so on. Equation Transcription: Text Transcription: ( cm 3)

Using the same first two classes from Exercise 1, identify the class boundaries of the first class.

Problem 2BSC Scatterplot What is a scatterplot? What type of data is required for a scatterplot? What characteristic of the data can be better understood by looking at a scatterplot?

Problem 2CRE In Exercises, refer to the below table, which summarizes results from 641 people who responded to a USA Today survey. Participants responded to this question: “Who do you most like to get compliments from at work?” Response Frequency Co-workers 260 Boss 241 Strangers 82 People who report to me 58 Level of Measurement Is the level of measurement of the 641 individual responses nominal, ordinal, interval, or ratio? Why?

Histogram of Brain Volumes Construct the histogram that corresponds to the frequency distribution from Exercise 1. Applying a very strict interpretation of the requirements for a normal distribution, does the histogram suggest that the data are from a population having a normal distribution?Why or why not?

SAT Scores Listed below are SAT scores from a sample of students (based on data from www.talk.collegeconfidential.com). Why is it that a graph of these data will not be very effective in helping us understand the data?

The first class described in Exercise 1 has a frequency of 51. If you know only the class limits given in Exercise 1 and the frequency of 51, can you identify the original 51 data values?

Problem 3CRE: In Exercises, refer to the below table, which summarizes results from 641 people who responded to a USA Today survey. Participants responded to this question: “Who do you most like to get compliments from at work?” Response Frequency Co-workers 260 Boss 241 Strangers 82 People who report to me 58 Sampling - The results in the table were obtained by posting the question on a Web site, and readers of USA Today could respond to the question if they chose to. What is this type of sampling called? Is this type of sample likely to be representative of the population of all workers? Why or why not?

Problem 3RE: Dotplot of California Lottery - In the California Daily 4 lottery, four digits are randomly selected each day. Listed below are the digits that were selected in one recent week. Construct a dotplot. Does the dotplot suggest that the lottery is fair?

SAT Scores Given that the data in Exercise 3 were obtained from students who made a decision to submit their SAT scores to a Web site, what type of sample is given in that exercise? If we had a much larger sample of that type, would a graph help us understand some characteristics of the population?

Problem 4CQQ A stemplot is created from the intervals (min) between eruptions of the Old Faithful geyser in Yellowstone National Park, and one row of that stemplot is 6 | 1222279. Identify the values represented by that row.

In Exercises 1–5, refer to the table below, which summarizes results from 641 people who responded to a USA Today survey. Participants responded to this question: “Who do you most like to get compliments from at work?” Misleading Graph How is the accompanying graph misleading? How could it be modified so that it would not be misleading? (The graph is on the top of the next page.)

Stemplot of IQ Scores Listed below are the first eight IQ scores from Data Set 6 in Appendix B. Construct a stemplot of these eight values. Is this data set large enough to reveal the true nature of the distribution of IQ scores for the population from which the sample is obtained?

Scatterplots. In Exercises 5–8, use the given paired data from Appendix B to construct a scatterplot. President's Heights Refer to Data Set 12 in Appendix B, and use the heights of U.S. presidents and the heights of their main opponents in the election campaign. Does there appear to be a correlation?

Problem 5CQQ In the California Daily 4 lottery, four digits between 0 and 9 inclusive are randomly selected each day. We normally expect that each of the ten different digits will occur about 1/10 of the time, and an analysis of last year’s results shows that this did happen. Because the results are what we normally expect, is it correct to say that the distribution of selected digits is a normal distribution?

Problem 5CRE In Exercises, refer to the below table, which summarizes results from 641 people who responded to a USA Today survey. Participants responded to this question: “Who do you most like to get compliments from at work?” Response Frequency Co-workers 260 Boss 241 Strangers 82 People who report to me 58 Statistic or Parameter? Among the 641 people who responded to the USA Today survey, what is the percentage of respondents who chose the category of boss? When considered in the context of the population of all workers, is that percentage a statistic or a parameter? Explain.

CO Emissions Listed below are the amounts (million metric tons) of carbon monoxide emissions in the United States for each year of a recent ten-year period. The data are listed in order. Construct the graph that is most appropriate for these data. What type of graph is best? What does the graph suggest?

Scatterplots. In Exercises 5–8, use the given paired data from Appendix B to construct a scatterplot. Brain Volume and IQ Refer to Data Set 6 in Appendix B, and use the brain volumes \((\mathrm{cm} 3)\) and IQ scores. A simple hypothesis is that people with larger brains are more intelligent and thus have higher IQ scores. Does the scatterplot support that hypothesis? Equation Transcription: Text Transcription: ( cm 3)

Problem 6CQQ In an investigation of the travel costs of college students, which of the following does not belong: center; variation; distribution; bar graph; outliers; changing patterns over time?

Problem 6CRE Grooming Time Listed below are times (minutes) spent on hygiene and grooming in the morning (by randomly selected subjects) (based on data from a Svenska Cellulosa Aktiebolaget survey). Construct a table representing the frequency distribution. Use the classes 0–9, 10–19, and so on. 0 5 12 15 15 20 22 24 25 25 25 27 27 28 30 30 35 35 40 45

CO and NO Emissions Exercise 5 lists the amounts of carbon monoxide emissions, and listed below are the amounts (million metric tons) of nitrous oxide emissions in the United States for the same ten-year period as in Exercise 5. What graph is best for exploring the relationship between carbon monoxide emissions and nitrous oxide emissions? Construct that graph. Does the graph suggest that there is a relationship between carbon monoxide emissions and nitrous oxide emissions?

Scatterplots. In Exercises 5–8, use the given paired data from Appendix B to construct a scatterplot. Bear Chest Size and Weight Refer to Data Set 7 in Appendix B, and use the measured chest sizes and weights of bears. Does there appear to be a correlation between those two variables?

Problem 7CQQ In an investigation of the relationship between SAT scores and grade point averages (GPA) of college students, which of the following graphs is most helpful: histogram; pie chart; scat-terplot; stemplot; dotplot?

Histogram of Grooming Times Use the frequency distribution from Exercise 6 to construct a histogram. Based on the result, do the data appear to be from a population with a normal distribution? Explain.

Problem 7RE Sports Equipment According to USA Today, the largest categories of sports equipment sales are as follows: fishing ($2.0 billion); firearms and hunting ($3.1 billion); camping ($1.7 billion); golf ($2.5 billion). Construct the graph that best depicts these different categories and their relative amounts. What type of graph is best?

Scatterplots. In Exercises 5–8, use the given paired data from Appendix B to construct a scatterplot. Coke Volume and Weight Refer to Data Set 19 in Appendix B, and use the volumes and weights of regular Coke. Does there appear to be a correlation between volume and weight? What else is notable about the arrangement of the points, and how can it be explained?

Problem 8CQQ As a quality control manager at Sony, you find that defective CDs have various causes, including worn machinery, human error, bad supplies, and packaging mistreatment. Which of the following graphs would be best for describing the causes of defects: histogram; scatterplot; Pareto chart; dotplot; pie chart?

Stemplot of Grooming Times Use the data from Exercise 6 to construct a stemplot.

Time-Series Graphs. In Exercises 9 and 10, construct the time-series graph. Harry Potter Listed below are the gross amounts (in millions of dollars) earned from box office receipts for the movie Harry Potter and the Half-Blood Prince. The movie opened on a Wednesday, and the amounts are listed in order for the first 14 days of the movie's release. Suggest an explanation for the fact that the three highest amounts are the first, third, and fourth values listed.

Problem 9CQQ What characteristic of a data set can be better understood by constructing a histogram?

Time-Series Graphs. In Exercises 9 and 10, construct the time-series graph. Home Runs Listed below are the numbers of home runs in major league baseball for each year beginning with 1990 (listed in order by row). Is there a trend?

A histogram is to be constructed from the brain sizes listed in Data Set 6 of Appendix B. Without actually constructing that histogram, simply identify two key features of the histogram that would suggest that the data have a normal distribution.

Dotplots. In Exercises 11 and 12, construct the dotplot. Coke Volumes Refer to Data Set 19 in Appendix B, and use the volumes of regular Coke. Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution? Why or why not? Are there any outliers?

Dotplots. In Exercises 11 and 12, construct the dotplot. Car Pollution Refer to Data Set 14 in Appendix B, and use the greenhouse gas (GHG) emissions from the sample of cars. Does the configuration of the points appear to suggest that the amounts are from a population with a normal distribution? Why or why not?

Stemplots. In Exercises 13 and 14, construct the stemplot. Car Crash Tests Refer to Data Set 13 in Appendix B and use the 21 pelvis (PLVS) deceleration measurements from the car crash tests. Is there strong evidence suggesting that the data are not from a population having a normal distribution?

Stemplots. In Exercises 13 and 14, construct the stemplot. Car Braking Distances Refer to Data Set 14 in Appendix B and use the 21 braking distances (ft). Are there any outliers? Is there strong evidence suggesting that the data are not from a population having a normal distribution?

Problem 15BSC Pareto Charts. In Exercises construct the Pareto chart. Awful Sounds In a survey, 1004 adults were asked to identify the most frustrating sound that they hear in a day. In response 279 chose jackhammers, 388 chose car alarms, 128 chose barking dogs, and 209 chose crying babies (based on data from Kelton Research).

Problem 16BSC Pareto Charts. In Exercises construct the Pareto chart. School Day Here are weekly instruction times for school children in different countries: 23.8 hours (Japan), 26.9 hours (China), 22.2 hours (U.S.), 24.6 hours (U.K.), 24.8 hours (France). What do these results suggest about education in the United States?

Problem 17BSC Pie Charts. In Exercises construct the pie chart. Awful Sounds In a survey, 1004 adults were asked to identify the most frustrating sound that they hear in a day. In response 279 chose jackhammers, 388 chose car alarms, 128 chose barking dogs, and 209 chose crying babies (based on data from Kelton Research).

Problem 18BSC Pie Charts. In Exercises construct the pie chart. School Day Here are weekly instruction times for school children in different countries: 23.8 hours (Japan), 26.9 hours (China), 22.2 hours (U.S.), 24.6 hours (U.K.), 24.8 hours (France). What do these results suggest about education in the United States? Does it make sense to use a pie chart for the given data?