Identify the Wʹs for the description of data.

Review Identify the Wʹs for the description of data. 1) A survey of bicycles parked outside college dormitories at a small university recorded the style (mountain bike, ten speed, etc.), the brand, the color, and the age. 2) The State Athletic Association requires coaches to keep these records on all athletes: age, days absent, medical history, emergency contact, and any allergies the athlete may have. Name the variables in each description of data, then tell whether they are quantitative or categorical. For each quantitative variable name its unit of measure. 3) When determining the batting average for a baseball player you must have data on the number of hits in the season, and the number of at-bats in the season. A) Number of hits, quantitative, hits; number of at-bats, quantitative, at-bats. B) Number of hits, comparative; number of at-bats, quantitative, at-bats; players, categorical. C) Number of hits, quantitative, hits; number of at-bats, comparative. D) Number of hits, comparative; number of at-bats, quantitative, at-bats. E) Number of hits, quantitative, games; number of at-bats, quantitative, at-bats; player, categorical. Classify the variable as categorical or quantitative. 4) A personʹs height in feet A) Quantitative B) Categorical 5) A personʹs political affiliation A) Categorical B) Quantitative ) The speed of a car in miles per hour A) Categorical B) Quantitative Provide an appropriate response. 7) A magazine article reported on Springfield School Districtʹs magnet school programs. Of the 1470 qualified applicants, 79 were accepted, 252 were wait-listed, and 420 were turned away for lack of space. Find the relative frequency distribution of the decisions made, and write a sentence describing it. A) 1470 students applied for admission to the magnet schools program. 54% were accepted, 17% were wait-listed, and 29% were turned away. B) 1470 students applied for admission to the magnet schools program. 54% were accepted, and 4% were turned away. C) 1470 students applied for admission to the magnet schools program. 54% were accepted, 32% were wait-listed, and 29% were turned away. D) 1470 students applied for admission to the magnet schools program. 54% were accepted, 32% were wait-listed, and 53% were turned away. E) 1470 students applied for admission to the magnet schools program. 71% were accepted, and 29% were turned away. Provide an appropriate response. Round to the nearest tenth of a percent if necessary. ) A survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Driver Student Staff American 10 5 European 3 22 Asian 9 5 What percent of all the cars surveyed were foreign? Origin

9) Just how accurate are the weather forecasts we hear every day? The table below compares the daily forecast with a cityʹs actual weather for a year. Actual Weather Rain No rain Rain 2 52 No rain 9 27 On what percent of days was rain predicted? Provide an appropriate response. 10) A magazine article reported on Springfield School Districtʹs magnet school programs. Of the 107 qualified applicants, 514 were Black or Hispanic, 22 were Asian, and 31 were White. Summarize the relative frequency distribution of ethnicity with a sentence or two in the proper context. A) Of the 107 students who applied for admission to the magnet schools program, 32% were Black or Hispanic, 1% were Asian, and 52% were White. B) Of the 107 students accepted in the magnet schools program, 32% were Black or Hispanic, 1% were Asian, and 52% were White. C) Of the 107 students who applied for admission to the magnet schools program, 1% were Black, 1% were Hispanic, 1% were Asian, and 52% were White. D) Of the 107 students who applied for admission to the magnet schools program, 2% were Black or Hispanic, 32% were Asian, and 52% were White. E) Of the 107 students who applied for admission to the magnet schools program, 3% were Black or Hispanic, 2% were Asian, and 5% were White. 11) The Centers for Disease Control lists causes of death for individual states in 2002. The mortality data for one state is given. Cause of Death Percent Heart Disease 2.1 Cancer 23.1 Circulatory diseases and stroke 7.4 Respiratory diseases 5.2 Accidents 4.7 Is it reasonable to conclude that, in this state, cancer or respiratory diseases were the cause of approximately 2% of deaths in 2002? 12) The Centers for Disease Control lists causes of death for individual states in 2002. The mortality data for one state is given. Cause of Death Percent Heart Disease 29. Cancer 22.3 Circulatory diseases and stroke.1 Respiratory diseases.3 Accidents 4.4 In this state, what percent of deaths were from causes not listed here? 13) A local park district is planning to build a recreation center. The park district conducted a poll to find out the types of physical activities the local population would be interested in. The poll was based on telephone responses from 1013 randomly selected adults. The table shows the percentages of people who expressed interest in various activities. Activity Percent Running/Walking 5 Weight Training 47 Biking 39 Aerobics 24 Swimming 1 Is it reasonable to conclude that 3% expressed interest in either biking or aerobics?

Create the requested display for the data. 14) The focus of a recent survey was was on teenagersʹ familiarity with and use of modern technology. The teenagers were asked if they used each of the following technologies on a daily basis and if the technology was critically important to own. For each question, the percentage of those responding ʺYesʺ is given. Subtracting the ʺUse dailyʺ percentage from the ʺCritically important to ownʺ percentage gives the ʺImportance Gap.ʺ Here are the results: Use daily Critically important to own Importance gap Computer 47% 79% 32 Telephone 54% 71% 17 DVD 3% 51% 13 Calculator 72% 7% Stereo/audio 90% 72% -1 Video games 4% 21% -27 Create a bar chart for the ʺImportance Gapʺ. 1) Using the table in problem #17, which of the following displays is the most appropriate for these data? I II III A) II B) III C) I D) All of these displays are equally appropriate. E) None of these displays are appropriate. 1) The weights, in pounds, of the members of the varsity football team are listed below. Create a stem -and-leaf display of the data. Do not use split stems. 144 152 142 151 10 152 131 14 141 153 140 149 144 135 15 147 133 172 159 135 159 14 171 13 Provide an appropriate response. Round to the nearest tenth of a percent if necessary. 17) Students in a political science course were asked to describe their politics as ʺLiberalʺ, ʺModerateʺ, or ʺConservative.ʺ Here are the results: Politics Liberal Moderate Conservative Total Female 43 3 5 Male 52 55 1 125 Total 95 91 24 210 What percent of the females in the class consider themselves to be ʺLiberalʺ? Sex

1) Just how accurate are the weather forecasts we hear every day? The table below compares the daily forecast with a cityʹs actual weather for a year. Actual Weather Rain No Rain Rain 27 59 No Rain 10 29 What percent of the time was the forecast correct? A) 1.9% B) 7.4% C) 7.4% D) 73.7% E) 1.1% Forecast Provide an appropriate response. Round to the nearest tenth of a percent if necessary. 19) Students in a political science course were asked to describe their politics as ʺLiberalʺ, ʺModerateʺ, or ʺConservative.ʺ Here are the results: Politics Liberal Moderate Conservative Total Sex Female 37 27 14 7 Male 44 39 23 10 Total 1 37 14 What percent of all students in the class are males who consider themselves to be ʺLiberalʺ? A) 54.3% B) 20.1% C) 23.9% D) 41.5% E) 44% 20) Students in a political science course were asked to describe their politics as ʺLiberalʺ, ʺModerateʺ, or ʺConservative.ʺ Here are the results: Politics Liberal Moderate Conservative Total Female 45 37 12 94 Male 3 39 21 9 Total 1 7 33 190 What percent of all ʺModeratesʺ in the class are male? Sex 21) A magazine article reported on Springfield School Districtʹs magnet school programs. The article examined the impact of an applicantʹs ethnicity on the likelihood of admission. The data are summarized in the table below. Admission Decision Accepted Wait-listed Turned away Total Black/Hispanic 455 0 30 45 Asian 10 45 145 29 White 324 245 351 920 Total 5 290 52 1701 What percent of all applicants were Black or Hispanic? Ethnicity Would you expect the distribution of this variable to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. 22) Number of times each face of a fair five-sided die shows in 50 tosses. A) The distribution would likely be uniform, with around 50 occurrences of each side. B) The distribution would likely be uniform, with around 10 occurrences of each side. C) The distribution would likely be unimodal and skewed right. The average of the numbers on the face of the die would be around 3, with more tosses greater than 3. D) The distribution would likely be unimodal and symmetric. The average of the numbers on the face of the die would be around 3, with a some tosses greater than 3 and some less than 3. E) The distribution would likely be unimodal and skewed left. The average of the numbers on the face of the die would be around 3, with more tosses less than 3.

23) Ages of high school students. A) The distribution would likely be unimodal and slightly skewed to the right. The average age of the high school students would be about the same. The distribution would be slightly skewed to the right, since there are more seniors. B) The distribution would likely be bimodal and slightly skewed to the right. The average age of the freshman and sophomores would be at one mode, and the average age of the juniors and seniors would be at the other mode. The distribution would be slightly skewed to the right, since there are more seniors. C) The distribution would likely be unimodal and slightly skewed to the left. The average age of the high school students would be about the same. The distribution would be slightly skewed to the left, since there are more freshmen. D) The distribution would likely be unimodal and symmetric. The average age of the high school students would be about the same, with some students that are older and some that are younger than the average age. E) The distribution would likely be uniform. Freshmen tend to be about 14 years old; sophomores, 15; juniors, 1; and seniors, 17. Since there is about an equal number of students in each class, the distribution is uniform. Describe the distribution (shape, center, spread, unusual features). 24) Atlanta area animal shelters euthanize more animals per year than most other major city shelters. The following stemand-leaf display shows the number of homeless cats and dogs that had to be euthanized each year in the Atlanta area for the period 195-2004. Use both the stemplot and timeplot to describe the distribution. Euthanized Animal Totals 1 0 0 1 3 3 2 1 1 5 7 3 4 5 7 0 5 7 4 4 4 9 9 3 90 0 Key: 7 5 = 7,500 cats and dogs euthanized Compare the distributions (shape, center, spread, unusual features). 25) The back-to-back dotplot shows the number of fatalities per year caused by tornadoes in a certain state for two periods: 1950-1974 and 1975-1999. In addition to comparing these distributions, state a reason explaining any differences.

A fitness instructor measured the heart rates of the participants in a yoga class at the conclusion of the class. The data is summarized in the histogram below. There were fifteen people who participated in the class between the ages of 25 and 45. Use the histogram to answer the question. 2) How many participants had a heart rate between 120 and 130 bpm? A) 3 B) 5 C) 2 D) 4 27) What percentage of the participants had a heart rate greater than 130 bpm? A) 33% B) 13% C) 53% D) 27% Describe the distribution (shape, center, spread, unusual features). 2) A student at a local university took a total of 20 exams during freshman year. The student recorded the exam scores as percentages and created the following stemand-leaf display. The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9. In addition to describing the distribution, give a reason to account for the shape of this distribution. Exam Grades 9 7 9 9 0 1 2 2 5 7 7 9 7 2 4 5 Key: 9 1 = 91% 29) A dotplot of the number of tornadoes each year in a certain county from 194 to 2004 is given. Each dot represents a year in which there were that many tornadoes. Create the requested display for the data. 30) In a college health course, 49 students participated in a physical fitness assessment. One measure used in the assessment was body fat. The body fat percentages for the 4 students is broken into two groups, men and women. Create a back-to-back stem-and-leaf display of the data. Use split stems. Let the lower leaf represent digits 0-4 and the upper leaf represent 5-9. Menʹs Body Fat (%) 20 15 12 7 1 9 14 21 14 1 17 13 19 14 1 20 12 14 21 19 19 1 23 Womenʹs Body Fat (%) 33 2 25 2 30 15 2 20 29 27 1 1 35 1 21 25 24 19 11 25 27 27 21 30

Compare the distributions (shape, center, spread, unusual features). 31) The histograms show the cost of living, in dollars, for 32 U.S. cities. The histogram on the left shows the cost of living for the 32 cities using bins $10 wide, and the histogram on the right displays the same data using bins that are $ wide. Collection 1 1 Histogram Collection 1 12 Histogram 14 12 10 10 4 2 4 2 0 90 100 110 120 130 140 Cost_of_Living 90 100 110 120 130 140 Cost_of_Living 32) The histograms below show the distribution of quiz scores on a ten point math quiz with and without a fifteen minute review before the quiz. Describe the different shapes of the distributions. Does it appear that the fifteen minute review resulted in improved quiz scores? Explain the evidence that supports your conclusion. Without 15 minutes review before quiz With 15 minutes review before quiz 9 10 7 5 4 3 2 4 2 1 4 5 7 9 10 Quiz_Scores_out_of_10_points 4 5 7 9 10 Quiz_Scores_out_of_10_points Answer Key 1) Who: Bicycles parked at college dormitories.; Cases: Each bicycle is a case; What: Style, brand, color, and age of bicycle; When: Not specified; Where: A small university; Why: Not specified; How: A survey was taken outside college dormitories. 2) Who: Athletes; Cases: Each athlete is an individual case; What: Age, days absent, medical history, emergency contact, and allergy history; When: Current; Where: Not specified; Why: State requirement; How: Information is collected and stored as athletic records.

3) A 4) A 5) A ) B 7) A ) 49.2% 9) 21.4% 10) A 11) Yes, because these categories do not overlap. 12) 29.3% 13) No, because these categories overlap. 14) 15) B 1) 13 1 3 5 5 14 0 1 2 4 4 7 9 15 1 2 2 3 9 9 1 0 3 4 17 1 2 Key: 14 2 = 142 pounds 17) 50.% 1) E 19) C 20) 51.3% 21) 2.5% 22) B 23) E 24) The distribution of the number of cats and dogs that were euthanized is bimodal. The upper cluster is between 7,000 and 90,000 euthanized, with a center at around,400. The lower cluster is between 1,000 and 2,000 euthanized, with a center at around 1,000. The timeplot shows that the number of animals euthanized has increased over the period 195-2004, with a significant increase between 1994 and 199. 25) The distribution of the number of fatalities per year for the period 1950-1974 is unimodal and approximately symmetric. The center of the distribution is about 2 fatalities per year. The number of fatalities per year ranges from 0 to 5 deaths. For the period 1975-1999, the distribution of the number of fatalities per year is also unimodal, but skewed to the right. A typical number of fatalities for this distribution is 0 fatalities, with a range of 0 to 5 deaths. Before 1975, there were more fatalities as a result of tornadoes. Higher construction standards, better warning systems, or medical advancements could all account for this difference. 2) A 27) C 2) The distribution of exam scores is skewed to the left. Typically, the student scored 9% on exams, and the exam scores are tightly clustered in the 90s. Two exam scores are outliers, when the student scored below 5%. It is possible that the student had a difficult time with one of his or her courses in that year. Regardless of the possible reasons, these two scores were unusual compared to the studentʹs other exam scores. 29) The distribution of the number of tornadoes per year is unimodal and skewed to the left, with a center around 5 tornadoes per year. The number of tornadoes per year ranges from 0 to 7. 30) Menʹs Body Fat Womenʹs Body Fat (%) (%) 9 7 0 4 4 4 4 3 2 2 1 1 9 9 9 7 5 1 5 9 3 1 1 0 0 2 0 1 1 4 2 5 5 5 7 7 7 9 3 0 0 3 3 5 Key: 1 5 = 15% body fat 31) The distribution in the left histogram of the cost of living in the 32 U.S. cities is unimodal and skewed to the right. The distribution is centered around $100, and spread out, with values ranging from $0 to $140. The distribution in the right histogram appears bimodal, with many cities costing just under $104 and another smaller cluster around $119. There also appears to be an outlier in the right histogram at $134 that was not apparent in the histogram on the left. 32) Without the 15 minute review the distribution of quiz scores is roughly symmetrical with a typical score of out of 10. With the 15 minute review the distribution of quiz scores is left-skewed with a typical score of out of 10. The 15 minute review worked. Without the review roughly 23% scored higher than out of 10, but after the review roughly 70% scored higher than out of 10.