# 45 (use Stapplet) 51,57, 59(Stapplet), 61, 69(Stapplet), 75, 80-85

52 CHAPTER 1 DATA ANALYSIS these cereal brands Between what two values 77. Birth does it her student (ed) About what percent of the cereal beauis have (30 or Draw more calories per serving' of birth . Paying for championships Does par ing high salaries lead to more victories in professional sports? 78. Die ro The New York Yankees have long been koown a plaus High school graduate for having Major League Baseball's highest teams use a b payroll And over the years, the team has won many 79. AP championships. This strategy didn't pay off in 2008, grades when the Philadelphia Phillies won the World Series. AB an Maybe the Yankees didn't spend enough money that year. The figure shows histograms of the salary 2016 distributions for the two teams during the 2008 season. Why can't you me these graphs to effectively 10% Calcul compare the team payrolls? 0 20 100 120 140 Statistic Yankees Phillies Total personal income ($1000s) Make (a) Would it be appropriate to use frequency hishes grade instead of relative frequency histograms in the (b) Write Explain why or why not. of exa Frequ (b) Compare the distributions of total personal incus Multiple C the two groups. 80. Here 6 1 10 sh 0 5 10 15 20 25 30 35 2 4 6 8 10 12 14 76. Strong paper towels In commercials for Bountypa 65. T Salary (S millions) Salary ($ millions) towels, the manufacturer claims that they are the (a) 0, 2, 74. Paying for championships Refer to Exercise 73. Here picker-upper," but are they also the stronger picker is a better graph of the 2008 salary distributions for upper? Two of Mr. Tabor's statistics students, Wesley (b) 0, 1, the Yankees and the Phillies. Write a few sentences Maverick, decided to find out. They selected a rand ( c) 0, 3, comparing these two distributions. sample of 30 Bounty paper towels and a random as of 30 generic paper towels and measured their sheng 81. The Yankees Phillies when wet. To do this, they uniformly soaked each pe high towel with 4 ounces of water, held two opposite cle desc of the paper towel, and counted how many quarter Frequency Frequency each paper towel could hold until ripping, alteman brands. The data are displayed in the relative frequs histograms. Compare the distributions. 8 16 24 Frequency 8 16 24 32 30% Salary ($ millions) Salary ($ millions) 20% 75. Value of a diploma Do students who graduate from 3 10% high school earn more money than students who do 0% not? To find out, we took a random sample of 371 U.S. 12 30% residents aged 18 and older. The educational level and Gener 20% total personal income of each person were recorded, 10% The data for the 57 non-graduates (No) and the 314 (a) Ro graduates (Yes) are displayed in the relative frequency histograms. ( b) Ro 70 80 90 100 110 120 130 140 Number of quarters (c) Ro (a) Would it be appropriate to use frequency histop (d) Ske instead of relative relative frequency histograms in this s (e) Sk Explain why or why not 82. (b) Compare the distributions of number of quarters breaking for the two paper towel brands.Section 1.2 Summary You can use a dotplot, stemplot, or histogram to show the distribution of a quantitative variable. A dotplot displays individual values on a number line. Stemplots separate each observation into a stem and a one-digit leaf. Histo- grams plot the frequencies (counts) or relative frequencies (proportions or percents) of values in equal-width intervals. Some distributions have simple shapes, such as symmetric, skewed to the left, or skewed to the right. The number of peaks is another aspect of overall shape. So are distinct clusters and gaps. A single-peaked graph is sometimes called unimodal, and a double-peaked graph is sometimes called bimodal. When examining any graph of quantitative data, look for an overall pattern and for clear departures from that pattern. Shape, center, and variability describe the overall pattern of the distribution of a quantitative variable. Out- liers are observations that lie outside the overall pattern of a distribution. When comparing distributions of quantitative data, be sure to compare shape, center, variability, and possible outliers. Remember: histograms are for quantitative data; bar graphs are for categor- ical data. Be sure to use relative frequencies when comparing data sets of different sizes. 1.2 Technology Corner TI-Nspire and other technology instructions are on the book's website at highschool.bfwpub.com/updatedtps6e. 2. Making histograms Page 43 Section 1.2 Exercises 5. Feeling sleepy? Students in a high school statistics (a) Make a dotplot of these data. pg 131 class responded to a survey designed by their teacher. One of the survey questions was "How much sleep did (b) Long words can make a book hard to read. What you get last night?" Here are the data (in hours): percentage of words in the sample have 8 or more letters? 9 6 8 7 8 8 6 6.5 7 7 9.0 4 3 4 47. U.S. women's soccer-2016 Earlier, we examined 5 6 11 6 3 6 10.0 7 8 4.5 9 7 7 data on the number of goals scored by the 2016 a) Make a dotplot to display the data. U.S. women's soccer team in 20 games played. The following dotplot displays the goal differential for those b) Experts recommend that high school students sleep at same games, computed as U.S. goals scored minus least 9 hours per night. What proportion of students in opponent goals scored. this class got the recommended amount of sleep? 16. Easy reading? Here are data on the lengths of the . . . . . . . first 25 words on a randomly selected page from Toni Morrison's Song of Solomon: Difference (U.S. - Opponent) in goals scored 2 3 4 10 2 11 2 8 4 3 7 2 (a) Explain what the dot above 3 represents. 5 3 6 4 4 2 5 8 2 3 4 4 (b) What does the graph tell us about how well the team did in 2016? Be specific.Section 1.2 Exercises 51 23.6 25. 17.7 OH 22.1 22.3 OK 71. Returns on common stocks The return on a 25.0 20.0 30.6 stock is the change in its market price plus any OR 20.7 21.8 MA 26.6 dividend payments made. Return is usually PA 26.8 25.0 expressed as a percent of the beginning price. 23.4 RI 23.9 22.3 The figure shows a histogram of the distribution MIN 22.0 SC 22.9 of monthly returns for the U.S. stock market over 24.1 MS 24.0 SD a 273-month period. 3 DE 15.9 23.6 MO 22.9 TN FL 23.5 25.9 MT 17.6 TX ants GA 24.6 27.3 NE rich 17.7 UT 20.8 50 - I O 25.5 NV 24.2 VT 21.2 ID 20.1 NH 24.6 /A 26.9 Number of months 10- 27.9 NJ 29.1 NA 25.2 Z 22.3 NM 20.9 25.6 20 - h 2 IA 18.2 NY 30.9 WI 20.8 KS 18.5 NC 23.4 NY 17.9 KY 22.4 ND 15.5 DC 29.2 -25 -20-15 -10 Monthly percent return on common stocks (a) Make a histogram to display the travel time data using intervals of width 2 minutes, starting at 14 minutes. (a) Describe the overall shape of the distribution of monthly returns. .8 (b) Describe the shape of the distribution. What is the (b) What is the approximate center of this distribution? most common interval of travel times? (c) Explain why you cannot find the exact value for 69. DRP test scores There are many ways to measure the the minimum return. Between what two values reading ability of children. One frequently used test does it lie? is the Degree of Reading Power (DRP). In a research study on third-grade students, the DRP was administered (d) A return less than 0 means that stocks lost value in that to 44 students."Their scores were as follows. month. About what percent of all months had returns less than 0? 40 26 39 14 42 18 25 43 46 27 19 72. Healthy cereal? Researchers collected data on calories 47 19 26 35 34 15 44 40 38 31 46 per serving for 77 brands of breakfast cereal. The 52 25 35 35 33 29 34 41 49 28 52 histogram displays the data. 34 47 35 48 22 33 41 51 27 14 54 45 30 - Make a histogram to display the data. Write a few 25 9.0 sentences describing the distribution of DRP scores. 20 - 70. Country music The lengths, in minutes, of the 50 Frequency 15 most popular mp3 downloads of songs by country artist 0.2 Dierks Bentley are given here. 10 3.8 3.7 4.7 4.2 4.0 3.9 3.4 4.4 5.0 4.6 3.7 4.0 3.2 47 50 60 70 80 90 100 110 120 130 140 150 160 4.6 4.4 4.1 3.0 4.4 Calories 7.9 3.5 3.7 43 3.7 4.8 3.9 76 4.2 4.7 6.2 4.0 7.0 (a) Describe the overall shape of the distribution of 4.0 4.2 3.4 3.4 2.9 3.3 calories. 6.9 3.2 3.4 3.7 3.5 3.4 3.7 (b) What is the approximate center of this distribution? 3.6 1.7 3.9 3.7 3.8 3.1 3.7 (c) Explain why you cannot find the exact value for 4.5 3.7 the maximum number of calories per serving for day Make a histogram to display the data. Write a few ge sentences describing the distribution of song lengths. ch 16CHAPTER 1 DATA ANALYSIS Women | Men 50 03333 90 56668999 64. Watch that caffeine! The U.S. Food and Drug 22222222 02222222 558 Administration (USFDA) limits the amount of 853888888875555 4440 00344 caffeine in a 12-ounce can of carbonated beverage WWNN. to 72 milligrams. That translates to a maximum of 48 milligrams of caffeine per 8-ounce serving. Data on the caffeine content of popular soft drinks (in milligrams per 8-ounce serving) are displayed in the Key: 23 = 225-234 minutes stemplot. 1 556 033344 67. Carbon dioxide emissions Burning fuels in power play 55667778888899 p9142 and motor vehicles emits carbon dioxide (COz), which WWNN. 113 contributes to global warming. The table displays CO. 55567778 33 emissions per person from countries with populations of at least 20 million. 30 (a) Make a histogram of the data using intervals of width (a) Why did we split stems? starting at 0. (b) Give an appropriate key for this graph. (b) Describe the shape of the distribution. Which (c) Describe the shape of the distribution. Are there any countries appear to be outliers? outliers? CO2 Country COz 65. Acorns and oak trees Of the many species of oak trees Country ( b) 3.3 Mexico 3.8 in the United States, 28 grow on the Atlantic Coast Algeria and 1 1 grow in California. The back-to-back stemplot Argentina 45 Morocco displays data on the average volume of acorns (in cubic Australia 16.9 Myanmar 0.2 69. I centimeters) for these 39 oak species. " Write a few 0.4 Nepal 0.1 Bangladesh sentences comparing the distributions of acorn size for Brazil 2.2 Nigeria 0.5 the oak trees in these two regions. 0.9 Canada 14.7 Pakistan Atlantic Coast | | California 6.2 Peru 20 China 998643 0 4 Colombia 1.6 Philippines 0.9 88864211111 1 50 2 06 Congo 0.5 Poland 8.3 6640 Egypt 2.6 Romania 3.9 8 4 15 59 Ethiopia 0.1 Russia 12.2 16 France 5.6 Saudi Arabia 17.0 9.0 8 Germany 9.1 South Africa 1 9 Ghana 0.4 Spain 6.8 5 Key: 26 = An oak species 70. 10 11 1 1.7 whose acorn volume India Sudan 0.3 12 is 2.6 cm'. Indonesia 1.8 Tanzania 0.2 131 141 Iran 7.7 Thailand 4.4 15 Iraq 3.7 Turkey 4.1 16 Italy 17 6.7 Ukraine 6.6 Japan 9.2 United Kingdom 7.9 66. Who studies more? Researchers asked the students Kenya 0.3 United States 17.6 in a large first-year college class how many minutes Korea, North 11.5 they studied on a typical weeknight. The back-to-back Uzbekistan 3.7 Korea, South 2.9 6.9 stemplot displays the responses from random samples Venezuela Malaysia 17 of 30 women and 30 men from the class, rounded 7.7 Vietnam to the nearest 10 minutes. Write a few sentences comparing the male and female distributions of 68. Traveling to work How long do people travel each da study time. to get to work? The following table gives the average travel times to work (in minutes) "minutes ) for workers in each state and the District of Columbia who are at least 10 years old and don't work at home.3148 CHAPTER 1 DATA ANALYSIS (44 individuals). Compare the distributions of total family incomes in these two samples, 43. Fuel efficiency The dotplot shows the difference (Highway - City) in EPA mileage ratings, in miles per gallon (mpg) for each of 24 model year 2018 cars. Indians -... .6839: 1:: 81 ... 25 New Jersey , 208: 81, .1.8,.... 75 100 125 150 Total family income ($1000s) Difference (Highway - City) in EPA mileage rating (mpg) 56. Healthy streams Nitrates are organic compounds (a) Explain what the dot above -3 represents. that are a main ingredient in fertilizers. When (b) What does the graph tell us about fuel economy in the those fertilizers run off into streams, the nitrates can city versus on the highway for these car models? Be have a toxic effect on fish. An ecologist studying specific. nitrate pollution in two streams measures nitrate 49. Getting older How old is the oldest person you know? concentrations at 42 places on Stony Brook and 42 g133 Prudential Insurance Company asked 400 people to places on Mill Brook. The parallel dotplots display place a blue sticker on a huge wall next to the age of the data. Compare the distributions of nitrate the oldest person they have ever known. An image of concentration in these two streams. the graph is shown here. Describe the shape of the distribution. Stony Brook - Mill Brook 4 6 8 10 12 14 16 18 Nitrate concentration (mg/L) 57. Enhancing creativity Do external rewards- things like money, praise, fame, and grades-promote creativity? Researcher Teresa Amabile recruited 47 experienced 50. Pair-o-dice The dotplot shows the results of rolling creative writers who were college students and divided a pair of fair, six-sided dice and finding the sum of them at random into two groups. The students in one the up-faces 100 times. Describe the shape of the group were given a list of statements about external distribution. reasons (E) for writing, such as public recognition, making money, or pleasing their parents. Students in the other group were given a list of statements about intema reasons (1) for writing, such as expressing yourself and .......... enjoying wordplay. Both groups were then instructed to write a poem about laughter. Each student's poem was . . . ........ ....... rated separately by 12 different poets using a creativity . . ...... ....... . . ..... scale.2 These ratings were averaged to obtain an overall 5 -... .. creativity score for each poem. Parallel dotplots of the two groups' creativity scores are shown here. Sum of the up-faces on a pair of dice 51. Feeling sleepy? Refer to Exercise 45. Describe the shape of the distribution. 52. Easy reading? Refer to Exercise 46. Describe the shape Reward Internal (I) External (E : . of the distribution. .:. ...: :: ... 53. U.S. women's soccer-2016 Refer to Exercise 47. pg135 Describe the distribution. 10 54. Fuel efficiency Refer to Exercise 48. Describe the 15 20 distribution. Average rating (a) Is the variability in creativity scores similar or different 55. Making money The parallel dotplots show the for the two groups? Justify your answer. gBE total family income of randomly chosen individuals from Indiana (38 individuals) and New Jersey (b) Do the data suggest that external rewards promote creativity? Justify your answer.Section 1.2 Exercises 53 Birth months Imagine asking a random sample of 60 students from your school about their birth months. to $500,000 in price. The few houses on the water, Draw a plausible (believable) graph of the distribution however, are priced up to $15 million. The distribution of birth months. Should you use a bar graph or a of house prices will be histogram to display the data? (a) skewed to the left. (d) single-peaked. 78. Die rolls Imagine rolling a fair, six-sided die 60 times. Draw b) roughly symmetric. a plausible graph of the distribution of die rolls. Should you (e) approximately uniform. use a bar graph or a histogram to display the data? (c) skewed to the right. 79. AP exam scores The table gives the distribution of 83. The histogram shows the distribution of the percents of grades earned by students taking the AP Calculus women aged 15 and over who have never married in each AB and AP Statistics exams in 2016.35 of the 50 states and the District of Columbia. Which of the following statements about the histogram is correct? Grade 5 4 3 2 1 Total 12 - Calculus AB 76,486 53,467 53,533 30,017 94,712 308,215 10 - 120 140 160 Statistics 29,627 44,884 51,367 32,120 48,565 206,563 ($1000s) Number of states 8 - (a) Make an appropriate graphical display to compare the 6- ency histograms grade distributions for AP Calculus AB and AP Statistics. ams in this setting (b) Write a few sentences comparing the two distributions of exam grades. 2 - Multiple Choice: Select the best answer for Exercises 80-85. 20 24 28 32 ersonal income far 36 48 52 80. Here are the amounts of money (cents) in coins carried by Percent of women over age 15 who never married 10 students in a statistics class: 50, 35, 0, 46, 86, 0, 5, 47, 23, or Bounty paper (a) The center (median) of the distribution is about 36%. 65. To make a stemplot of these data, you would use stems hey are the "quicka b) There are more states with percentages above 32 than onger picker- (a) 0, 2, 3, 4, 6, 8. (d) 00, 10, 20, 30, 40, 50, there are states with percentages less than 24. dents, Wesley and (b) 0, 1, 2, 3, 4, 5, 6, 7, 8. 60, 70, 80, 90. (c) It would be better if the values from 34 to 50 were deleted elected a random ( c ) 0, 3, 5, 6, 7. (e) None of these. on the horizontal axis so there wouldn't be a large gap. a random sample 81. The histogram shows the heights of 300 randomly selected (d) There was one state with a value of exactly 33%. red their strength high school students. Which of the following is the best (e) About half of the states had percentages between 24% soaked each paper description of the shape of the distribution of heights? and 28%. opposite edges 70 - 84. When comparing two distributions, it would be best to many quarters use relative frequency histograms rather than frequency 60 - ing, alternating histograms when elative frequency 50 - (a) the distributions have different shapes. 40- (b) the distributions have different amounts of variability. Frequency 30 - (c) the distributions have different centers. 20 (d) the distributions have different numbers of observations. 10 (e) at least one of the distributions has outliers. 52 64 72 76 85. Which of the following is the best reason for choosing a stemplot rather than a histogram to display the Height distribution of a quantitative variable? (a) Roughly symmetric and single-peaked (unimodal) (a) Stemplots allow you to split stems; histograms don't. (b) Roughly symmetric and double-peaked (bimodal) (b) Stemplots allow you to see the values of individual (e) Roughly symmetric and multi-peaked (multimodal) observations. (d) Skewed to the left (c) Stemplots are better for displaying very large sets of data. ency lustages ums in this mania (e) Skewed to the right (d) Stemplots never require rounding of values. 82. You look at real estate ads for houses in Naples, (e) Stemplots make it easier to determine the shape of a Florida. There are many houses ranging from $200,000 distribution, hidsSection 1.2 Exercises 49 58. Healthy cereal? Researchers collected data on 76 brands of cereal at a local supermarket.27 For each 61. South Carolina counties Here is a stemplot of the brand, the sugar content (grams per serving) and the areas of the 46 counties in South Carolina. Note that shelf in the store on which the cereal was located the data have been rounded to the nearest 10 square (1 = bottom, 2 = middle, 3 = top) were recorded. A miles (mi-). dotplot of the data is shown here. 3 9999 0116689 vauin 01115566778 3 : . . .. . . .. . : :. . : 47899 01245579 0011 9 Key: 64 represents Shelf 13 a county with an area 10 8 21 of 635 to 644.99 11 233 12 square miles. (a) What is the area of the largest South Carolina county? 12 (b) Describe the distribution of area for the 46 South Sugar content (grams per serving) Carolina counties. (a) Is the variability in sugar content of the cereals on the 62. Shopping spree The stemplot displays data on the three shelves similar or different? Justify your answer. amount spent by 50 shoppers at a grocery store. Note that the values have been rounded to the nearest dollar. (b) Critics claim that supermarkets tend to put sugary 20 cereals where kids can see them. Do the data from 399 this study support this claim? Justify your answer. 1345677889 000123455668888 JAWN - (Note that Shelf 2 is at about eye level for kids in most 25699 s like supermarkets.) 1345579 ity? 0359 59. Snickers" are fun! Here are the weights (in grams) of Key: 9 3 = $92.50 ed pg 138 17 Snickers Fun Size bars from a single bag: to $93.49 spent ded 366 one 17.1 17.4 16.6 17.4 17.7 17.1 17.3 17.7 17.8 3 19.2 16.0 15.9 16.5 16.8 16.5 17.1 16.7 (a) What was the smallest amount spent by any of the in the (a) Make a stemplot of these data. shoppers? ternal (b) What interesting feature does the graph reveal? (b) Describe the distribution of amount spent by these 50 ind shoppers. ed to (c ) The advertised weight of a Snickers Fun Size bar is 17 63. Where do the young live? Here is a stemplot of the was grams. What proportion of candy bars in this sample ity weigh less than advertised? percent of residents aged 25 to 34 in each of the 50 states: verall 60. Eat your beans! Beans and other legumes are a great the source of protein. The following data give the protein 11 44 content of 30 different varieties of beans, in grams per 11 66778 12 0134 100 grams of cooked beans. 28 12 666778888 13 0000001111444 7.5 8.2 8.9 9.3 7.1 8.3 8.7 9.5 8.2 9.1 13 7788999 9.0 9.0 9.7 9.2 8.9 8.1 9.0 7.8 8.0 7.8 14 0044 14 567 7.0 7.5 13.5 8.3 6.8 10.6 8.3 7.6 7.7 8.1 15 11 15 (a) Make a stemplot of these data. 16 (b) What interesting feature does the graph reveal? (a) Why did we split stems? (c) What proportion of these bean varieties contain more (b) Give an appropriate key for this stemplot. than 9 grams of protein per 100 grams of cooked rent beans ? (c) Describe the shape of the distribution. Are there any outliers