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xxxivTest yourself None 10 59.50 33.90 3.00 38.00 53.00 92.00 108.00 Soap 10 6.80 4.80 1.00 4.00 5.50 10.00 18.00 Hand sanitizer 10 9.90 8.67 2.00 4.00 6.50 14.00 27.00 1. Compare the three distributions. 2. Explain why the mean is much greater than the median for the hand sanitizer group. 3. Give a possible reason why the variability in number of bacteria is so much larger for the group that didn%u2019t wash their hands at all. 4. Based on the data, does it appear that hand sanitizer kills bacteria? Better than soap and water? Give appropriate evidence to support your answers. Chapter 1 Main Points %u2022 Statistics is the science and art of collecting, analyzing, and drawing conclusions from data. Organizing Data %u2022 A data set contains information about a number of individuals. Individuals may be people, animals, or things. %u2022 A variable is any attribute that can take different values for different individuals. %u2022 A categorical variable takes values that are labels, which place each individual into a particular group, called a category. %u2022 A quantitative variable takes numerical values that count or measure some characteristic of each individual. %u2022 The distribution of a variable describes which values the variable takes and how often it takes each value. You can use a frequency table or a relative frequency table to quickly summarize the distribution of a variable. Displaying Data Categorical Variables%u2022 You can use bar charts and pie charts to display the distribution of a categorical variable. You can 02_StarnesSPA5e_53579_ch01_002_097.indd 91 22/11/24 12:45 PMChapter 1 %u2022 Review Exercises 93v1. NYC trees (1.1) Researchers collected detailed information about trees on New York City streets. The following table displays some data for 8 of the trees. 116 Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative. Tree ID Diameter at breast height (in.) Curb location Health Zip code 28 4 On curb Fair 10455 74 3 On curb Poor 10459 187 26 On curb Good 11360 599 9 On curb Fair 11372 950 5 On curb Good 10463 1025 21 Offset from curb Good 11235 1196 16 On curb Good 11225 1212 7 On curb Good 11225 2. Disc dogs (1.1, 1.2) Here is a list of the breeds of dogs that won the World Canine Disc Championships over a 37-year period. 117 Whippet Labrador retriever Australian shepherd Whippet Mixed breed Australian shepherd Whippet Australian shepherd Australian shepherd Mixed breed Border collie Mixed breed Mixed breed Australian shepherd Border collie Other purebred Mixed breed Border collie Labrador retriever Mixed breed Border collie Mixed breed Mixed breed Other purebred Mixed breed Border collie Border collie Border collie Border collie Mixed breed Mixed breed Australian shepherd Mixed breed Mixed breed Border collie Mixed breed Labrador retriever (a) Summarize the distribution of dog breed with a frequency table. (b) Make a bar chart to display the data. Describe what you see. 3. Popular online sites (1.2) Common Sense Media surveyed a random sample of 1306 U.S. 8- to 18-year-olds in a recent year. One question asked on the survey was %u201cIf you had to pick one online site you didn%u2019t want to live without, which would it be?%u201d The figure shows the percentage of respondents who chose YouTube, Snapchat, TikTok, and Instagram. 118 Explain how the graph gives a misleading impression. 035YouTube30252015105Snapchat TikTok Instagram32%20%13% 13%Site you don%u2019t want to live withoutPercent4. Comparing family income (1.3) The dotplots show the annual income of 40 randomly chosen households each from Connecticut, Indiana, and Maine, based on U.S. Census data. Compare the distributions of income in these three states. 0MaineIndianaConnecticut50 100 150 200Annual household income ($1000s)250 300 3505. Density of the earth (1.4) In 1798, the English scientist Henry Cavendish measured the density of Earth several times by careful work with a torsion balance. The variable recorded was the density of Earth as a multiple of the density of water. Here are Cavendish%u2019s 29 measurements: 119 5.50 5.61 4.88 5.07 5.26 5.55 5.36 5.29 5.58 5.65 5.57 5.53 5.62 5.29 5.44 5.34 5.79 5.10 5.27 5.39 5.42 5.47 5.63 5.34 5.46 5.30 5.75 5.68 5.85 (a) Make a stemplot of the data. (b) Describe the distribution of density measurements. (c) The currently accepted value for the density of Earth is 5.51 times the density of water. How does this value compare to the mean of the distribution of density measurements? 6. Words and music (1.5, 1.6) For a final project in their statistics class, two students studied the impact of different types of background music on students%u2019 ability to remember words from a list they were allowed to study for 5 minutes. Here are data on the number of Chapter 1 Review Exercises 94 Chapter 1 %u2022 Analyzing One-Variable Datawords remembered by one group of students who listened to Beethoven%u2019s Fifth Symphony: 11 12 23 15 14 15 14 15 10 14 15 9 11 13 25 11 13 13 12 20 17 23 11 12 12 11 20 20 12 12 19 13 15 10 14 11 7 17 13 18 (a) Make a histogram that effectively displays the distribution of number of words remembered. (b) We used technology to compute the mean and median of this distribution. One is 13 and the other is 14.3. Based on the histogram, explain how you know which is which without doing any calculations. 7. Words and music II (1.7, 1.8) Refer to Exercise 6. (a) Find the range of the data. (b) Find the interquartile range of the data. (c) Identify any outliers in this distribution. (d) The standard deviation is 4.05. Interpret this value. 8. Comparing reaction times (1.8) Researchers suspect that athletes typically have a faster reaction time than non-athletes do. To test this theory, the researchers gave an online reflex test to 63 students at their school: 33 athletes and 30 non-athletes. The following parallel boxplots display the reaction times (in milliseconds) for the two groups of students. 150Athlete StudentReaction time (ms)Non-athlete200 250 300 350 400 450 500(a) About what percentage of each group had reaction times of at least 300 milliseconds? Explain your answer. (b) What do the data suggest about the researchers%u2019 suspicion? Explain your answer. Chapter 1 Practice Test 1. Researchers record the age, employment status, and earned income for a sample of 1463 adults. The number and type of variables recorded is (A) 3 quantitative, 0 categorical. (B) 3 quantitative, 1 categorical. (C) 2 quantitative, 1 categorical. (D) 2 quantitative, 2 categorical. 2. For which of the following variables would it be more appropriate to use a bar chart than a histogram to display the distribution? (A) Time to run a mile (min) (B) Number of pets (C) Age (D) Marital status 3. The bar chart summarizes the responses of dog owners to the question %u201cWhere in the car do you let your dog ride?%u201d Which of the following statements is true? 203040506070PercentageWhere does the dog ride?Back seatFront passengerseatFloorPassenger%u2019s lapDriver%u2019s lap(A) A majority of owners do not allow their pets to ride in the front passenger seat. (B) Roughly twice as many pets are allowed to sit in the front passenger seat as in the passenger%u2019s lap. (C) The vertical scale of this graph exaggerates the difference between the percentage who let their dogs ride in the driver%u2019s lap versus a passenger%u2019s lap. (D) These data could also be presented in a pie chart. Section I: Multiple Choice Select the best answer for each question. takes numerical values that count or measure some characteristic of each of a variable describes which values the variable takes and how often it takes frequency table or a to quickly summarize the REVIEW WHAT YOU KNOW . See how well you have learned the contents of the chapter. Use the chapter Main Points as a quick review and work the Chapter Review Exercises . If you have trouble, watch a Chapter Review Video to get detailed help on the solution to each question, or check the answer to an exercise in the Solutions Appendix . TAKE THE PRACTICE TEST. Finally, take the Practice Test to gauge your mastery of the material. Check your answers against those in the Solutions Appendix. All of the Practice Test solutions are given there. %u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.