Assignment Assignment for Lesson.1 Name Date To New Heights! Variance in Subjective and Random Samples 1. Suppose that you have collected data for the weights of all of the crates in a warehouse. a. Give an example of how you could choose a subjective sample of the data. b. Give an example of how you could choose a random sample of the data. The following table shows the ages, in months, of dogs in an obedience class. The obedience trainer assigns each dog an identification number, which is also shown in the table. Dog ID Number Age (in months) Dog ID Number Age (in months) 11 8 19 60 12 12 20 4 13 9 21 10 14 9 22 6 15 23 24 16 6 24 2 1 10 25 11 18 14 26 8 Use the table to answer Questions 2 through. 2. What is the range of the ages of the dogs in the obedience class? Chapter Assignments 131
3. What is the mean of the ages of the dogs in the obedience class? 4. Create a box-and-whisker plot of the data in the table. 5. Suppose that you take a subjective sample of the data in the table by choosing the first six dogs listed in the table. a. Enter each dog s ID number and age in the following table. Dog ID Number Age (in months) b. What is the range of the subjective sample? c. What is the mean of the subjective sample? 132 Chapter Assignments
Name Date d. Create a box-and-whisker plot of the data in the subjective sample. 6. Take a random sample of the data in the table by generating six random numbers from 11 through 26. a. Enter each dog s ID number and age in the following table. Dog ID Number Age (in months) b. What is the range of the random sample? c. What is the mean of the random sample? d. Create a box-and-whisker plot of the data in the random sample.. Compare the statistics and box-and-whisker plots of the subjective and random samples. Which of the two samples do you feel best represents the actual data? Explain your reasoning. Chapter Assignments 133
134 Chapter Assignments
Assignment Assignment for Lesson.2 Name Date Size How Sample Size Affects Results The following table shows the weights, in ounces, of the twenty lobsters in a tank in a restaurant. Each lobster has a tag with an identification number, which is also shown in the table. Lobster ID Number Weight (in ounces) Lobster ID Number Weight (in ounces) 101 18 111 20 102 16 112 14 103 22 113 30 104 30 114 34 105 24 115 19 106 11 116 23 10 20 11 25 108 18 118 28 109 24 119 20 110 22 120 26 Use the table to answer Questions 1 through 6. 1. Calculate the following summary statistics for the population of lobsters in the tank and their weights. a. Range b. First quartile c. Median d. Third quartile Chapter Assignments 135
e. Mean 2. Suppose you randomly select five lobsters from the tank. The following table shows the ID numbers and weights of the five lobsters that were randomly selected. Calculate the following summary statistics for the random sample of lobsters. Lobster ID Number Weight (in ounces) 101 18 10 20 115 19 119 20 112 14 a. Range b. First quartile c. Median d. Third quartile e. Mean 136 Chapter Assignments
Name Date 3. Suppose you randomly select ten lobsters from the tank. The following table shows the ID numbers and weights of the ten lobsters that were randomly selected. Calculate the following summary statistics for the random sample of lobsters. Lobster ID Number Weight (in ounces) Lobster ID Number Weight (in ounces) 120 26 10 20 105 24 111 20 108 18 118 28 101 18 106 11 119 20 102 16 a. Range b. First quartile c. Median d. Third quartile e. Mean 4. Use the summary statistics that you calculated in Questions 1 through 3 to draw box-and-whisker plots for the entire population of lobsters in the tank, the random sample of five lobsters, and the random sample of ten lobsters. Chapter Assignments 13
5. Compare the box-and-whisker plots in Question 4 and describe how well each represents the population data. 6. The standard deviation for the entire population of lobsters in the tank is 5.55, the standard deviation for the random sample of five lobsters is 2.49 and the standard deviation for the random sample of ten lobsters is 4.95. Compare the standard deviations and describe how well each represents the population data. 138 Chapter Assignments
Assignment Assignment for Lesson.3 Name Date Sampling Comparing Sampling Techniques A housing plan contains 24 homes. The following table shows the total living area in square feet of the 24 homes and their address numbers. In the housing plan, the addresses are numbered from 201 to 224. House Address Number Living Area (in square feet) House Address Number Living Area (in square feet) 201 1450 213 1500 202 1600 214 165 203 1550 215 1110 204 115 216 1240 205 1025 21 1400 206 2000 218 1625 20 1620 219 1550 208 145 220 1220 209 1350 221 1080 210 1200 222 135 211 1880 223 1200 212 1450 224 1500 Use the table to answer Questions 1 through 6. 1. Calculate the following summary statistics for the population of homes in the housing plan and their total living area. a. Range b. First quartile Chapter Assignments 139
c. Median d. Third quartile e. Mean 2. There are two streets in the housing plan. Homes numbered 201 through 212 are located on Apple Street and homes numbered 213 through 224 are located on Blueberry Drive. Suppose that you take a stratified random sample by selecting the even-numbered homes on Blueberry Drive. Complete the following table by entering the house address numbers and living areas for those homes in the stratified random sample. Then calculate the following summary statistics for the stratified random sample. House Address Number Living Area (in square feet) a. Range b. First quartile c. Median d. Third quartile 140 Chapter Assignments
Name Date e. Mean 3. The housing plan is divided into clusters of four homes based on their house address numbers as shown in the table. Choose three homes from the first clustered sample of homes in the table and calculate the following summary statistics for those three homes. Cluster Number 1 2 3 4 5 6 House Address Numbers 201, 20, 213, 219 202, 208, 214, 220 203, 209, 215, 221 204, 210, 216, 222 205, 211, 21, 223 206, 212, 218, 224 a. Range b. First quartile c. Median d. Third quartile e. Mean 4. Use the summary statistics that you calculated in Questions 1 through 3 to draw box-and-whisker plots for the entire population of homes in the housing plan, the stratified random sample of even-numbered homes on Blueberry Drive, and the first clustered sample of four homes. Chapter Assignments 141
5. Compare the box-and-whisker plots in Question 4 and describe how well each represents the population data. 6. Give possible reasons why one sample may have better represented the population data than the other. 142 Chapter Assignments
Assignment Assignment for Lesson.4 Name Date It s the Ladies Turn! Designing an Experiment and Bias Each elementary school in the Green Valley School District has a baseball team that consists of first-, second-, and third-grade students. Each baseball player is assigned an I.D. number. The I.D. numbers for the first-grade players begin at 101, the I.D. numbers for the second-grade players begin at 112, and the I.D. numbers for the third-grade players begin at 128. The following table shows the batting averages for all of the baseball players in the Green Valley School District. Student I.D. Number Batting Average Student I.D. Number Batting Average Student I.D. Number Batting Average 101 0.100 121 0.140 141 0.335 102 0.095 122 0.130 142 0.245 103 0.050 123 0.145 143 0.230 104 0.085 124 0.190 144 0.210 105 0.200 125 0.165 145 0.20 106 0.280 126 0.195 146 0.210 10 0.110 12 0.140 14 0.135 108 0.115 128 0.220 148 0.390 109 0.090 129 0.260 149 0.410 110 0.05 130 0.20 150 0.180 111 0.150 131 0.290 151 0.155 112 0.220 132 0.150 152 0.195 113 0.160 133 0.350 153 0.210 114 0.155 134 0.180 154 0.260 115 0.100 135 0.185 155 0.205 116 0.115 136 0.195 156 0.10 11 0.305 13 0.200 15 0.220 118 0.340 138 0.205 158 0.160 119 0.180 139 0.260 159 0.215 120 0.15 140 0.310 160 0.185 Chapter Assignments 143
There are three elementary schools in the Green Valley School District. The following is a summary of the baseball players from each school. Washington Elementary School: 101, 102, 103, 104, 112, 113, 114, 115, 116, 128, 129, 130, 131, 132, 133, 134, 135, 136, 13, 138, 139, 140, 141 Jefferson Elementary School: 105, 106, 11, 118, 119, 120, 121, 122, 123, 124, 142, 143, 144, 145, 146, 14, 148 Lincoln Elementary School: 10, 108, 109, 110, 111, 125, 126, 12, 149, 150, 151, 152, 153, 154, 155, 156, 15, 158, 159, 160 Use this summary information to answer Questions 1 through 4. 1. Explain how you could use a random sample of 10 baseball players to perform an experiment to examine the distribution of the batting averages of the first-, second-, and third-grade students in the Green Valley School District. 2. Explain how you could use a stratified random sample of 10 baseball players to perform an experiment to examine the distribution of the batting averages of the first-, second-, and third-grade students in the Green Valley School District. 3. Explain how you could use a clustered sample to perform an experiment to examine the distribution of the batting averages of the first-, second-, and third-grade students in the Green Valley School District. 144 Chapter Assignments
Name Date 4. Choose one of the sample methods from Questions 1 through 3 to make a box-and-whisker plot of the data. What conclusions can you make about the batting averages based on the box-and-whisker plot? Explain how each sampling method is biased. 5. The lengths of the 100 fish caught in a bass tournament are arranged from largest to smallest. The fish are then clustered into groups of five so that the first twenty are in one group, the next twenty are in the second group, and so on. You randomly choose ten fish from the last group to perform an experiment to analyze the lengths of the fish caught in the tournament. 6. A scientist is preparing an experiment in which he will analyze the bacteria levels in a lake. He walks to the edge of the lake and fills 40 vials with water to represent the water supply in the lake.. You want to analyze the fitness levels of runners after running in a marathon by performing a stress test on the runners. There are 1000 runners in the marathon. You choose the first 25 runners that finish the marathon to represent the population of runners for your experiment. Chapter Assignments 145
8. You want to perform an experiment to determine the amount of money that Americans feel the government should be spending on public transit. You choose a random sample of 50 bus drivers and interview them to represent the population for your experiment. 146 Chapter Assignments
Assignment Assignment for Lesson.5 Name Date On Your Own! Designing, Implementing, Analyzing, and Reporting a Data Experiment There are twenty teams in a bowling league. There are four members on each team. Teams 1 through 10 are men s teams and Teams 11 through 20 are women s teams. The following are the scores for each team member s first game. Team 1: 205, 150, 168, 219 Team 11: 211, 119, 105, 150 Team 2: 242, 18, 162, 145 Team 12: 14, 185, 190, 164 Team 3: 98, 1, 200, 190 Team 13: 80, 12, 215, 161 Team 4: 221, 203, 220, 203 Team 14: 215, 206, 146, 18 Team 5: 148, 188, 239, 12 Team 15: 165, 122, 115, 108 Team 6: 215, 95, 90, 129 Team 16: 198, 165, 144, 111 Team : 120, 188, 14, 165 Team 1: 95, 115, 206, 140 Team 8: 199, 192, 183, 16 Team 18: 10, 86, 126, 135 Team 9: 245, 13, 218, 18 Team 19: 135, 144, 168, 152 Team 10: 160, 111, 104, 129 Team 20: 212, 218, 109, 15 Chapter Assignments 14
Use this scoring information to answer Questions 1 through 3. 1. Perform an experiment to examine the distribution of men s bowling scores in the league. Use a random sample of size 15. Find the mean, median, quartiles, minimum, and maximum of the sample data. Draw a box-and-whisker plot of the sample data. Use the box-and-whisker plot and the summary statistics to make a conclusion about the distribution of men s bowling scores. 148 Chapter Assignments
Name Date 2. Perform an experiment to examine the distribution of women s bowling scores in the league. Use a stratified random sample of size 10. Find the mean, median, quartiles, minimum, and maximum of the sample data. Draw a box-and-whisker plot of the sample data. Use the box-and-whisker plot and the summary statistics to make a conclusion about the distribution of women s bowling scores. Chapter Assignments 149
3. Perform an experiment to examine the distribution of all bowling scores in the league. Use a clustered sample of size 16. Find the mean, median, quartiles, minimum, and maximum of the sample data. Draw a box-and-whisker plot of the sample data. Use the box-and-whisker plot and the summary statistics to make a conclusion about the distribution of the bowling scores. 150 Chapter Assignments