Assignment. To New Heights! Variance in Subjective and Random Samples. Use the table to answer Questions 2 through 7.

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1 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) 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

2 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

3 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

4 134 Chapter Assignments

5 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) Use the table to answer Questions 1 through 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

6 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) a. Range b. First quartile c. Median d. Third quartile e. Mean 136 Chapter Assignments

7 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) 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

8 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 Compare the standard deviations and describe how well each represents the population data. 138 Chapter Assignments

9 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) Use the table to answer Questions 1 through 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

10 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

11 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 House Address Numbers 201, 20, 213, , 208, 214, , 209, 215, , 210, 216, , 211, 21, , 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

12 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

13 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 Chapter Assignments 143

14 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 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

15 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

16 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

17 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

18 Use this scoring information to answer Questions 1 through 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

19 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

20 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

The Five Magic Numbers

The Five Magic Numbers Objective: Students will review the five numbers needed to construct a box and whisker plot. Students will also answer questions using a box and whisker plot they created. Background