1ACE Exercise 2 Investigation 1 2. Use the totals in the last row of the table on page 16 for each color of candies found in all 15 bags. a. Make a bar graph for these data that shows the percent of each color found in the 15 bags. HINT Refer to page 8 for an example of a bar graph. Example in finding percents: There are 101 green candies out of 101 854 total. Thus, are green, or 854 11.8% (about 12%). b. Describe the data by writing two or more comparison statements. 1. 2. c. Look back at the bar graph you made for Problem 1.1, Question B. Compare this graph with the graph you made in part (a). How would you now answer the original question, Did the Mars Company plan a specific distribution of colors of candies? Explain your reasoning. HINT For example: The bags were more likely to have red candy than blue candy. 122
2ACE Exercises 3 6 Investigation 2 Caffeine Content of Selected Beverages Soda Drinks Other Drinks Name Caffeine in 8 Ounces (mg) Name Caffeine in 8 Ounces (mg) Soda A 38 Energy Drink A 77 Soda B 37 Energy Drink B 70 Soda C 27 Energy Drink C 25 Soda D 27 Energy Drink D 21 Soda E 26 Iced Tea A 19 Soda F 24 Iced Tea B 10 Soda G 21 Coffee Drink 83 Soda H 15 Hot Cocoa 2 Soda J 23 Juice Drink 33 Use the table above for Exercises 3 6. 3. a. What is the mean amount of caffeine in the soda drinks? b. Make a line plot of the amount of caffeine in the soda drinks. c. What is the mean amount of caffeine in the other drinks? 123
2ACE Exercise 3 6 (continued) Investigation 2 d. Make a line plot of the amount of caffeine for the other drinks. e. Write three statements comparing the amount of caffeine in soda and in other drinks. 1. 2. 3. 4. Indicate whether each statement is true or false. a. Soda B has more caffeine than Soda F or Soda D. b. Energy Drink C has about 3 times as much caffeine as the same amount of Energy Drink A. c. Of the drinks in the table, 75% have 25 mg or less of caffeine in an 8-ounce serving. How many drinks are listed in the chart? How many of the drinks have 25 mg or less of caffeine for an 8-ounce serving? What is the percent of drinks with 25 mg or less in an 8-ounce serving? 124
2ACE Exercise 3 6 (continued) Investigation 2 5. Moderate caffeine intake for adults is 300 mg per day, but it is recommended that 10- to 12-year-olds have no more than 85 mg per day. Has a middle school student who drinks three 12-ounce cans of Soda F consumed more of his or her recommended intake of caffeine than an adult who drinks two servings of Coffee Drink? How many total ounces of Soda F will the student drink in three 12 ounce cans? From the table, 8 ounces of Soda F has 24 milligrams of caffeine (24 mg of caffeine per 8 ounces). How many milligrams of caffeine did he/she drink with three 12-ounce cans? How much more is this amount of caffeine than what is recommended for a 10 12 year old? How much caffeine does an adult drink if he/she drinks two Coffee Drinks (83 mg of caffeine per 16 ounces)? How much more is this amount of caffeine than what is recommended for an adult? 6. Are the mean and median for caffeine content in the graph below almost the same values? What is the mean? What is the median? Are they almost the same? Explain. Caffeine in Drinks 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Caffeine per 8-Ounce Serving (g) 125
3ACE Exercise 8 Investigation 3 8. Use the line plots and table. Trial 1 Reaction Times With Dominant Hand Mean 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Trial 1 (seconds) Trial 1 Reaction Times With Non-Dominant Hand 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Trial 1 (seconds) Trial 1 Reaction Times Statistic Mean Minimum Value Maximum Value Range Dominant Hand (seconds) 1.048 1.015 0.64 2.10 1.50 Non-Dominant Hand (seconds) 1.324 1.22 0.83 2.14 1.31 How much slower are the Trial 1 reaction times for non-dominant hands than the Trial 1 reaction times for dominant hands? How much slower is the mean reaction time of non-dominant hands than the mean reaction time of dominant hands? 126
3ACE Exercise 8 (continued) Investigation 3 How much slower is the median reaction time of non-dominant hands than the median reaction time of dominant hands? What is the slowest reaction time of non-dominant hands and what is the slowest reaction time of dominant hands? Which one has the slowest reaction time? Explain how you found out how much slower the Trial 1 reaction times for non-dominant hands are than the times for dominant hands. HINT What statistics can you use to decide this. 127
4ACE Exercise 2 Investigation 4 7. The 3 pairs of line plots display data about 50 wood roller coasters. Means and medians are marked on each graph. Graph A: Maximum Drop for Each Wood Coaster 1960 2004 Mean 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 1902 1959 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 Maximum Drop (ft) Graph B: Maximum Height for Each Wood Coaster 1960 2004 Mean 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 1902 1959 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 1960 2004 Maximum Height (ft) 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 1902 1959 Graph C: Top Speed for Each Wood Coaster Mean 128 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Top Speed (mi/h)
4ACE Exercise 2 (continued) Investigation 4 a. Write 3 statements comparing wood roller coasters built before 1960 with wood roller coasters built in 1960 or later. 1. 2. 3. b. Hector says there are too few roller coasters to make comparisons. Do you agree or disagree with Hector? Explain. 129
Unit Test Part I The PTA at Snow Camp Middle School is concerned that more and more teenagers are reporting back problems. Doctors think that many of these problems may be related to carrying backpacks that are too heavy. The PTA decides to put on an assembly to educate students in the school about the problem. The PTA also wants to know if the assembly succeeds in getting students to carry less in their backpacks. One team of middle school students in Mrs. James class decided to weigh students backpacks both before and after the assembly. A week before the assembly, they randomly selected 79 students walking in the halls before school. The students took off their backpacks so the backpacks could be weighed on a scale. The weight of each backpack was recorded to the nearest half pound. A month later, after the assembly, the team of students weighed another sample of students backpacks using the same method stopping students in the halls before school. The first period bell surprised them; they were only able to weigh the backpacks of 51 students. Here is a graph showing the results. Backpacks Group 79 before 51 after 0 5 10 15 20 25 WeightBkp (pounds) 130
Unit Test (continued) 1. The PTA President wants to know what the results show about how much backpacks weighed before the assembly. Briefly summarize the data for her. Mean What is the mean of the data before the assembly? What is the mean of the data after the assembly? Mode What is the mode of the data before the assembly? What is the mode of the data after the assembly? What is the median of the data before the assembly? What is the median of the data after the assembly? Range What is the range of the data before the assembly? What is the range of the data after the assembly? 2. The PTA President also wants to know if the students are carrying less or more in their backpacks since the assembly. Are students carrying less, more or the same weight in their backpacks after the assembly? If they are carrying less or more, how much less or more weight are they carrying than before the assembly? 3. Based on the data, was the assembly effective in influencing students to carry less weight in their backpacks? Explain why or why not. 131