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Unit 5 Investigation 1 Answer Key Activity 5.1.1 Page 1 which category hurricane has been more likely to happen. 1a. mean = 117 1b. median = 105 1c. mode = 75, 80, 85 and 115 7. 2. The mean is larger than the median. An acceptable justification is that there were a few hurricanes with very high maximum wind speeds that caused the mean to increase. 3. Varies by student. The mode is often not unique. 8. 4. Name Max Wind Speed Category Cindy 75 1 Dennis Emily Irene Katrina Maria Nate Ophelia Philippe Rita Stan Vince Wilma Beta Epsilon 150 160 105 175 115 90 85 80 180 80 75 185 115 85 4 5 2 5 3 1 1 1 5 1 1 5 3 1 5. mean = 2.6 median = 2 mode = 1 6. Varies by student. An acceptable response is that the mean is larger than the median. In this case, the mode depicts 9. Varies by student 10. Varies by student 11. n = 15. Yes 12. Varies by student 13. 110 14. Max Wind Speeds Bin 60 ≤ x < 80 80 ≤ x < 100 100 ≤ x < 120 75, 75 90, 85, 80, 80, 85 105, 115, 115 120 ≤ x < 140 Frequency 2 5 3 0 140 ≤ x < 160 150 1 160 ≤ x < 180 160, 175 2 180 ≤ x < 200 180, 185 2 15. Unit 5 Investigation 1 Answer Key Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key Page 2 19. mean = 93.5 median = 90 range = 40 20. 16. A similar histogram 21. 17. Varies by student. An acceptable response is that the histograms contain the same data, but histograms with smaller bins allow us to see the spread more clearly. 18. 2012 Atlantic Ocean Hurricanes Name Dates 6/19 – 6/22 8/1 – Ernesto 8/10 8/15 – Gordon 8/20 8/21 – Isaac 9/1 8/28 – Kirk 9/2 8/30 – Leslie 9/11 9/3 – Michael 9/11 9/10 – Nadine 10/3 10/12 – Rafael 10/17 10/22 – Sandy 10/29 Chris Max Wind (mph) Category 75 1 22. Varies by student 85 1 Activity 5.1.2 110 2 1. 80 1 105 2 75 1 Mode = 29 115 3 Minimum = 23 90 1 Maximum = 43 90 1 110 2 Unit 5 Investigation 1 Answer Key American League Mean= 31.6 Median = 30 Range = 17 Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key National League Page 3 National League Mean= 30.65 Median = 31 Mode = 26 Minimum = 23 Maximum = 39 Range = 16 2. American League Interval Frequency 20 ≤ x < 24 0 24 ≤ x < 28 3 28 ≤ x < 32 10 32 ≤ x < 36 3 36 ≤ x < 40 2 40 ≤ x < 44 2 National League Interval Frequency 20 ≤ x < 24 1 24 ≤ x < 28 5 28 ≤ x < 32 6 32 ≤ x < 36 4 36 ≤ x < 40 4 40 ≤ x < 44 0 3. American League 4. Mean Median Mode Minimum Maximum Range $3.904 $3.869 $3.894 $3.626 $4.605 $0.979 Varies by student. An acceptable response may include the following: XMin = 0 YMin = 0 XMax = 50 YMax = 10 XScl = 5 YScl = 1 5. It changes the bin width. 6. The National League histogram is more mound-shaped than the American League histogram. 7. The American League histogram is more skewed than the National League histogram. 8. Yes, the mean is 30.65 and the median is 31. 9. Yes, the mean is 31.6 and the median is 30. Since the tail is to the right of 31.6 and the mean is to the right of the median, then the mean is closer to the tail than the median. 10. Varies by student Unit 5 Investigation 1 Answer Key Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key Activity 5.1.3 5b. Varies by student 5c. Varies by student 5d. Varies by student 1. Mean Median Mode Minimum Maximum Range Page 4 430 360 250, 350, 510 250 760 510 2. Varies by student. Example: Calories Bin Frequency 200 ≤ x < 300 2 300 ≤ x < 400 6 400 ≤ x < 500 1 500 ≤ x < 600 4 600 ≤ x < 700 1 700 ≤ x < 800 1 3. Varies by student based on answer found in #2. Example: 6. Skewed right 7. Skewed right 8. Varies by student 9. Connecticut gas prices are well above the mean, median and mode. One possible reason for this is due to the amount of tax Connecticut residents pay per gallon of gasoline. Activity 5.1.4 1. Min: 148 Q1: 152 Median: 162 Q3: 170 Max: 181 2a. 75, 75, 80, 80, 85, 85, 90, 105, 115, 115, 150, 160, 175, 180, 185 2b. Minimum: 75 Q1: 80 Median: 105 Q3: 160 Maximum: 185 3a. 9, 11, 12, 20, 25, 28, 30, 30, 30, 32 32, 35, 39, 40, 43, 45, 48, 50, 61, 70 5a. Mean Median Mode Minimum Maximum Range $3.90 $3.87 $3.89 $3.63 $4.61 $0.98 Unit 5 Investigation 1 Answer Key 3b. Minimum: 9 Q1: 26.5 Median: 132 Q3: 44 Maximum: 70 4a. 321, 328, 330, 334, 337, 340, 340, 351, 357, 370, 373, 377, 377, 380, 402, 404, 415, 423, 431, 435, 436, 461, 533, 601, 761 Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key Page 5 4b. Minimum: 321 Q1: 340 Median: 377 Q3: 433 Maximum: 761 3b. 5.45 Activity 5.1.5 Activity 5.1.6 1a. 33; It is extremely low when compared to the rest of the scores. 1. 1b. Varies by student 1c. Minimum: 33 Q1: 76.5 Median: 83 Q3: 90.5 Maximum: 99 1d. 24 1e. Lower fence = 40.5 Upper fence = 126.5 3c. Lower fence = -5.975 Upper fence = 15.825 3d. LeBron James, Dwyane Wade and Chris Bosh High Avg. Low Min 63 56 43 High Avg. Low Q3 78 68 57 Q1 70.75 60 50.75 Max 82 74 66 Med 75 63.5 55 IQR 7.25 8 6.25 SD 5.87 5.16 6.11 2. 1f. 33 2a. Minimum: 0 Q1: 4 Median: 7.35 Q3: 9.8 Maximum: 29.7 2b. 5.8 2c. Lower fence = -4.7 Upper fence = 18.5 2d. LeBron James 3a. Minimum: 1 Q1: 2.2 Median: 5.6 Q3: 7.65 Maximum: 26.7 Unit 5 Investigation 1 Answer Key 3a. 3b. 3c. 3d. 3e. Plot 2 Plot 5 Plot 4 Plot 3 Plot 1 4. Minimum: 0.9 Q1: 1.8 Median: 9.05 Q3: 14.85 Maximum: 32 Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key Page 6 5j. In this case it raised the mean and standard deviation. 6. Varies by student 7. No, this is univariate data and the temperature is not compared to another data set. 5a. Minimum: 30 million Q1: 31 million Median: 33 million Q3: 42 million Maximum: 110 million Range: 80 million IQR: 11 million 8a. Varies by student 8b. Varies by student 8c. The whisker will not extend past the lower fence or upper fence. 8d. Varies by student 8e. If there is a bin that contains a data value and the bin is very far from the rest of the data. 5b. Lower fence = 14.5 million Upper fence = 58.5 million 9. Varies by student 10. Varies by student 5c. Yes, 110 million is greater than 58.5 million Activity 5.1.7 5d. Minimum: 30 million Q1: 31 million Median: 32.5 million Q3: 41 million Maximum: 49 million Range: 19 million IQR: 10 million 5e. The maximum was most affected. 5f. The minimum and Q1 were not affected. 5g. IQR; this is not affected by outliers 5h. mean ≈ 39.04 million S.D. ≈ 15.9 million 5i. mean ≈ 36.083 million S.D. ≈ 6 million Unit 5 Investigation 1 Answer Key 1. First Class mean: 80 median: 80 mode: 80 range: 20 standard deviation: approximately 4.104 Second Class mean: 80 median: 80 mode: 79, 80, 81 range: 40 standard deviation: approximately 9.067 Third Class mean: 80 median: 80 mode: 66, 94 range: 40 standard deviation: approximately 12.982 Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key 2. First Class Q1: 78 Q3: 82 Page 7 5. Second Class Q1: 76.5 Q3: 83.5 Third Class Q1: 66.5 Q3: 93.5 3. First Class IQR: 4 Second Class IQR: 7 Third Class IQR: 27 4. First Class 1.5*IQR = 6 Lower fence: 72 Upper fence: 88 The outliers are the test scores 70, 90. Second Class 1.5*IQR = 10.5 Lower fence: 66 Upper fence: 94 The outliers are the following test scores: 60, 65, 95, and 100. Third Class 1.5*IQR = 40.5 Lower fence: 26.5 Upper fence: 134 There are no outliers. Unit 5 Investigation 1 Answer Key 6. Varies by student based on bin width 7. Varies by student 8. The mean and median are the same for all three sets of data. 9. The third set of data. The IQR and standard deviation help us to see this spread. 10. Varies by student Exit Slip 5.1.1 1. Interval Frequency 0≤x<5 0 5 ≤ x < 10 2 10 ≤ x < 15 1 15 ≤ x < 20 2 20 ≤ x < 25 3 25 ≤ x < 30 3 30 ≤ x < 35 2 35 ≤ x < 40 1 40 ≤ x < 45 1 Algebra I Model Curriculum Version 3.0 Unit 5 Investigation 1 Answer Key Page 8 2. Exit Slip 5.1.2 Min: 25 Q1: 40 Median: 57.5 Q3: 100 Max: 120 IQR: 60 Range: 95 Unit 5 Investigation 1 Answer Key Algebra I Model Curriculum Version 3.0