Chapter 1 Exploring Data
Back to Lesson 1-1
the percentage of skaters with no gear who were beginners.
Chapter 1 Exploring Data Lesson 1-1
(pp. 6–13)
1. Answers vary. Sample: eye color, arm span, birth month 2. Answers vary. Sample: It is too expensive to study the entire population. It is unsafe or implausible to subject the entire population to a study, as in eating all the apples in a store to check quality. The population does not stay in one place, as in a population of animals. 3. The population is the batch of cookies. The data are based on a sample. The variable of interest is the number of raisins per cookie. 4. The population is WNBA players. The data are based on a population. The variable of interest is free-throw percentage. 5. in decreasing order: falls, motor-vehicle, and suffocation by ingestion or inhalation 6. a. Answers vary. Sample: motor vehicles (~130) + drowning (~20) + falls (~20) + fires, flames, and smoke (~20) + poisoning (~20) + suffocation, by ingestion, and inhalation (~20) 230 b. Answers vary. Sample: motor vehicles (~1300) + poisoning (~250) + drowning (~80) + falls (~40) + fires, etc. (~30) 1700 7. A representative sample is a sample that accurately reflects the important features of the population. 8. a. 2,145 inline skaters in Boston b. Answers vary. Sample: all inline skaters in Boston 9. a.
beginner no gear total no gear
= 188 21.5% 874
b. Example 1 Part d asks for the percentage of beginner skaters in the sample who wore no gear, whereas Part a asked for 1
Functions, Statistics and Trigonometry Solution Manual
10.
advanced no gear total no gear
=
372 874
42.6%
11. a. categorical (ex: male, female) b. categorical (ex: bus, car, bike) c. numerical (ex: 65 inches, 2.1 meters) d. numerical (ex: 1 mile, 2 miles) 12. total number of households: 107,590,000. Some college: 28,874,000. 28,874,000 So, 107590,000 26.8% 13. 13.3% + 16.7% + 18.9% + 9.4% + 9.3% = 67.6% 14. a. 9,130(12.8% + 17.3%) + 6,088(21.7% + 15.6%) 5,019 thousand households 5,019 b. 107,590 4.7% 15. Answers vary. Sample: The median income of households headed by someone who has at least a bachelor’s degree is more than twice as high as the median income of households headed by someone with only a high school diploma. 16. a. type of sport and gender b. boys in basketball: about 55%; girls in basketball: about 45%; boys in track & field: about 55% c. The percent values are rounded to the nearest 1%, so although about 0.29% of baseball players are girls, that value is rounded to 0%. d. Answer vary. Sample: Participants in baseball and football are almost always boys, and the large majority of volleyball participants are girls. The sports with more equal levels of participation between boys and girls are basketball, soccer, and track & field. 17. a. the age distribution of trout in a certain lake
Chapter 1, Lesson 1-1
Back to Lesson 1-1
b. sample; The population is all of the trout in the lake. The trout were captured from different parts of the lake in order to make the sample more representative. 96 (53 + 29) 14.6% c. 96 18. a. Traveling Distance to School Distance to School 2 blocks or less 2–6 blocks 6 blocks or more Total
Elementary School 72
Middle School 34
High School 12
Total
132
107
89
328
80
83
108
271
284
224
209
717
118
b. 23. Answers vary. Sample:
The data concern the State of the Union address, which the U.S. President gives annually each January to Congress. The variables are the number of times the President was applauded, the duration of the applause, and the total length of the speech. One possible observation from this data is that the number of periods of applause during the speech is in a state of decline. We might conclude that Congress was increasingly less pleased with the content of the speech.
c. categorical = 20 19. a. x = 260 13 b. x = c. x = d. x =
260 0.13 13 260 0.13 260
= 2, 000 = 0.05 = 0.0005
20. slope: m; y-intercept: b 21. a. Answers vary. Sample: (0, -13), (1, -16) b. y = -3x – 13 22.
2
(x + 3) + (x + 7) + (x + 29) 3
= x + 13
Functions, Statistics and Trigonometry Solution Manual
Chapter 1, Lesson 1-1
the percentage of skaters with no gear who were beginners.
Chapter 1 Exploring Data Lesson 1-1
(pp. 6–13)
1. Answers vary. Sample: eye color, arm span, birth month 2. Answers vary. Sample: It is too expensive to study the entire population. It is unsafe or implausible to subject the entire population to a study, as in eating all the apples in a store to check quality. The population does not stay in one place, as in a population of animals. 3. The population is the batch of cookies. The data are based on a sample. The variable of interest is the number of raisins per cookie. 4. The population is WNBA players. The data are based on a population. The variable of interest is free-throw percentage. 5. in decreasing order: falls, motor-vehicle, and suffocation by ingestion or inhalation 6. a. Answers vary. Sample: motor vehicles (~130) + drowning (~20) + falls (~20) + fires, flames, and smoke (~20) + poisoning (~20) + suffocation, by ingestion, and inhalation (~20) 230 b. Answers vary. Sample: motor vehicles (~1300) + poisoning (~250) + drowning (~80) + falls (~40) + fires, etc. (~30) 1700 7. A representative sample is a sample that accurately reflects the important features of the population. 8. a. 2,145 inline skaters in Boston b. Answers vary. Sample: all inline skaters in Boston 9. a.
beginner no gear total no gear
= 188 21.5% 874
b. Example 1 Part d asks for the percentage of beginner skaters in the sample who wore no gear, whereas Part a asked for 1
Functions, Statistics and Trigonometry Solution Manual
10.
advanced no gear total no gear
=
372 874
42.6%
11. a. categorical (ex: male, female) b. categorical (ex: bus, car, bike) c. numerical (ex: 65 inches, 2.1 meters) d. numerical (ex: 1 mile, 2 miles) 12. total number of households: 107,590,000. Some college: 28,874,000. 28,874,000 So, 107590,000 26.8% 13. 13.3% + 16.7% + 18.9% + 9.4% + 9.3% = 67.6% 14. a. 9,130(12.8% + 17.3%) + 6,088(21.7% + 15.6%) 5,019 thousand households 5,019 b. 107,590 4.7% 15. Answers vary. Sample: The median income of households headed by someone who has at least a bachelor’s degree is more than twice as high as the median income of households headed by someone with only a high school diploma. 16. a. type of sport and gender b. boys in basketball: about 55%; girls in basketball: about 45%; boys in track & field: about 55% c. The percent values are rounded to the nearest 1%, so although about 0.29% of baseball players are girls, that value is rounded to 0%. d. Answer vary. Sample: Participants in baseball and football are almost always boys, and the large majority of volleyball participants are girls. The sports with more equal levels of participation between boys and girls are basketball, soccer, and track & field. 17. a. the age distribution of trout in a certain lake
Chapter 1, Lesson 1-1
Back to Lesson 1-1
b. sample; The population is all of the trout in the lake. The trout were captured from different parts of the lake in order to make the sample more representative. 96 (53 + 29) 14.6% c. 96 18. a. Traveling Distance to School Distance to School 2 blocks or less 2–6 blocks 6 blocks or more Total
Elementary School 72
Middle School 34
High School 12
Total
132
107
89
328
80
83
108
271
284
224
209
717
118
b. 23. Answers vary. Sample:
The data concern the State of the Union address, which the U.S. President gives annually each January to Congress. The variables are the number of times the President was applauded, the duration of the applause, and the total length of the speech. One possible observation from this data is that the number of periods of applause during the speech is in a state of decline. We might conclude that Congress was increasingly less pleased with the content of the speech.
c. categorical = 20 19. a. x = 260 13 b. x = c. x = d. x =
260 0.13 13 260 0.13 260
= 2, 000 = 0.05 = 0.0005
20. slope: m; y-intercept: b 21. a. Answers vary. Sample: (0, -13), (1, -16) b. y = -3x – 13 22.
2
(x + 3) + (x + 7) + (x + 29) 3
= x + 13
Functions, Statistics and Trigonometry Solution Manual
Chapter 1, Lesson 1-1
