Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data

This handy Spectrum Math Grade 7 Answer Key Chapter 6 Lesson 6.5 Problem Solving with Data provides detailed answers for the workbook questions

Spectrum Math Grade 7 Chapter 6 Lesson 6.5 Problem Solving with Data Answers Key

When a scientific question is identified, data can be collected based on an experiment. Then, the data can be compared using statistics.

Maria wants to know how much time she should spend studying for a test. She asks 15 classmates how long they studied for their last tests and then asks them how they scored on their tests. Here is the information she gathered:
Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data 1
The mean score for the students who studied 0-2 hours is 84.38, and the mean for the students who studied 2 or more hours is 91.86. So, students who studied 2 or more hours had better results overall than students who studied 0-2 hours. For Maria to have the best possible result on her next test, she should study for 2 or more hours.

Analyze the data sets below to make an inference about the situation.

Question 1.
Robert wants to know how many hours of light are best for growing tomato plants. He plants 20 tomato plants that are all close together in height. He gives one group of 10 plants 4 hours of light every day and gives the other 10 plants 10 hours of light every day. He measures them at the end of 3 weeks to find out how much each plant has grown.
Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data 2
Answer:
The mean growth for plants that were given light for 4 hours was 4.6 inches.
The mean growth for plants that were given light for 10 hours was 9.4 inches.
Therefore, the plants that are given for 10 hours light grow more successfully.

Explanation:
Given that,
Robert plants 20 tomato plants that are all close together in height.
He gives one group of 10 plants 4 hours of light every day,
and gives the other 10 plants 10 hours of light every day.
He measures them at the end of 3 weeks to find out how much each plant has grown.
So, growth of the plants that were given light for 4 hours was,
Set of data: 3, 5, 5, 6, 4, 6, 3, 4, 6, 4
Mean: average of a set of 10 plants given 4 hours light.
3 + 5 + 5 + 6 + 4 + 6 + 3 + 4 + 6 + 4 = \(\frac{46}{10}\) = 4.6 inches.
The mean growth for plants that were given light for 10 hours was,
set of data: 9, 10, 12, 8, 10, 11, 9, 8, 8, 9
Mean: average of a set of 10 plants given 10 hours light.
9 + 10 + 12 + 8 + 10 + 11 + 9 + 8 + 8 + 9 = \(\frac{94}{10}\) = 9.4 inches.
Therefore, the plants that are given for 10 hours light grow more successfully.

Question 2.
Cheri wants to find out how different activities affect tablet battery life. She tested 10 of the same tablet with full batteries. She had one group watch videos until the battery ran out. She had the other group play a game until the battery ran out. She measured how long it took each tablet battery to run out.
Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data 3
Answer:
The mean battery life for tablets playing videos was 5.7 hours.
The mean battery life for tablets playing games was 7.54 hours.
Overall, tablets playing games lasted almost two hours longer than tablets playing videos.

Explanation:
Given that,
Cheri tested 10 of the same tablet with full batteries.
She had one group watch videos until the battery ran out are: 5.4, 5.6, 6.0, 5.9, 5.6
Mean: average of a set of battery life with videos.
5.4 + 5.6 + 6.0 + 5.9 + 5.6 = \(\frac{28.5}{5}\) = 5.7 hours.
She had the other group play a game until the battery ran out are: 7.6, 7.7, 7.7, 7.3, 7.4
Mean: average of a set of battery life with games.
7.6 + 7.7 + 7.7 + 7.3 + 7.4 = \(\frac{37.7}{5}\) = 7.54 hours.
Therefore, tablets playing games lasted almost two hours longer than tablets playing videos.

Analyze the data sets below to make an inference about the situation.

Question 1.
Samantha is on the track team and wonders if height plays a role in long-jump ability. She talked to 20 people at her last track meet to check their heights and see how far they jumped during the meet. Here is the data she collected:
Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data 4
Inference:
Answer:
Inference: It appears the students of 70 inches or taller travel on average 18 inches farther in the long jump than the students who are less than 70 inches tall.

Explanation:
Given that,
Samantha talked to 20 people at her last track meet to check heights and see how far they jumped during meet.
Students who are 70 inches tall are: 180, 161, 129, 115, 193, 154, 130, 109, 152, 160
Average height of the students = \(\frac{180+161+129+115+193+154+130+109+152+160}{10}\)
A = \(\frac{1483}{10}\) = 148.3 inches
Students who are less than 70 inches tall are: 165, 109, 129, 115, 150, 142, 136, 113, 121, 120
Average height of the students = \(\frac{165+109+129+115+150+142+136+113+121+120}{10}\)
A = \(\frac{1300}{10}\) = 130 inches.
Difference between the two set of students = 148.3 – 130 = 18 inches.
Therefore, inference of the students of 70 inches or taller travel on average of 18 inches farther in the long jump than the students who are less than 70 inches tall.

Question 2.
Ms. Daniel’s is a math teacher and wonders if the amount of study time each night is related to how well students perform on final tests. She talked to 30 students in her math class to check their study times and compared that to their grades on the final math test. Here is the data she collected:
Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data 5
Inference:
Answer:
Inference: Students who study between 1 and 3 hours per night scored on average about 10 points higher than students who study less than an hour each night.

Explanation:
Given that,
Ms. Daniel’s talked to 30 students in her math class to check their study times.
Students who study less than an hour each night = 65, 75, 69, 81, 95, 62, 78, 84, 83, 55, 68, 75, 90, 68, 95
Average study time = \(\frac{65+75+69+81+95+62+78+84+83+55+68+75+90+68+95}{15}\)
A = \(\frac{1143}{15}\) = 76.2
Students who studied 1 to 3 hours each night = 85, 95, 94, 89, 91, 75, 65, 93, 92, 90, 84, 89, 78, 90, 92
Average study time = \(\frac{85+95+94+89+91+75+65+93+92+90+84+89+78+90+92}{15}\)
A = \(\frac{1302}{15}\) = 86.8
The average difference of the scores between the two study times = 86.8 – 76.2 = 10.6 points.
So, the inference is that the students who study between 1 and 3 hours per night scored on average about 10 points higher than students who study less than an hour each night.

Question 3.
Ross is a fisherman and wonders if how many pounds of bait you bring on a fishing trip is related to how many fish you catch. He talked to 20 fishermen at his marina to record the amount of bait brought and the amount of fish caught. Here is the data he collected:
Spectrum Math Grade 7 Chapter 6 Lesson 5 Answer Key Problem Solving with Data 6
Inference:
Answer:
Inference: There is a correlation between the amount of bait brought and the amount of fish caught.
The fishermen who brought less than 50 pounds of bait caught on average of 0.6 more fish than those who brought 50 pounds or more.

Explanation:
Given that,
Ross talked to 20 fishermen at his marina to record the amount of bait brought and the amount of fish caught.
The following is the data set:
50 pounds are less bait: 18, 20, 15, 15, 14, 20, 25, 17, 19, 10
Average fish caught = \(\frac{18+20+15+15+14+20+25+17+19+10}{10}\) = 173/10 = 17.3
51 pounds or more bait: 17, 18, 22, 22, 14, 13, 16, 19, 15, 11
Average fish caught = \(\frac{17+18+22+22+14+13+16+19+15+11}{10}\) = 167/10 = 16.7
Difference of fish caught = 17.3 – 16.7 = 0.6
The fishermen who brought less than 50 pounds of bait caught on average of 0.6 more fish than those who brought 50 pounds or more.
Therefore, there is a correlation between the amount of bait brought and the amount of fish caught.

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