LESSON 1: WHAT IS BIVARIATE DATA? EXERCISESrusdmath.weebly.com/uploads/1/1/1/5/11156667/g8_u8... · Grade 8 Unit 8: Bivariate Data LESSON 3: COLLECTING DATA EXERCISES 2. Jacob collected

Copyright © 2015 Pearson Education, Inc. 4

Grade 8 Unit 8: Bivariate Data

EXERCISESLESSON 1: WHAT IS BIVARIATE DATA?

• Review your Unit Assessment from the previous unit.

• Write your wonderings about bivariate data.

• Write a goal stating what you plan to accomplish in this unit.

• Based on your previous work, write three things you will do differently during this unit to increase your success.



EXERCISESLESSON 2: ARM SPAN AND HEIGHT

EXERCISES

Erin measured the height and arm span of 10 of her friends. She recorded these data in a chart.

Name Height (in.) Arm Span (in.)

Abby 50 51

Blake 54 53

Carlos 60 59

Donna 52 52

Emma 72 75

Franz 70 70

Gabby 65 66

Heimlich 56 54

Inez 48 49

Josh 61 60

1. Which of these scatter plots best represents the data that Erin found?

A

30

40

50

60

10

20

70

80

90

604020 x80

y

Arm

Spa

n (in

.)

Height (in.)

B

30

40

50

60

10

20

70

80

90

604020 x80

yA

rm S

pan

(in.)

Height (in.)

C

30

40

50

60

10

20

70

80

90

604020 x80

y

Arm

Spa

n (in

.)

Height (in.)

D

30

40

50

60

10

20

70

80

90

604020 x80

y

Arm

Spa

n (in

.)

Height (in.)



EXERCISESLESSON 2: ARM SPAN AND HEIGHT

2. On a graph like the previous ones (with height on the x-axis and arm span on the y-axis), what would a point that is close to the x-axis but far away from the origin represent?

A A tall person with very short arms

B A short person with very long arms

C A person with equal arm span and height

D A tall person with very long arms

3. How could Erin get a more diverse sample of data on height versus arm span?

A Measure the same 10 people again

B Measure every eighth grade student in the school

C Measure a random sample from students in all grades K–12 in the whole city

D Measure her three family members at home

4. Which of these scatter plots could be modeled by a linear function?

A y

x

B

x

y

C y

x

D y

x

5. A new scatter plot shows a positive association for hand length (y-axis) versus hand span (x-axis). What would an outlier close to the y-axis, but with a high y-value, indicate?

Challenge Problem

6. Collect data on the arm span and height of a few of your family members or friends. Organize the data on a graph. Do you notice any correlation? Explain your results.



EXERCISESLESSON 3: COLLECTING DATA

EXERCISES

1. Marshall thinks that the data on hours spent watching TV and hours spent playing video games will be related. He thinks that people who play a lot of video games probably don’t watch much TV. If Marshall is right, these data would show a negative association (a person who plays a lot video games will spend less time watching TV).

Which graph best represents Marshall’s theory?

A

x

y

TV

Tim

e (h

r)

Video Game Time (hr)

B

x

y

TV

Tim

e (h

r)


C

x

y

TV

Tim

e (h

r)


D T

V T

ime

(hr)

Video Game Time (hr) x

y




2. Jacob collected data on hours playing video games and hours watching television. He figured people who watch a lot of TV will also play a lot of video games. He recorded his data as a scatter plot.

Do the data show a negative or positive association?

2

4

6

8

10

12

14

105 15 20Video Game Time (hr)

TV

Tim

e (h

r)

x

y

3. What does the point way off to the right represent?

A Someone who doesn’t watch TV or play any video games

B Someone who plays lots of video games but doesn’t watch any TV

C Someone who watches lots of TV but doesn’t play any video games

D Someone who watches and plays an equal amount of TV and video games




4. Pedra collected data on students’ age and forearm length, thinking that the older students would have longer forearms. She organized her data as a scatter plot.

4

6

12

10

8

14

2

16

18

20

10050 150 200Age (mo)

Fore

arm

Len

gth

(in.)

x

y

What type of association is shown in this scatter plot?

A Positive association

B Negative association

C No clear association

D Clear linear association

5. The average 2-year-old boy is 34 in. tall. If the average 3-year-old is 37 in. tall, and the average 4-year-old is 40 in. tall, how tall would the average 20-year-old be? Does your answer make sense? Why or why not?

Challenge Problem

6. Determine another set of traits about people that you think would have a strong positive association. Collect data on your family or friends to see if your idea is supported by your findings.



EXERCISESLESSON 4: GRAPHING DATA

EXERCISES

1. Which scatter plots would show a strong positive association? There may be more than one correct answer.

A Height vs. head circumference

B Hand width vs. hand span

C Cost vs. the quantity of an item purchased

D Foot length vs. neck circumference

2. How would you describe the association shown in this scatter plot?

2

4

6

8

10

12

10 15 205 x

y

3. In the graph above, if there were a point with an x-value of 20 what do you think its y-value would most likely be?

A 4

B 6

C 10

D Cannot be determined

4. Which points are likely to be from a scatter plot with a strong positive association?

A (2, 2), (2, 5), (2, 9), (2, 14)

B (4, 7), (5, 6), (8, 5), (10, 4)

C (5, 7), (8, 7), (13, 7), (15, 7)

D (1, 1), (3, 2), (6, 6), (10, 12)



EXERCISESLESSON 4: GRAPHING DATA

5. Marshall collected data on hours spent playing video games and the results from a ruler drop test. In a ruler drop test, a person attempts to catch a falling ruler as quickly as possible. Lower values for the ruler drop indicate faster reaction times, since they mean that the ruler fell less distance before being caught.

His thoughts were that people who play lots of video games would have faster reaction times. Here are the data he collected.

2

4

6

8

10

12

10 15 205Video Game Time (hr)

Inch

Ma

rk o

n R

uler

Dro

p

x

y

Was Marshall’s idea right? Explain why the data support or do not support his claim.

Challenge Problem

6. Graph the following points and explain any correlation you see from the graph.

x 3 5 7 8 9 10 3 5 6 7 2 9 0 10 11 16 17 12 6

y 6 7 9 8 2 3 15 16 12 2 3 10 8 9 6 4 17 18 10



EXERCISESLESSON 5: ARM SPAN VS� HEIGHT

EXERCISES

1. Which line indicates that any change in x will result in the same change in y?

A

2

4

6

8

10

12

10 155

y

x

B

12

2

4

6

8

10

10 155

y

x

C

12

2

4

6

8

10

10 155

y

x

D

12

2

4

6

8

10

10 155

y

x

2. How would an outlier affect the placement of the line that best describes the data in a scatter plot?

3. The equation for the line on a scatter plot is y = 0.75x + 4. If the value of the independent variable is 12, what is the value of the other variable?

A 12

B 13

C 14

D 15



EXERCISESLESSON 5: ARM SPAN VS� HEIGHT

4. What does a slope of 0 for the line of a scatter plot indicate? Can you think of a situation where this slope could occur?

5. Draw a line of best fit for this scatter plot. What is the equation of the line?

2

4

6

8

10

105

y

x

Challenge Problem

6. A scatter plot has a strong nonlinear association. Would a line be the best representation of the data? Why or why not?



EXERCISESLESSON 6: WHAT’S MY LINE?

EXERCISES

1. Where do you think a line should be placed to best describe the data, knowing that the line will pass through the origin?

8

2

4

6

10 155 x

y

2. Why should the line be placed there?

Pedra drew this line to describe the data:

2

4

6

8

10 155 x

y

3. What is the slope of the line?

A

x y x y

y y x x

my yx x

m

m

y x

y x

y x

y mx b

y x

y x

y x

y x

, ,

4 810 0

410

0.4

0.4 8

12

14

14

14

0.25

14

5

5

15

5

5

2028

71%

3in.yr

1 1 2 2

2 1 2 1

2 1

2 1

( )( )

( )( )( )( )

− = −

=−−

= −−

= − = −

= − +

= ⎛⎝⎜

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=

= +

== +

= ⎛⎝⎜

⎞⎠⎟ +

= −

≈

⎛⎝⎜

⎞⎠⎟

B

x y x y

y y x x

my yx x

m

m

y x

y x

y x

y mx b

y x

y x

y x

y x

, ,

4 810 0

410

0.4

0.4 8

12

14

14

14

0.25

14

5

5

15

5

5

2028

71%

3in.yr

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2 1 2 1

2 1

2 1

( )( )

( )( )( )( )

− = −

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C 1 D 4

4. What is the location of the y-intercept?

A (2, 0) B (1, 1) C (0, 0) D (0, 2)

5. What is the equation of the line?



EXERCISESLESSON 6: WHAT’S MY LINE?

Challenge Problem

6. Draw a scatter plot where the line that best represents the data does not pass through any points.



EXERCISESLESSON 7: CHOOSING AN INVESTIGATION

EXERCISES

The owner of an ice cream truck records the amount of sales each day during the summer, and also keeps track of how hot it was outside each day. This table shows the data he collected.

Temperature (°C) 14 16 12 15 18 22 19 25 23 18 23 17

Sales ($) 215 325 186 334 407 520 413 619 545 422 446 409

1. Without creating a scatter plot, how do you think these data will be associated?

A Hotter days will have clearly lower sales.

B Hotter days will have clearly higher sales.

C There is no correlation between temperature and sales.

D There will be a weak correlation, with many outliers.

2. The owner thinks that hotter days will be associated with more sales. Which scatter plot best shows this hypothesis?

A

Sale

s

Temperature

y

x

B Sa

les

Temperature

y

x

C

Sale

s

Temperature

y

x

D

Sale

s

Temperature

y

x



EXERCISESLESSON 7: CHOOSING AN INVESTIGATION

3. Using the data table from problem 1, create the scatter plot of the data the ice cream truck owner collected.

200

400

600

800

1,000

1,200

20 3010 x

y

Sale

s ($

)

Temperature (°C)

4. What type of association is shown from your scatter plot?

5. Was the owner right? Explain how the real data justify or do not justify his hypothesis.

Challenge Problem

6. Describe another scenario where an external force would dramatically change the sales of a product. Describe the correlation that you think would exist, and explain how you would collect data to support your claim.



EXERCISESLESSON 8: BIVARIATE INVESTIGATION

EXERCISES

1. Scientists recently discovered a new species of bird that lives by swamps and wades in the water, eating small things at the bottom of the swamp. They recorded the following statistics.

Bird Sample Leg Length (in.) Beak Length (in.)

A 12 17B 10 15C 14 19D 13 17E 10 16F 15 20G 11 17H 12 18I 11 15J 13 18K 11 16L 14 18

Do you think there is a relationship between leg length and beak length? Why or why not?

2. Graph the data from the table and place a line in the location that you think best represents the data. Explain why you placed the line where you did.

2

4

6

8

10

12

14

16

18

20

10 155 20 x

y

Leg Length (in.)

Bea

k Le

ngth

(in.

)



EXERCISESLESSON 8: BIVARIATE INVESTIGATION

Marshall graphed the data and drew a line to represent the data.

2

4

6

8

10

12

14

16

18

20

10 155 20 x

y

Leg Length (in.)

Bea

k L

engt

h (in

.)

3. What is the slope and y-intercept for the line?

A Slope 1; y-intercept 0

B Slope 5; y-intercept 0

C Slope 1; y-intercept 5

D Slope 5; y-intercept 5

4. What is the equation of the line?

A

B

x y x y

y y x x

my yx x

m

m

y x

y x

y x

y mx b

y x

y x

y x

y x

, ,

4 810 0

410

0.4

0.4 8

12

14

14

14

0.25

14

5

5

15

5

5

2028

71%

3in.yr

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2 1 2 1

2 1

2 1

( )( )

( )( )( )( )

− = −

=−−

= −−

= − = −

= − +

= ⎛⎝⎜

⎞⎠⎟

=

= +

== +

= ⎛⎝⎜

⎞⎠⎟ +

= −

≈

⎛⎝⎜

⎞⎠⎟

C

D

x y x y

y y x x

my yx x

m

m

y x

y x

y x

y mx b

y x

y x

y x

y x

, ,

4 810 0

410

0.4

0.4 8

12

14

14

14

0.25

14

5

5

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5

5

2028

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3in.yr

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2 1 2 1

2 1

2 1

( )( )

( )( )( )( )

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= ⎛⎝⎜

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= ⎛⎝⎜

⎞⎠⎟ +

= −

≈

⎛⎝⎜

⎞⎠⎟

5. Describe the relationship between leg length and beak length.

Challenge Problem

6. If a bird of the same species were measured and found to have a beak 22 in. long, what would be a good estimate of the leg length? Why?

x y x y

y y x x

my yx x

m

m

y x

y x

y x

y mx b

y x

y x

y x

y x

, ,

4 810 0

410

0.4

0.4 8

12

14

14

14

0.25

14

5

5

15

5

5

2028

71%

3in.yr

1 1 2 2

2 1 2 1

2 1

2 1

( )( )

( )( )( )( )

− = −

=−−

= −−

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= − +

= ⎛⎝⎜

⎞⎠⎟

=

= +

== +

= ⎛⎝⎜

⎞⎠⎟ +

= −

≈

⎛⎝⎜

⎞⎠⎟

x y x y

y y x x

my yx x

m

m

y x

y x

y x

y mx b

y x

y x

y x

y x

, ,

4 810 0

410

0.4

0.4 8

12

14

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5

5

2028

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3in.yr

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2 1

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= ⎛⎝⎜

⎞⎠⎟

=

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== +

= ⎛⎝⎜

⎞⎠⎟ +

= −

≈

⎛⎝⎜

⎞⎠⎟



EXERCISESLESSON 9: TWO-WAY TABLES

EXERCISES

1. How many people participated in the survey shown?

Do you get good grades?

Yes No

Do you play sports?Yes 20 8

No 6 6

A 20 people B 28 people

C 30 people D 40 people

2. What percent of students who play sports also get good grades, according to the table in problem 1?

A 50% B 71%

C 77% D 85%

3. Which of these statements are supported by the table? There may be more than one correct statement.

Height

≤ 65 in. > 65 in.

Boys 3 11

Girls 12 4

A Most boys are taller than 65 in.

B Most of the students that are 65 in. tall or less are girls.

C Most girls are 65 in. tall or less.

D Most of the students that are taller than 65 in. are boys.



EXERCISESLESSON 9: TWO-WAY TABLES

4. What does the table show?

How do you get to school?

Bike Car Bus Walk

Do you eat breakfast regularly?

Yes 2 4 10 1

No 1 3 6 9

5. How is the Venn diagram like a two-way table?

Do you do chores?

6 8

3

17

Do you get an allowance?

Challenge Problem

6. Talisha asked 100 classmates if they wear shoes or sandals, and if they like the beach or not. Create a two-way table based on the following survey results:

80 of the 100 students said they liked the beach. Of those 80, 30 students wear shoes regularly as well.

55 of the 100 students said they wore sandals. Of those 55 only 5 said they don’t like the beach.

Use this blank table as a guide.

Likes Beach Doesn’t Like Beach

Shoes

Sandals



EXERCISESLESSON 10: CREATING TWO-WAY TABLES

EXERCISES

1. Fill in the missing values of this two-way table. This table represents data for 50 students in total.

Plays a Sport Doesn’t Play Sports Total

Takes a Language Class 14 37

Doesn’t Take a Language Class 3

Total 26 50

2. A two-way table shows that 75% of students who are in the band also are on the track team. However, only 10% of the students surveyed were both in the band and on the track team. What might the table look like?

3. Talisha surveyed 100 students at her school. She found that of the 100 students 86 of them own a smart phone; 45 of those students also own an MP3 player. There are 10 students who don’t have a phone but do have an MP3 player. There are 4 students who don’t have either device.

Create a two-way table to show this information, using the blank table as a guide.

MP3 Player No MP3 player Total

Smart Phone 86

No Smart Phone

Total 100

4. There were 100 customers in a restaurant who were asked whether they liked chicken or beef and whether they liked rice or pasta. Out of 30 customers that liked rice 20 liked chicken. There were 60 customers that liked chicken. Use this information to construct a two-way table.

5. As a group of 105 people entered a movie theater, Erin counted how many of the people had popcorn and how many had a drink. She found that out of 84 people who had popcorn only 10 people did not have a drink. Six people walked in without popcorn or a drink. Use this information to construct a two-way table.



EXERCISESLESSON 10: CREATING TWO-WAY TABLES

Challenge Problem

6. Take a survey (of your friends and/or family) of two characteristics that you believe will show a strong association. Put your data into a two-way table and explain whether or not your data supported your idea.



EXERCISESLESSON 11: PUTTING IT TOGETHER

• Read through your Self Check and think about your work in this lesson.

• Write down what you have learned during the lesson.

• What would you do differently if you were starting the Self Check task now?

• Which method would you prefer to use if you were doing the task again? Why?

• Compare the new approaches you learned about with your original method.

• Record your ideas—keep track of problem-solving strategies.

• Complete any exercises from this unit you have not finished.

Documents

LESSON 1: WHAT IS BIVARIATE DATA? EXERCISESrusdmath.weebly.com/uploads/1/1/1/5/11156667/g8_u8... · Grade 8 Unit 8: Bivariate Data LESSON 3: COLLECTING DATA EXERCISES 2. Jacob collected