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Data Chapter Questions

1. How do scatter plots help us analyze data from bivariate data?

2. What is the prediction equation and what information can it tell us?

3. What is a two-way table? What is relative frequency?

4. How does a two-way table and relative frequencies help determine if there is an association

between two variables?

NJ Center for Teaching and Learning ~ 1 ~ ww.njctl.org

Bivariate DataClassworkIdentity the scatter plots as linear or non-linear with a positive or negative association.

1. _______________________ 2. _______________________

3. _______________________ 4. _______________________

5. _______________________ 6. _______________________


Plot the following data from the table onto a scatter plot. Identity the scatter plot as linear or non-linear with a positive or negative association.

7.

8.

9.

10.


HomeworkIdentity the scatter plots as linear or non-linear with a positive or negative association.

11. _______________________ 12. _______________________

13. _______________________ 14. _______________________

15. _______________________ 16. _______________________


Plot the following data from the table onto a scatter plot. Identity the scatter plot as linear or non-linear with a positive or negative association.

17.

18.

19.


20.

Line of Best FitClassworkIdentify which line is the line of best fit for each scatter plot.

21.

22.


23. For the graph at the right, which two points would you use to draw the line of best fit?

a. A and C

b. A and B

c. A and D

d. C and B

24. Which two points would you use to draw the line of best fit for the scatter plot at the right?

a. A and B

b. A and D

c. C and B

d. C and D

25. The following table shows the number of hours 10 students studied and their resulting test scores where x = the number of hours studied and y = test score. Graph the data onto a scatter plot and draw the line of best fit for the graph.


26. The following table shows the shoe sizes of ten different men and their heights where x = height and y = shoe size. Graph the data onto a scatter plot and draw the line of best fit for the graph.

HomeworkIdentify which line is the line of best fit for each scatter plot.

27.


28.

29. For the graph at the right, which two points would you use to draw the line of best fit?

a. A and B

b. A and C

c. A and D

d. C and D

30. For the graph at the right, which two pointswould you use to draw the line of best fit?

a. A and B

b. A and C

c. A and D

d. D and B


31. The table below shows the average movie ticket prices every five years since 1970. Plot the data on a scatter plot. Draw the line of best fit through the points.

32. The table below shows the number of music CD’s sold from the year 2000 through 2008. Plot the data on a scatter plot. Draw the line of best fit.

Determining the Prediction EquationClasswork

33. Determine the prediction equation using the two labeled points in the graph.a. Prediction equation: ____________________b. What would be the predicted value for x = 7?

_________________


c. Will the result for y when x = 7 be an interpolation or extrapolation? ___________________

34. Determine the prediction equation using the two labeled points in the graph.a. Prediction equation: __________________b. What would be the predicted value for x =

40? _______________c. Will the result for y when x = 40 be an

interpolation or extrapolation? ______________________

35. Determine the prediction equation using the two labeled points in the graph.a. Draw the line of best fit.b. Prediction equation: __________________c. What would be the predicted value for x = -2?

______________________d. Will the result for y when x = -2 be an

interpolation or extrapolation? _______________________

36. Determine the prediction equation.a. Draw the line of best fit using the two

labeled points.b. Prediction equation: _____________


1

c. What would be the predicted shoe size for a girl that has a height of 62 inches? ____________

d. Will the result from part c. be an extrapolation or interpolation? _____________________

37. Use the data from the table below to make a scatter plot. Draw the line of best fit and determine the prediction equation.

38. Use the data to make a scatter plot. Determine the prediction equation.

Homework39. Determine the prediction equation using the

two labeled points in the graph.


a. Draw the line of best fit.b. Prediction equation: __________________c. What would be the predicted value for x = 3? _________________d. Will the result for y when x = 3 be an interpolation or extrapolation?

40. Determine the prediction equation using the two labeled points in the graph.a. Draw the line of best fit.b. Prediction equation: _________________c. What would be the predicted value for x =

110? ___________________d. Will the result for y when x = 110 be an

interpolation or extrapolation?

41. Determine the prediction equation using the two labeled points in the graph.a. Draw the line of best fit.b. Prediction equation: _________________c. What would be the predicted value for x

= -3? ________________d. Will the result for y when x = -3 be an

interpolation or extrapolation? __________________

42. a. Draw the line of best fit.


b. Prediction equation: ___________________c. What would be the predicted shoe size for a man whose height is 72 in.? __________d. Will the result from part c. be an extrapolation or interpolation? _____________________

43. Use the data from the table below to make a scatter plot. Draw the line of best fit and determine the prediction equation.

44. Use the data to make a scatter plot. Draw the line of best fit and determine the prediction equation.


Two-Way TableClasswork

45.

a. Fill in the totals.

b. How many people have a cell phone but don’t have a landline phone? _____________________

c. How many people don’t have a cell phone but have a landline phone? _____________________

d. How many people don’t have a cell phone nor a landline phone? _____________________

e. How many people have a landline phone? _____________________

f. How many people don’t have a landline phone? _____________________

46. Using the table above, find the relative frequencies by row and by column.


a. What is the relative frequency of people who have a cell phone but do not have a

landline phone to all people that have a cell phone? _____________________

b. What is the relative frequency of people that have a have a cell phone and have a

landline phone to all people who have a landline phone? _____________________

47. Sam surveyed his classmates to find out if they played a sport after school or practiced in

the school band. Fourteen of his classmates played a sport. Of those 14, only 5 participated

in the school band. Eight students played in the school band, out of those 8, 3 did not play

sports. There were ten students who did not play a sport nor participate in the school band.

a. Fill out a two-way table using the data.

b. Find the relative frequencies by row.

c. Find the relative frequencies by column.


d. How many people are in a band and play sports after school? _____________________

e. How many people play sports but do not participate in band? _____________________

f. How many people do not play sports but are in band? _____________________

g. What is the relative frequency of students who do not play sports and are in the band to

all students who play sports? _____________________

h. What is the relative frequency of students who are in band and play sports to all

students who practice in band? _____________________

Homework

48.

a. Fill in the totals.

b. How many elementary students play computer games? _____________________

c. How many high school students play video games? _____________________

d. How many elementary school students participated in this survey? _____________________

e. How many high school students participated in this survey? _____________________


49. Using data from the previous table, calculate the relative frequencies by row and by column.

a. What is the relative frequency of elementary students that play computer games to all

students that play computer games? _____________________

b. What is the relative frequency of high school students that play computer games to the

total number of high school students? _____________________

c. What is the relative frequency of high school students that play video games to the total

number of students that play video games? _____________________

50. The school district’s records show that there are 90 elementary students. A total of 175

students attend the middle school and elementary school. The students either walk or ride

the bus to school. There are 30 elementary students that walk to school, and there are 10

middle school students that take the bus to school. There are a total of 70 students that take

the bus to school. There are 75 middle school students that walk to school.

a. Fill out the two-way table with the information given.


b. Find the relative frequencies by row.

c. Find the relative frequencies by column.

d. How many students walk to school? e. How many elementary students ride the bus to school? _____________________

f. How many middle school students are in the school district? _____________________

g. What is the relative frequency of elementary students that walk to school to the total

number of students that walk to school? _____________________

h. What is the relative frequency of elementary students that walk to school to the total

number of elementary students? _____________________

i. What is the relative frequency of middle school students that walk to school to the total

number of middle school students? _____________________


j. Is there an association between grade level and how students get to school?

_____________________


Data Unit Review

Multiple Choice

1. What kind of scatter plot is shown to the right?

a. linear, positive correlationb. linear, negative correlationc. non-lineard. linear, no correlation

2. What kind of scatter plot is shown at the right? a. linear, positive correlationb. linear, negative correlationc. non-lineard. linear, no correlation

3. What conclusion can be drawn from this graph?

a. The number of meals eaten in a day increases as the number of miles driven in a car increases.

b. The number of meals eaten in a day decreases as the number of miles driven in a car increases.

c. The amont of meals eaten in a day is equal to the number of miles driven in a car.

d. There is no relationship between the number of meals eaten in a day and the number of miles driven in a car.


4. Which of the following graphs show a linear scatter plot with negative correlation?

a. b.

c d.

5. A study showed that the more hours a child spends playing video games, their math test scores decrease. Which of the following graphs shows this relationship?

a. b.


c. d.


6. Which of the following is the line of best fit for this graph?

a. A

b. B

c. C

d. None of these

7. Which of the following is the line of best fit for this graph?

a. A

b. B

c. C

d. None of these

8. Which points would you use to draw the line of best fit for the graph below?

a. A and B

b. A and C

c. A and D

d. C and B


9. Which points would you use to draw the line of best fit for the graph below?

a. A and B

b. A and C

c. A and D

d. B and D

10. What is the slope of the trend line for this graph?

a.−23

b.23

c.32

d.−32

11. What is the prediction equation for the previous graph?

a. y=23x+ 14

3

b. y=−23x+ 22

3

c. y=32x+3

d. y=−32x−3

12. The table shows the data that was used to make the scatter plot from question 9. What would be the predicted value for x = 9? Will it be an extrapolation or interpolation?

a.34 , interpolation


b.−34 , extrapolation

c.43 , extrapolation

d.43 , interpolation

13. Using the same prediction equation from question 10, what is the expected value of 5.5? Is the value an extrapolation or interpolation?

a.113 , interpolation

b.113 , extrapolation

c.73 , interpolation

d.73 , extrapolation

14. What is the prediction equation for this scatter graph?

a. y=34x+ 34

b. y=12x+ 34

c. y=13x+ 34

d. y=23x+ 34


15. This is the table used to create the scatter plot from question 14. What is the predicted value for x = 2? Is the result an extrapolation, or interpolation?

a.74 , extrapolation

b. 2, interpolation

c.54 , interpolation

d.74 , interpolation

June surveyed the 7th and 8th grades to see which class they liked better, math or English. The results are shown in the two-way table below. Answer the questions that follow.

16. How many 7th grade students did June survey?

a. 112 students

b. 131 students

c. 145 students

d. 164 student

17. How many 8th grade students did June survey?

a. 112 students

b. 131 students

c. 145 students

d. 164 students

18. What is the relative frequency of 7th grade students that chose math to all 7th grade students?

a. 0.54

b. 0.48

c. 0.47

d. 0.40

19. What is the relative frequency of 8th grade students that chose English to all students that chose English?

a. 0.54 b. 0.40


c. 0.47 d. 0.48

20. What is the relative frequency of 7th grade students that chose English to all students that chose English?

a. 0.59

b. 0.58

c. 0.48

d. 0.60

Short Constructed Response

Identify the scatter graphs as linear or non-linear.

21. ________________________ 22. ________________________


23. ________________________ 24. ________________________

True or False25. The graph at the right shows a positive association between the number of hours studied and a student’s test score. ________________________

26. The graph at the right shows a positive association between men’s heights and their shoe sizes.________________________

27. Use the following table to make a scatter plot. Determine if the graph is linear or non-linear and if it has a positive or negative association.


28. Calculate the prediction equation for this graph using the two labeled points.

The following table shows the data used to create the scatter plot from question 28

29. What is the predicted value for x = 4? Is this an interpolation or extrapolation? What is the predicted value for 10? Is this an interpolation or extrapolation?

Extended Constructed Reponse


30. The following survey shows the data of 8 different employees that work for the same company. Their hourly pay rate is dependent upon their years of experience. Graph the information onto a scatter plot. Then answer the questions. Make sure to label your axes and title the graph.

a. What kind of relationship is shown from the scatter plot? ________________________b. Draw the line of best fit and calculate the prediction equation.

________________________c. What does the slope of the prediction equation tell us? ________________________d. What would be the predicted wage for a person that has 10 years of experience?

________________________e. What would be the predicted wage for a person that has 5 years of experience?

________________________

31. Cathy wanted to know what kind of shows the 8th grade class preferred – dramas or comedies. 55 students said they liked comedies and 56 students said they preferred dramas. 25 students liked both dramas and comedies. There were 41 students who did not like dramas nor comedies. Complete a two way table using the information given.


a. How many students were surveyed? ________________________b. How many students enjoy dramas but not comedies? ________________________c. How many students like comedies but not dramas? ________________________d. Calculate the relative frequencies by row:

e. Calculate the relative frequencies by column:

32. Paul surveyed the 7th and 8th grades to find out if they participated in sports, or a non-sport activity after school such as chess club, yearbook, or band. He surveyed 215 7th graders, which 90 participated in sports. He surveyed 231 8th graders, and 146 participated in a non-sport activity. Make a two way table using the information.

a. How many 7th graders play a sport? ________________________b. How many students play a sport? ________________________


c. How many students are involved in a non-sport activity? ________________________d. Find the relative frequencies by row:

e. Find the relative frequencies by column:

f. Does there seem to be an association between the grades and what activities they are involved in?

Answer Key

1. non-linear2. linear: negative association3. linear: positive association4. linear: negative association5. linear: negative association6. linear: no association7. linear: positive association 8. linear: negative association


9. non-linear

10. linear: positive association

11. linear: negative association12. non-linear13. linear: positive association14. linear: positive association15. non-linear16. linear: negative association17. non-linear


60

18. linear: negative association

19. linear: negative association


21. B22. A23. b24. c25.


56

400

26.

27. B28. B29. c30. b31.

32.

33. a. y=75x+ 35

b. 10.4c. extrapolation

34. a. y=1315x+ 113

b. 3813

c. interpolation 35. a.


b. y=1316x+ 3316

c. 716

d. interpolation 36. a.

b. y=16x−52

c. 7 56

d. interpolation

37. y=710x+ 1110

38. y=−354x+17,828 3

4

39. a.


b. y=23x+2

c. 4d. interpolation

40. a.

b. y=−1125

x+104

c. 55.6d. extrapolation

41. a.

b. y=−45x+ 24

5c. 7.2d. interpolation

42. a.

b. y=12x−25.5

c. 10.5d. interpolation

43. y=−34

+1

44. y=−2256

+75,525


31

38

69861

1

1

2

45. a.

b. 35c. 5d. 3e. 31f. 38

46.

a. 0.57b. 0.84

47. a.


Plays a sport Doesn’t Play a Sport

Plays in Band

Not in Band

Total

Total

10

5

9

3 8

14 13 27


Plays in Band

Not in Band

Total

Total

1

2


Plays in Band

Not in Band

Total

Total 1 1 2

79 73

69

83

152

b.

c.

d. 5e. 9f. 3g. 0.21h. 0.625

48. a.


1

1

2

1 1 2

Walk to School Ride the Bus Total

Total

Elementary School Students

Middle School Students

30

10

70

75

60

105

90

85

175


Total



1

1

2

b. 23c. 27d. 69e. 83

49.

a. 0.29b. 0.67c. 0.37

50. a.

b.



Total



11 2

c.

d. 105e. 60f. 85g. 0.29h. 0.33i. 0.88j. yes

Unit Review Answer Key1. a2. d3. d4. a5. a6. b7. a8. a9. c10. a11. b12. c13. a

14. b15. d16. c17. b18. a19. b20. d21. linear22. non-linear23. linear24. non-linear25. true26. false



years

Pay

Rat

e

Likes Comedies

Likes Dramas Total

Doesn’t Like Comedies

Doesn’t Like Dramas

Total

25

41

55

56

8196

97

80

177

28. y=−37

+ 457

29. when x=4: 337 , an interpolation

when x=10, 157 , an extrapolation

30.

a. linear

b. y=67x+ 587

c. The slope tells us that every 7 years, the pay rate increases by 6

d. 1187

e. 887

31.


Doesn’t Like Dramas Likes Dramas

Likes Comedies


Total

Total

1

1

2

Total

Likes Comedies


Doesn’t Like Dramas Likes Dramas Total

211

Non-Sport Activity Sport Activity

7th Graders

8th Graders

Total

Total

90 215

231146

125

85

175 271 446

Total

8th Graders

7th Graders

Sport Activity Non- Sport Activity

a. 177 studentsb. 56 studentsc. 55 studentsd.

e.

32.

a. 90b. 175c. 271d.


Sport Activity Non- Sport Activity Total

Total

7th Graders

8th Graders

e.

f.

f. no


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