Data Chapter Questions. 1. How do scatter plots help us analyze data from bivariate data?
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1 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
2 Bivariate Data Classwork Identity the scatter plots as linear or non-linear with a positive or negative association NJ Center for Teaching and Learning ~ 2 ~ ww.njctl.org
3 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 NJ Center for Teaching and Learning ~ 3 ~ ww.njctl.org
4 Homework Identity the scatter plots as linear or non-linear with a positive or negative association NJ Center for Teaching and Learning ~ 4 ~ ww.njctl.org
5 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 NJ Center for Teaching and Learning ~ 5 ~ ww.njctl.org
6 Line of Best Fit Classwork Identify which line is the line of best fit for each scatter plot 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 NJ Center for Teaching and Learning ~ 6 ~ ww.njctl.org
7 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. NJ Center for Teaching and Learning ~ 7 ~ ww.njctl.org
8 Homework Identify which line is the line of best fit for each scatter plot 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 NJ Center for Teaching and Learning ~ 8 ~ ww.njctl.org
9 30. 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. D and B 31. The table below shows the average movie ticket prices every five years since 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 Plot the data on a scatter plot. Draw the line of best fit. NJ Center for Teaching and Learning ~ 9 ~ ww.njctl.org
10 Determining the Prediction Equation Classwork 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? NJ Center for Teaching and Learning ~ 10 ~ ww.njctl.org
11 36. Determine the prediction equation. a. Draw the line of best fit using the two labeled points. b. Prediction equation: 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 Use the data to make a scatter plot. Determine the prediction equation. NJ Center for Teaching and Learning ~ 11 ~ ww.njctl.org
12 Homework 39. 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? NJ Center for Teaching and Learning ~ 12 ~ ww.njctl.org
13 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. NJ Center for Teaching and Learning ~ 13 ~ ww.njctl.org
14 Two-Way Table Classwork 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? NJ Center for Teaching and Learning ~ 14 ~ ww.njctl.org
15 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. NJ Center for Teaching and Learning ~ 15 ~ ww.njctl.org
16 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. NJ Center for Teaching and Learning ~ 16 ~ ww.njctl.org
17 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. NJ Center for Teaching and Learning ~ 17 ~ ww.njctl.org
18 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? NJ Center for Teaching and Learning ~ 18 ~ ww.njctl.org
19 Data Unit Review Multiple Choice 1. What kind of scatter plot is shown to the right? a. linear, positive correlation b. linear, negative correlation c. non-linear d. linear, no correlation 2. What kind of scatter plot is shown at the right? a. linear, positive correlation b. linear, negative correlation c. non-linear d. 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. NJ Center for Teaching and Learning ~ 19 ~ ww.njctl.org
20 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. NJ Center for Teaching and Learning ~ 20 ~ ww.njctl.org
21 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 NJ Center for Teaching and Learning ~ 21 ~ ww.njctl.org
22 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. 2 3 b. c d What is the prediction equation for the previous graph? a. y = 2 14 x b. y = 2 22 x c. y = 3 x d. y = 3 2 x 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? 3 a., interpolation 4 b. 3, extrapolation 4 c. d. 4, extrapolation 3 4, interpolation 3 NJ Center for Teaching and Learning ~ 22 ~ ww.njctl.org
23 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. b. c. d. 11 3, interpolation 11 3, extrapolation 7, interpolation 3 7, extrapolation What is the prediction equation for this scatter graph? a. y = 3 x b. y = 1 x c. y = 1 x d. y = 2 x 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? 7 a., extrapolation 4 b. 2, interpolation c. d. 5, interpolation 4 7, interpolation 4 NJ Center for Teaching and Learning ~ 23 ~ ww.njctl.org
24 June surveyed the 7 th and 8 th 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 7 th grade students did June survey? a. 112 students b. 131 students c. 145 students d. 164 student 17. How many 8 th grade students did June survey? a. 112 students b. 131 students c. 145 students d. 164 students 18. What is the relative frequency of 7 th grade students that chose math to all 7 th grade students? a b c d What is the relative frequency of 8 th grade students that chose English to all students that chose English? a b c d What is the relative frequency of 7 th grade students that chose English to all students that chose English? a b c d NJ Center for Teaching and Learning ~ 24 ~ ww.njctl.org
25 Short Constructed Response Identify the scatter graphs as linear or non-linear True or False 25. The graph at the right shows a positive association between the number of hours studied and a student s test score. NJ Center for Teaching and Learning ~ 25 ~ ww.njctl.org
26 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. NJ Center for Teaching and Learning ~ 26 ~ ww.njctl.org
27 The following table shows the data used to create the scatter plot from question 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. NJ Center for Teaching and Learning ~ 27 ~ ww.njctl.org
28 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 8 th 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: NJ Center for Teaching and Learning ~ 28 ~ ww.njctl.org
29 32. Paul surveyed the 7 th and 8 th grades to find out if they participated in sports, or a nonsport activity after school such as chess club, yearbook, or band. He surveyed th graders, which 90 participated in sports. He surveyed th graders, and 146 participated in a non-sport activity. Make a two way table using the information. a. How many 7 th 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? NJ Center for Teaching and Learning ~ 29 ~ ww.njctl.org
30 Answer Key 1. non-linear 2. linear: negative association 3. linear: positive association 4. linear: negative association 5. linear: negative association 6. linear: no association 7. linear: positive association 10. linear: positive association 8. linear: negative association 11. linear: negative association 12. non-linear 13. linear: positive association 14. linear: positive association 15. non-linear 16. linear: negative association 17. non-linear 9. non-linear 18. linear: negative association NJ Center for Teaching and Learning ~ 30 ~ ww.njctl.org
31 19. linear: negative association linear: positive association 27. B 28. B 29. c 30. b B 22. A 23. b 24. c NJ Center for Teaching and Learning ~ 31 ~ ww.njctl.org
32 33. a. y = 7 x b c. extrapolation 34. a. y = x b c. interpolation 35. a. 37. y = 7 11 x y = 35 4 x + 17, b. y = x c d. interpolation 36. a. b. y = 1 6 x 5 2 c d. interpolation NJ Center for Teaching and Learning ~ 32 ~ ww.njctl.org
33 39. a. 42. a. b. y = 2 3 x + 2 c. 4 d. interpolation 40. a. b. y = 1 x c d. interpolation 43. y = b. y = 11 x c d. extrapolation 41. a. b. y = 4 24 x c. 7.2 d. interpolation NJ Center for Teaching and Learning ~ 33 ~ ww.njctl.org
34 44. y = , a b. 35 c. 5 d. 3 e. 31 f a b NJ Center for Teaching and Learning ~ 34 ~ ww.njctl.org
35 47. a. Plays a sport Doesn t Play a Sport Plays in Band Not in Band b. Plays a sport Doesn t Play a Sport Plays in Band Not in Band c. d. 5 e. 9 f. 3 g h a. Plays in Band Not in Band Plays a sport Doesn t Play a Sport b. 23 NJ Center for Teaching and Learning ~ 35 ~ ww.njctl.org
36 c. 27 d. 69 e a b c a. Walk to School Ride the Bus Elementary School Students Middle School Students b. Walk to School Ride the Bus Elementary School Students Middle School Students NJ Center for Teaching and Learning ~ 36 ~ ww.njctl.org
37 c. Walk to School Ride the Bus Elementary School Students Middle School Students d. 105 e. 60 f. 85 g h i j. yes Unit Review Answer Key 1. a 2. d 3. d 4. a 5. a 6. b 7. a 8. a 9. c 10. a 11. b 12. c 13. a 27. linear: positive association 14. b 15. d 16. c 17. b 18. a 19. b 20. d 21. linear 22. non-linear 23. linear 24. non-linear 25. true 26. false NJ Center for Teaching and Learning ~ 37 ~ ww.njctl.org
38 28. y = when x=4: 33 7 when x=10, 15 7, an interpolation, an extrapolation 30. Pay Rate a. linear years b. y = 6 58 x c. The slope tells us that every 7 years, the pay rate increases by 6 d e Doesn t Like Dramas Likes Dramas Doesn t Like Comedies Likes Comedies NJ Center for Teaching and Learning ~ 38 ~ ww.njctl.org
39 a. 177 students b. 56 students c. 55 students d. Doesn t Like Dramas Likes Dramas Doesn t Like Comedies Likes Comedies e. Doesn t Like Dramas Likes Dramas Doesn t Like Comedies Likes Comedies Sport Activity Non-Sport Activity 7 th Graders th Graders a. 90 b. 175 c. 271 d. Sport Activity Non- Sport Activity 7 th Graders th Graders ,265 49,665 2 NJ Center for Teaching and Learning ~ 39 ~ ww.njctl.org
40 e. f. Sport Activity Non- Sport Activity 7 th Graders 8 th Graders f. no NJ Center for Teaching and Learning ~ 40 ~ ww.njctl.org
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