8th Grade. Data.

Transcription

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2 8th Grade Data

3 Table of Contents click on the topic to go to that section Two Variable Data Line of Best Fit Determining the Prediction Equation Two Way Table Glossary Teacher Notes 3

4 Two Variable Data Return to Table of Contents 4

5 Two Variable Data Two Variable Data is also called Bivariate Data With bivariate data there are two sets of related data that you want to compare. 5

6 Temperature degrees F Ice Cream Sales $ Scatter Plot Example 1: An ice cream shop keeps track of how much ice cream they sell versus the temperature on that day. This table shows 10 days of data. The two variables are: Temperature and Ice Cream Sales. We can create a scatter plot by plotting the points. Temperature is the x variable Sales is the y variable

7 Scatter Plot Ten Days of Ice Cream Shop Sales Ice Cream Sales $ Temperature degrees F 7

8 Scatter Plot What did the scatter plot show us? Using the Scatter Plot it is easy to see that: warmer weather leads to more sales. click to reveal 8

9 Scatter Plot Scatter Plots are either: Linear Non linear 9

10 Scatter Plot These scatter plot are also non linear. 10

11 Scatter Plot If a scatter plot is linear it can be described 3 ways: Negative Association Positive Association No Association 11

12 1 What type of scatter plot is shown from the Ice Cream Shop example 1? A B C D non linear linear, positive association linear, negative association linear, no association Ice Cream Sales $ Temperature degrees F Answer 12

13 Example 2: Data for 10 students math and science grades are shown in the table. Plot the points to create the scatter plot. Math Grade Science Grade Scatter Plot Science Grades Math Grades 13

14 2 What type of scatter plot is shown for the math and science grades from example 2? A B C D non linear linear, positive association linear, negative association linear, no association Science Grades Click to reveal solved graph. Math Grades Answer 14

15 3 What kind of association is shown in the graph? A non linear B linear, positive association C linear, negative association D linear, no association Test Score Time spent studying Answer 15

16 4 What kind of association is shown in the graph? A non linear Shoe size & Height B linear, positive association C linear, negative association D linear, no association shoe size Answer height in inches 16

17 5 What association is shown in this graph? A non linear B linear, positive correlation C linear, negative correlation D linear, no correlation Weight in Pounds Boy's Height and Weight Height in inches Answer 17

18 6 Which of the following scenarios would produce a linear scatter plot with a positive correlation? A Miles driven and money spent on gas B Number of pets and how many shoes you own C Work experience and income D Time spent studying and number of bad grades Answer 18

19 7 Which of the following would have no association if plotted on a scatter plot? A Number of toys and calories consumed in a day B Number of books read and reading scores C Length of hair and amount of shampoo used D Person's weight and calories consumed in a day Answer 19

20 Predictions What kind of predictions can you make from looking at the graph? 20

21 Survey Data A student wanted to find out if there was a relationship between the number of hours a person exercised in one week and their resting heart rate. 15 people were surveyed and the table at the right shows the results. Number of Hours Resting Heart Rate

22 Scatter Plot Plot the results of the survey on a scatter plot. Number of Hours Resting Heart Rate

23 Linear Relationship? Association? Is there a linear relationship? Is there a positive or negative association? According to your scatter plot, does a person who exercise generally have a lower resting heart rate than a person that doesn't exercise? 23

24 Survey Data Sandy wanted to find out if there was a relationship between the number of hours a student spent browsing the Internet in each day and their math grades for the marking period. She surveyed several students and the results are shown in the table at the right. Math Hours Grade

25 Linear Relationship? Association? Look at your results. Is the scatter plot linear or non linear? Is there a positive or negative association? What can you say about the math scores as more hours are spent browsing the Internet? 25

26 Linear Relationship? Association? The table shows average temperatures for the month of January in New Jersey from 2000 to Is it linear? Is there a positive association, negative association, or neither? Year Temperatur e in F 2, , , , , , , , , , ,

27 Linear Relationship? Association? The table shows average temperature by month for New Jersey. Month 1 = January, Month 2 = February, etc. Make a scatter plot using the data from the table. Is the graph linear? Is there an association? Month Temperatur e in F Answer 27

28 8 What association is shown in this graph? A non linear B linear, positive association C linear, negative association D linear, no association Shoe Size Girl's Height in Inches Shoe Size v. Girl's Height Height in Inches Shoe Size Answer 28

29 Girls Height (in inches) Shoe Size Boys Height (in inches) Shoe Size Poll Poll 10 girls and 10 boys from your class on their heights and shoe size. Make a scatter plot for your observations. Teacher Notes 29

30 Wake Up Time How Long to Get Ready Survey Survey your classmates and to find out what time they wake up on a school day and how long it takes them to get ready. Make a scatter plot of your results. Is there an association with the time a student wakes up and how long it takes them to get ready? 30

31 Line of Best Fit Return to Table of Contents 31

32 Line of Best Fit Bivariate data plotted on a scatter plot shows us negative or positive association (correlation). A line of best fit, or trend line, can help us predict outcomes using the data that you already have. It is drawn on a scatter plot that best fits the data points. 32

33 Line of Best Fit Notice that the points form a linear like pattern. To draw a line of best fit, use two points so that the line is as close as possible to the data points. Our line is drawn so that it fits as close as possible to the data points. This line was drawn through (35,82) and (50,90). 33

34 Line of Best Fit Test Score Time spent studying Predict the test score of someone who spends 52 minutes studying. Predict the test score of someone who spends 75 minutes studying. 34

35 Line of Best Fit Shoe size & Height height in inches Draw a line of best fit, or trend line, on this graph. shoe size Predict the height of a person who wears a size 8 shoe. Predict the shoe size of a person who is 50 inches tall. 35

36 9 Consider the scatter graph to answer the following: Which 2 points would give the best line of fit? A A and D B B and C C C and D D there is no pattern A B C D X Y Answer 36

37 10 Consider the scatter graph to answer the following: Which 2 points would give the best line of fit? A A and D B B and C C C and D D there is no pattern B C D X Y A Answer 37

38 11 Which two points would you pick to draw the line of best fit? A A and B B B and C C C and D D A and D X Y A B C D Answer

39 12 Which two points would you use to draw the line of best fit? A A and D B C and D C B and D Shoe Size v. Girl's Height Height in Inches D C A B Shoe Size Shoe Size Girl's Height in Inches Answer 39

40 13 A scatter plot is shown on the coordinate plane. Which of these most closely approximates the line of best fit for the data in the scatter plot? A C Answer B D From PARCC EOY sample test non calculator #15 40

41 Line of Best Fit Using the scatter plot you created for shoe size v. girls' heights and shoe size v. boys' heights, determine line of best fit that goes through each of these scatter plots. 41

42 Determining the Prediction Equation Return to Table of Contents 42

43 Line of Best Fit The points form a linear like pattern, so use two of the points to draw a line of best fit. Our line is drawn so that it fits as close as possible to the data points. This line was drawn through (35,82) and (50,90). 43

44 Prediction Equation Use the two points that formed the line to write an equation for the line. Find m Find b Where S is the score for t minutes of studying. This equation is called the Prediction Equation. The slope also shows that a student's score will increase by 8 for every 15 minutes of studying they do. 44

45 Prediction Equation Prediction Equations can be used to predict other related values. If a person studies 15 minutes, what would be the predicted score? This is an extrapolation, because the time was outside the range of the original times. 45

46 Prediction Equation If a person studies 42 minutes, what would be the predicted score? This is an interpolation, because the time was inside the range of the original times. 46

47 Prediction Equation Interpolations are more accurate because they are within the set. The farther points are away from the data set the less reliable the prediction. Using the same prediction equation, consider: If a person studies 120 minutes, what will be their score? What is wrong with this prediction? 47

48 Prediction Equation If a student got an 80 on the test, What would be the predicted length of their study time? The student studied about 31 minutes. 48

49 14 Consider the scatter graph to answer the following: What is the slope of the line of best fit going through A and D? A B C D A (3, 9) (9, 3) D X Y Answer 49

50 15 Consider the scatter graph to answer the following: What is the y intercept of the line of best fit going through A and D? A 9 B 10 C 11 D 12 A (3, 9) D (9, 3) X Y Answer 50

51 16 Consider the scatter graph to answer the following: The equation for our line is y = 1x What would the prediction be if x = 7? Is this an interpolation or extrapolation? A 5, interpolation B 5, extrapolation C 6, interpolation D 6, extrapolation A D X Y Answer 51

52 17 Consider the scatter graph to answer the following: The equation for our line is y = 1x What would the prediction be if x = 14? Is this an interpolation or extrapolation? A 4, interpolation B 4, extrapolation C 2, interpolation D 2, extrapolation A D X Y Answer 52

53 18 Consider the scatter graph to answer the following: The equation for our line is y = 1x What would the prediction be if x = 11? Is this an interpolation or extrapolation? A 1, interpolation B 1, extrapolation C 2, interpolation D 2, extrapolation A D X Y Answer 53

54 19 In the previous questions, we began by using the table at the right. Which of the predicted values: (7,5) or (14, 2) will be more accurate and why? A B C D (7,5); it is an interpolation. (7,5); there already is a 5 and a 7 in the table (14, 2) it is an extrapolation (14, 2); the line is going down and will become negative X Y Answer 54

55 20 What is the slope of this best fit line that goes through A and C? A B C D X Y A C Answer 55

56 21 What is the y intercept of the line of best fit that goes through A and C? X Y 3 6 A B C A C D Answer 56

57 22 The equation for the line of best fit is. What would the prediction be if y = 4.5? Is this an interpolation or extrapolation? X Y Answer A 8, interpolation B 8, extrapolation C 6.5, interpolation D 6.5, extrapolation

58 23 The equation for the line of best fit is. What would the prediction be if y = 8? Is this an interpolation or extrapolation? X Y 3 6 Answer A B C D interpolation extrapolation interpolation extrapolation

59 Prediction Equation Calculate the prediction equation using the two labeled points. Shoe Size v. Girl's Height Height in Inches Shoe Size Shoe Size Girl's Height in Inches

60 24 What is the slope of the prediction equation for this graph? Shoe Size v. Girl's Height Height in Inches Shoe Size Shoe Size Girl's Height in Inches Answer 60

61 25 A girl with a size 7 shoe and height of 56 inches will be an interpolation. True Shoe Size v. Girl's Height False Height in Inches Shoe Size Girl's Height in Inches Answer Shoe Size

62 26 A girl with a size 4 shoe and height of 51 inches will be an interpolation. True Shoe Size v. Girl's Height False Height in Inches Shoe Size Girl's Height in Inches Answer 8 66 Shoe Size 62

63 27 What will the height be of a girl with a size 8.5? Shoe Size v. Girl's Height Height in Inches Shoe Size Shoe Size Girl's Height in Inches Answer 63

64 28 A girl with a size 10 shoe and height of 71 inches will be an extrapolation. True Shoe Size v. Girl's Height False Height in Inches Shoe Size Shoe Size Girl's Height in Inches Answer 64

65 29 Using the prediction equation, what will the height be of a girl who has a size 10 shoe? Shoe Size v. Girl's Height Height in Inches Shoe Size Girl's Height in Inches Answer Shoe Size 65

66 Prediction Equation Using the scatter plot you created for the shoe size v. girls' heights and shoe size v. boys' heights from your class, determine the prediction equation for each graph. Using the equation, how tall is a girl that wears a 9.5 size shoe? How tall is a boy that wears a 6.5 shoe? 66

67 Two Way Tables Return to Table of Contents 67

68 Two Way Tables We can also organize data gathered in a two way table. Two way tables display information as it pertains to two different categories. Here is an example of a two way table: Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total

69 Two Way Tables What does the two way table show us? The table below shows information gathered from 30 students. They were asked if they took a bus or a bicycle to school. Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total

70 Two Way Tables As you can see from the table, some students take the bus, other students ride their bicycles, take the bus or ride a bicycle to school. Several students do not take a bus nor ride their bicycles to school. Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total Let's answer some questions using the data from the table. 70

71 30 From this table, how many students take the bus or ride their bicycle to school? Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total Answer 71

72 31 How many students take the bus, but do not ride their bicycles to school? Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total Answer 72

73 32 How many students do not take the bus to school? Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total Answer 73

74 33 How many students ride their bicycles to school, but do not take the bus? Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total Answer 74

75 Two Way Tables Henry surveyed students from several classes to find out if they did chores and received an allowance. 65 students did chores. Of those 65 students, 49 received an allowance. There were 26 students that did not do chores and did not receive an allowance. 10 students that did not do chores, but received an allowance. Set up your table, and label the categories. Chores No Chores Total Allowance No Allowance Total 75

76 Two Way Tables 65 students did chores. Where would you write that number? Allowance No Allowance Total Chores 65 No Chores Total Notice that the "Chores" and "No Chores" categories are in the rows, and the "Allowance" and "No Allowance" categories are in the columns. 76

77 Two Way Tables Of those 65 students, 49 received an allowance. Where would you write the 49? Allowance No Allowance Total Chores No Chores Total Look at the "Chores" category, then "Allowance" since the 49 students who did chores received an allowance. 77

78 Two Way Tables There were 26 students that did not do chores and did not receive an allowance. Allowance No Allowance Total Chores No Chores 26 Total Look at the "No Chores" category and "No Allowance" category. 78

79 Two Way Tables 10 students that did not do chores, but received an allowance. Allowance No Allowance Total Chores No Chores Total Look for the "No Chores" category then "Allowance" category. 79

80 Allowance Two Way Tables This is the table filled using the information that was given. Although some of the cells are not filled, you can easily find the rest of the information with simple math. No Allowance Total Chores = No Chores = 36 Total = = = 101 or = 101 If you did your math correctly, the total row and column should be the same. 80

81 Two Way Tables Here is the final table. Now you can answer some questions using the data. Allowance No Allowance Total Chores No Chores Total

82 34 How many students took this survey? Allowance No Allowance Total Chores No Chores Total Answer 82

83 35 How many students do chores, but do not receive an allowance? Allowance No Allowance Total Chores No Chores Total Answer 83

84 36 How many students do not do chores, but still receive an allowance? Allowance No Allowance Total Chores No Chores Total Answer 84

85 Two Way Tables Survey your class to find out if each student has a laptop computer and/or desktop computer at home. Make a two way table showing your results. Desktop Computer No Desktop Computer Laptop Computer No Laptop Computer Total Total 85

86 Relative Frequency Using two way tables, we can calculate relative frequencies. Relative frequencies are ratios that compares the value of a certain category to the subtotal in that category. As you have previously learned, the frequency is the quantity of just how many of a certain event occurs. Relative frequency is how many compared to the subtotal. The relative frequency is written as a fraction or decimal. 86

87 Relative Frequency Example: There are 12 girls in a class of 20 students. The frequency of number of girls in a class is 12. The relative frequency of the number of girls in the class is or What is the frequency of girls in your class? What is the relative frequency? What is the frequency of boys in your class? What is the relative frequency? 87

88 Relative Frequency Calculate the relative frequency for the two way table from earlier by row and then by column. Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total

89 Relative Frequency For this cell, the relative frequency of students taking a bicycle to school or the bus to school is divided by the total number of students that take the bus to school. By row: Take the Bus to School Do Not Take the Bus to School Total Take a Bicycle to School Do Not Take a Bicycle to School Total = = =

90 Relative Frequency For relative frequency by column, the number of students that take a bicycle to school or take a bus to school is divided by the number of students that take a bicycle to school. By column: Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total

91 Relative Frequency Let's answer some questions using the relative frequencies. What is the relative frequency of students that take a bicycle to school and also take a bus to all students taking a bus to school? By row: Take the Bus to School Do Not Take the Bus to School Total Take a Bicycle to School Do Not Take a Bicycle to School Total = = = 1.00 Answer 91

92 Relative Frequency What is the relative frequency of students that do not take a bicycle to school and do not take a bus to all students that do not take a bus to school? By row: Take the Bus to School Do Not Take the Bus to School Total Take a Bicycle to School Do Not Take a Bicycle to School Total = = = 1.00 Answer 92

93 37 What is the relative frequency of students that take a bicycle to school but do not take a bus to the total number of students that do not take the bus? By row: Take the Bus to School Do Not Take the Bus to School Total Take a Bicycle to School Do Not Take a Bicycle to School Total = = = 1.00 Answer 93

94 38 What is the relative frequency of the students that do not take a bicycle to school, but do take the bus to the all the students that take the bus to school? By row: Take the Bus to School Do Not Take the Bus to School Total Take a Bicycle to School Do Not Take a Bicycle to School Total = = = 1.00 Answer 94

95 39 By Column: What is the relative frequency of students that take a bicycle to school and also take a bus to school, to the total number of students that take a bicycle to school? By column: Take a Bicycle to School Do Not Take a Bicycle to School Total Take the Bus to School Do Not Take the Bus to School Total Answer 95

96 40 What is the relative frequency of students that do not take a bicycle to school and do not take the school bus to the total number of students that do not take a bicycle to school? By column: Take the Bus to School Do Not Take the Bus to School Take a Bicycle to School Do Not Take a Bicycle to School Total Total Answer 96

97 41 What is the relative frequency of students that take a bicycle to school, but do not take the bus to all students that take a bicycle to school? By column: Take the Bus to School Do Not Take the Bus to School Take a Bicycle to School Do Not Take a Bicycle to School Total Total Answer 97

98 Relative Frequency By Row Use the following two way table to calculate the relative frequencies by row. Allowance No Allowance Total Chores No Chores Total Chores No Chores Total Allowance No Allowance Total 98

99 Relative Frequency Why do we calculate relative frequencies? We can use relative frequencies to determine if there is an association between the two categories. For example, does there seem to be a relationship between whether or not a student receives an allowance compared to whether or not a student does chores? By row: Allowance No Allowance Total Chores 1.00 No Chores 1.00 Total 1.00 Approximately 0.75 or 75% of students that receive an allowance do chores, and out of those that do chores only 0.25 or 25% of students receive no allowance. 99

100 Relative Frequency By Column Use the following two way table to calculate the relative frequencies by column. Allowance No Allowance Total Chores No Chores Total Chores Allowance No Allowance Total Is there a relationship between students that do chores to the amount of students that receive an allowance? No Chores Total 100

101 Two way Table Construct a two way table using the following information. Kelly found that 49 people had dogs in her school. Out of the 49 people, 30 people had cats. 50 people had cats in her school. 22 people had neither cats nor dogs at home. Dog No Dog Total Cat No Cat Total 101

102 Relative Frequency Using the two way table, calculate the relative frequencies by column and by row. By row: Dog No Dog Total Cat No Cat Total By column: Dog No Dog Total Cat No Cat Total 102

103 42 What is the relative frequency of the people who have a cat and a dog at home to the number of people that have cats? Dog No Dog Total Cat No Cat Total Cat No Cat Total Dog Answer No Dog Total

104 43 What is the relative frequency of the people who have a dog and a cat to the number of people that have a dog? Dog No Dog Total Cat No Cat Total Answer 104

105 44 What is the relative frequency of the people who have no cat, but have a dog to the number of people that have no cats? Dog No Dog Total Cat No Cat Total Answer 105

106 45 The table shows the results of a random survey of students in grade 7 and grade 8. Every student surveyed gave a response. Each student was asked if he or she exercised less than 5 hours last week or 5 or more hours last week. Based on the results of the survey, which statements are true? Select each correct statement. A More grade 8 students were surveyed than grade 7 students. B A total of 221 students were surveyed. C Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week. D More than 50% of the students surveyed exercised less than 5 hours last week. E A total of 107 grade 7 students were surveyed. Answer From PARCC EOY sample test calculator #3 106

107 Construct a Two way Table Survey your classmates to find out if they play sports and/or play an instrument. Construct a two way table displaying the results. (Write "yes" or "no") Then calculate the relative frequencies by row and by column. Is there a relationship between the number of students that play sports vs. the number of students that play an instrument? 107

108 Glossary Teacher Notes Return to Table of Contents 108

109 Bivariate Data Two sets of related data that is being compared. Data of two variables. (Two Variable Data) Variables: 1. Shoe Size Bivariate Data Variables: 1. Temperature 2. Sales Variables: 1. Hours 2. Math Grade 1 variable Univariate Data Back to Instruction 109

110 Extrapolation A data point that is outside the range of data. If it is 50 o outside, what would If it is 90 o outside, what would (77,610) be the predicted ice cream sales? be the predicted ice cream sales? (53,180) range = y = 17x 721 y = 17(50) 721 y = y = 129 $129 $129 < $180 y = 17x 721 y = 17(90) 721 y = 1, y = 809 $809 $809 > $610 Back to Instruction 110

111 Frequency The quantity of just how many of a certain even occurs. The frequency of kids who take the bus to school is 12. The frequency of kids who ride their bikes to school is 11. The frequency of kids who do not take the bus to school is 18. Back to Instruction 111

112 Interpolation A data point that is inside the range of data. If it is 70 o outside, what would If it is 63 o outside, what would (77,610) be the predicted ice cream sales? be the predicted ice cream sales? (53,180) range = $610 $180 y = 17x 721 y = 17(70) 721 y = 1, y = 469 $469 $180 < $469 < $610 y = 17x 721 y = 17(63) 721 y = 1, y = 350 $350 $180 < $350 < $610 Back to Instruction 112

113 Linear A graph that is represented by a straight line. Back to Instruction 113

114 Line of Best Fit A line on a graph showing the general direction that a group of points seem to be heading. Trend Line. Back to Instruction 114

115 Negative Association A correlation of points that is linear with a negative slope. Back to Instruction 115

116 No Association A correlation of points that is linear with a slope of zero. A horizontal line graph. Back to Instruction 116

117 Non Linear A graph that is not represented by a straight line. A curved line. Back to Instruction 117

118 Positive Association A correlation of points that is linear with a positive slope. Back to Instruction 118

119 Prediction Equation An equation that is created using the line of best fit. A line that can predict outcomes using the given data. y = mx+b If it is 70 o outside, what would be the predicted ice cream sales? Ice Cream Sales $ (53,180) (73,520) Temperature degrees F y = 17x 721 y = 17x 721 y = 17(70) 721 y = 1, y = 469 $469 Back to Instruction 119

120 Relative Frequency Ratios that compares the value of a certain category to the subtotal in that category. The relative frequency of students who only take the bus to the total bus riders is The relative frequency of students who only ride their bikes to the total bike riders is The relative frequency of students who only ride their bikes to the total students is Back to Instruction 120

121 Scatter Plot A graph of plotted points that show the relationship between two sets of data. Back to Instruction 121

122 Two Way Table A table that displays information as it pertains to two different categories. Allowance vs. Chores School Bus vs. Bicycle Back to Instruction 122