8th Grade. Two Variable Data. Slide 1 / 122 Slide 2 / 122. Slide 4 / 122. Slide 3 / 122. Slide 6 / 122. Slide 5 / 122. Data.

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1 Slide 1 / 122 Slide 2 / 122 8th Grade ata Slide 3 / 122 Slide 4 / 122 Table of ontents click on the topic to go to that section Two Variable ata Line of est Fit etermining the Prediction Equation Two-Way Table Two Variable ata Glossary Return to Table of ontents Slide 5 / 122 Two Variable ata Two Variable ata is also called ivariate ata With bivariate data there are two sets of related data that you want to compare. Ice Temperature ream degrees F Sales $ Slide 6 / 122 Scatter Plot Example 1: n 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 ream Sales. We can create a scatter plot by plotting the points. Temperature is the x variable Sales is the y variable.

2 Slide 7 / 122 Scatter Plot Ten ays of Ice ream Shop Sales Slide 8 / 122 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 Ice ream Sales $ Temperature degrees F Slide 9 / 122 Scatter Plot Scatter Plots are either: Slide 10 / 122 Scatter Plot Linear n-linear These scatter plot are also non-linear. Slide 11 / 122 Scatter Plot If a scatter plot is linear it can be described 3 ways: Positive ssociation Negative ssociation Slide 12 / What type of scatter plot is shown from the Ice ream Shop example 1? non-linear linear, positive association linear, negative association linear, no association Ice ream Sales $ Temperature degrees F ssociation

3 Slide 13 / 122 Example 2: ata 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 Slide 15 / 122 Math Grades 3 What kind of association is shown in the graph? Slide 14 / What type of scatter plot is shown for the math and science grades from example 2? non-linear linear, positive association linear, negative association linear, no association Science Grades Slide 16 / 122 lick to reveal solved graph. Math Grades 4 What kind of association is shown in the graph? non-linear non-linear size & Height linear, positive association linear, negative association linear, no association Test Score linear, positive association linear, negative association linear, no association height in inches Time spent studying shoe size Slide 17 / 122 Slide 18 / What association is shown in this graph? oy's Height and Weight 6 Which of the following scenarios would produce a linear scatter plot with a positive correlation? non-linear linear, positive correlation linear, negative correlation linear, no correlation Weight in Pounds Height in inches Miles driven and money spent on gas Number of pets and how many shoes you own Work experience and income Time spent studying and number of bad grades

4 Slide 19 / Which of the following would have no association if plotted on a scatter plot? Slide 20 / 122 Predictions Number of toys and calories consumed in a day Number of books read and reading scores Length of hair and amount of shampoo used Person's weight and calories consumed in a day What kind of predictions can you make from looking at the graph? Slide 21 / 122 Survey ata Slide 22 / 122 Scatter Plot 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. Resting Number of Heart Hours Rate Plot the results of the survey on a scatter plot. Resting Number of Heart Hours Rate Slide 23 / 122 Linear Relationship? ssociation? Slide 24 / 122 Survey ata Is there a linear relationship? Is there a positive or negative association? ccording to your scatter plot, does a person who exercise generally have a lower resting heart rate than a person that doesn't exercise? 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

5 Slide 25 / 122 Linear Relationship? ssociation? Slide 26 / 122 Linear Relationship? ssociation? 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? 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? Temperatur Year e in F 2, , , , , , , , , , , Month Temperatur e in F Slide 27 / 122 Linear Relationship? ssociation? 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? 8 Slide 28 / 122 What association is shown in this graph? non-linear linear, positive association Girl's Height in Inches linear, negative association linear, no association v. Girl's Height Height in Inches Slide 29 / 122 Slide 30 / 122 Girls Height (in inches) oys Height (in inches) Poll Poll 10 girls and 10 boys from your class on their heights and shoe size. Make a scatter plot for your observations. Teacher tes Wake Up Time 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. How Long to Get Ready Survey Is there an association with the time a student wakes up and how long it takes them to get ready?

6 Slide 31 / 122 Slide 32 / 122 Line of est Fit ivariate data plotted on a scatter plot shows us negative or positive association (correlation). Line of est Fit 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. Return to Table of ontents Slide 33 / 122 Line of est Fit Slide 34 / 122 Line of est Fit tice 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). Test Score size & Height Slide 35 / 122 Line of est Fit 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. Slide 36 / onsider the scatter graph to answer the following: Which 2 points would give the best line of fit? height in inches shoe size raw a line of best fit, or trend line, on this graph. Predict the height of a person who wears a size 8 shoe. Predict the shoe size of a person who is 50 inches tall. and and and there is no pattern

7 Slide 37 / 122 Slide 38 / onsider the scatter graph to answer the following: Which 2 points would give the best line of fit? 11 Which two points would you pick to draw the line of best fit? and and and there is no pattern and and and and Slide 39 / 122 Slide 40 / Which two points would you use to draw the line of best fit? and and and v. Girl's Height Height in Inches Girl's Height in Inches 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? From PR EOY sample test non-calculator #15 Slide 41 / 122 Slide 42 / 122 Line of est 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. etermining the Prediction Equation Return to Table of ontents

8 Slide 43 / 122 Line of est Fit The points form a linear like pattern, so use two of the points to draw a line of best fit. Slide 44 / 122 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. 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). Slide 45 / 122 Prediction Equation Prediction Equations can be used to predict other related values. 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. Slide 46 / 122 Prediction Equation If a person studies 42 minutes, what would be the predicted score? If a person studies 15 minutes, what would be the predicted score? This is an interpolation, because the time was inside the range of the original times. This is an extrapolation, because the time was outside the range of the original times. Slide 47 / 122 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. Slide 48 / 122 Prediction Equation If a student got an 80 on the test, What would be the predicted length of their study time? Using the same prediction equation, consider: If a person studies 120 minutes, what will be their score? What is wrong with this prediction? The student studied about 31 minutes.

9 Slide 49 / 122 Slide 50 / onsider the scatter graph to answer the following: What is the slope of the line of best fit going through and? (3, 9) (9, 3) onsider the scatter graph to answer the following: What is the y-intercept of the line of best fit going through and? (3, 9) (9, 3) Slide 51 / 122 Slide 52 / onsider 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? 5, interpolation 3 9 5, extrapolation , interpolation 5 7 6, extrapolation onsider 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? -4, interpolation 3 9-4, extrapolation , interpolation 5 7-2, extrapolation Slide 53 / 122 Slide 54 / onsider 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? 1, interpolation 3 9 1, extrapolation 2, interpolation 2, extrapolation 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? (7,5); it is an interpolation. 3 9 (7,5); there already is a 5 and a 7 in the table (14, -2) it is an extrapolation 5 7 (14, -2); the line is going down and will 6 5 become negative

10 Slide 55 / 122 Slide 56 / What is the slope of this best 21 What is the y-intercept of fit line that goes through the line of best fit that goes and? through and? X Y Slide 57 / 122 Slide 58 / The equation for the line of best fit 23 The equation for the line of best fit is. What would the prediction be if y = 4.5? Is this an interpolation or extrapolation? 8, interpolation 8, extrapolation 6.5, interpolation 6.5, extrapolation is. What would the prediction be if y = 8? Is this an interpolation or extrapolation? interpolation extrapolation interpolation extrapolation Slide 59 / 122 Slide 60 / 122 Prediction Equation 24 What is the slope of the alculate the prediction equation using the two labeled points. prediction equation for this graph? v. Girl's Height v. Girl's Height Height in Inches Girl's Height in Inches Height in Inches Girl's Height in Inches

11 Slide 61 / 122 Slide 62 / girl with a size 7 shoe and height of 56 inches will be an interpolation. 26 girl with a size 4 shoe and height of 51 inches will be an interpolation. True False v. Girl's Height Height in Inches Girl's Height in Inches True False v. Girl's Height Height in Inches Girl's Height in Inches Slide 63 / 122 Slide 64 / What will the height be of a girl with a size 8.5? 28 girl with a size 10 shoe and height of 71 inches will be an extrapolation. v. Girl's Height True v. Girl's Height Height in Inches Girl's Height in Inches False Height in Inches Girl's Height in Inches Slide 65 / 122 Slide 66 / Using the prediction Prediction Equation equation, what will the height be of a girl who has a size 10 shoe? v. Girl's Height Height in Inches Girl's Height in Inches 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?

12 Slide 67 / 122 Slide 68 / 122 Return to Table of ontents icycle to to 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: Slide 69 / 122 Slide 70 / 122 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. icycle to to s 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. icycle to to Let's answer some questions using the data from the table. Slide 71 / 122 Slide 72 / From this table, how many students take the bus or ride their bicycle to school? 31 How many students take the bus, but do not ride their bicycles to school? icycle to to icycle to to

13 Slide 73 / 122 Slide 74 / How many students do not take the bus to school? 33 How many students ride their bicycles to school, but do not take the bus? icycle to to icycle to to Slide 75 / 122 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. hores hores Slide 76 / students did chores. Where would you write that number? hores 65 hores tice that the "hores" and " hores" categories are in the rows, and the "" and " " categories are in the columns. Slide 77 / 122 Of those 65 students, 49 received an allowance. Where would you write the 49? hores hores Slide 78 / 122 There were 26 students that did not do chores and did not receive an allowance. hores hores 26 Look at the "hores" category, then "" since the 49 students who did chores received an allowance. Look at the " hores" category and " " category.

14 Slide 79 / students that did not do chores, but received an allowance. hores hores Slide 80 / 122 This is the table filled using the information that was given. lthough some of the cells are not filled, you can easily find the rest of the information with simple math. hores = hores = = 101 or = = = 101 Look for the " hores" category then "" category. If you did your math correctly, the total row and column should be the same. Slide 81 / 122 Slide 82 / How many students took this survey? Here is the final table. w you can answer some questions using the data. hores hores hores hores Slide 83 / 122 Slide 84 / How many students do chores, but do not receive an allowance? 36 How many students do not do chores, but still receive an allowance? hores hores hores hores

15 esktop omputer esktop omputer Slide 85 / 122 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. Laptop omputer Laptop omputer Slide 86 / 122 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. s 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. Slide 87 / 122 Relative Frequency Slide 88 / 122 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 alculate the relative frequency for the two-way table from earlier by row and then by column. 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? icycle to to Slide 89 / 122 Relative Frequency Slide 90 / 122 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. 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. y row: to icycle to y column: to icycle to

16 Slide 91 / 122 Slide 92 / 122 Relative Frequency 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? y row: to icycle to 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? y row: to icycle to Slide 93 / 122 Slide 94 / 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? 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? y row: to icycle to y row: to icycle to Slide 95 / 122 Slide 96 / y olumn: 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? 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? y column: to icycle to y column: to icycle to

17 y column: Slide 97 / 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? to icycle to Slide 98 / 122 Relative Frequency y Row Use the following two-way table to calculate the relative frequencies by row. hores hores hores hores Slide 99 / 122 Relative Frequency Why do we calculate relative frequencies? We can use relative frequencies to determine if there is an association between the two categories. Slide 100 / 122 Relative Frequency y olumn Use the following two-way table to calculate the relative frequencies by column. 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? y row: hores 1.00 hores pproximately 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. Slide 101 / 122 Two-way Table hores hores hores hores Slide 102 / 122 Relative Frequency Is there a relationship between students that do chores to the amount of students that receive an allowance? onstruct 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. og og at at Using the two-way table, calculate the relative frequencies by column and by row. y row: y column: og og og og at at at at

18 Slide 103 / 122 Slide 104 / 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? 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? og og at at og og at at at at og og Slide 105 / 122 Slide 106 / 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? og og at at 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. ased on the results of the survey, which statements are true? Select each correct statement. More grade 8 students were surveyed than grade 7 students. total of 221 students were surveyed. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week. More than 50% of the students surveyed exercised less than 5 hours last week. E total of 107 grade 7 students were surveyed. Slide 107 / 122 onstruct a Two-way Table From PR EOY sample test calculator #3 Slide 108 / 122 Survey your classmates to find out if they play sports and/or play an instrument. onstruct 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? Glossary Return to Table of ontents

19 Slide 109 / 122 ivariate ata Two sets of related data that is being compared. ata of two variables. (Two-Variable ata) Slide 110 / 122 Extrapolation data point that is outside the range of data. Variables: 1. Temperature 2. Sales Variables: 1. Hours 2. Math Grade Variables: 1. ivariate ata 1 variable Univariate ata (53,180) (77,610) range = If it is 50 o outside, what would be the predicted ice cream sales? y = 17x y = 17(50) y = y = 129 $129 $129 < $180 If it is 90 o outside, what would be the predicted ice cream sales? y = 17x y = 17(90) y = 1, y = 809 $809 $809 > $610 Slide 111 / 122 Frequency The quantity of just how many of a certain even occurs. Slide 112 / 122 Interpolation data point that is inside the range of data. 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. (53,180) (77,610) range = $610 - $180 If it is 70 o outside, what would be the predicted ice cream sales? y = 17x y = 17(70) y = 1, y = 469 $469 $180 < $469 < $610 If it is 63 o outside, what would be the predicted ice cream sales? y = 17x y = 17(63) y = 1, y = 350 $350 $180 < $350 < $610 Slide 113 / 122 Linear graph that is represented by a straight line. Slide 114 / 122 Line of est Fit line on a graph showing the general direction that a group of points seem to be heading. Trend Line.

20 Slide 115 / 122 Negative ssociation correlation of points that is linear with a negative slope. Slide 116 / 122 ssociation correlation of points that is linear with a slope of zero. horizontal line graph. Slide 117 / 122 n-linear graph that is not represented by a straight line. curved line. Slide 118 / 122 Positive ssociation correlation of points that is linear with a positive slope. Ice ream Sales $ (53,180) Slide 119 / 122 Prediction Equation n equation that is created using the line of best fit. line that can predict outcomes using the given data. (73,520) Temperature degrees F y = mx+b y = 17x If it is 70 o outside, what would be the predicted ice cream sales? y = 17x y = 17(70) y = 1, y = 469 $469 Slide 120 / 122 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 0.37.

21 Slide 121 / 122 Scatter Plot graph of plotted points that show the relationship between two sets of data. Slide 122 / 122 Two-Way Table table that displays information as it pertains to two different categories. vs. hores vs. icycle