Level H Lesson 26 Create and Interpret Circle Graphs In lesson 26 the objective is, the student will create and interpret scatter plots. We will have three essential questions that will be guiding our lesson. The first one is, when is it best to use a scatter plot? The second one is, what does it mean if a scatter plot shows a positive correlation? The third one is, how could scatter plot be used to predict what will happen? The SOLVE problem is, Jonathan just got back his Science test on weather. He scored an 86. He was curious to see how the amount of sleep a student got the night before affected their test score. He surveyed 10 of his friends, and the results are in the table below. Make a scatter plot of his data, and determine what type of correlation there is between the number of hours of sleep students got the night before and the test grade. The chart is right here. The first step of SOLVE is to underline our question. Our question is, you need to make a scatter plot of his data, and determine what type of correlation there is between the number of hours of sleep students got the night before and the test grade. The next part of the S step is to write the problem in our own words. This problem is asking me to find, the type of correlation between the number of hours of sleep and test grades. The next part of our lesson you are going to measure your height in inches and your foot length in inches. We are going to create a scatter plot with this data. A scatter plot is used to compare one set of data to another to see if they are related in some way. You will want to think about if there is any relationship between your height and your foot length. So the first thing we’re going to do, is we’re going to label our x and our y axis. We are going to label our x axis as height in inches. And we will label our y axis foot length in inches. In class you will be recording all the height and loot length of students in your class. We have a set of sample data over here. We have our height and our foot length, which are both in inches. The first thing we need to do after we have labeled our x and y axis is we need to think about the type of scale we’ll need to use on our x axis for height. So the next thing we need to do is to create our scales for our x and our y axis. Since our height is between 58 and 69, I went in increments of 1, from 50 to 70. You could go in increments of 2 if you like also. Since I started at 50 I will need to create a break line. On my y axis which is my foot length in inches, if you take a look at my data, you will see that I go from 8 point 5 all the way up to 9 point 7. So if I start at 8, you could probably go in increments of 2 tenths or 1 tenth all the way up to 10 to include all of your data. Since we are starting at 8 here, we’ll also want a break line. So now we’ll find our points. We’ll have a height of 66, and a foot length of 9.3. So we’ll go over 66, and up to 9.3. Our second point is 67, so that’s 67 inches, and up to 9.6 inches. Our next point is also 67 inches and up to 9.6. If you have someone that has the same exact measurements just put an x over your dot so that you know that it is more than 1. You will then go ahead and plot all of your points. So now after you plot all of your points, you can take a look at your graph. Now as you can see, we have a couple with the same exact measurements. But we also have 1 that is outside or away from the rest of them. That is considered an outlier. Now if you take a look at your graph and your points, you will see that most of the points seem to be around a line that you could create. Now if you take a look at your points, in your scatter plot you will see that most of them seem to be in a line. As then move from left to right, they also move upward. When you’re looking at your scatter plot, you can see as the height gets taller, the foot length get longer also. This is what is called a positive correlation, as one measurement goes up so does the second measurement. Now you want to take a look at your next graph. The title of it is Snakes. Your x axis is length in feet, and your y axis is your weight in pounds. You want to describe the height of the points from left to right. Well, if you take a look at this one as the x values increase, the y values also go up. So the type of correlation you would call this is positive. So as the length of the snake increases, the weight also increases. Now if you take a look at your second one on Free Time, Your x axis is your Hours Outside, and your y-axis is your Hours Watching TV. Now what you can see is as your x value increase, your y values go down. You can also see this if you place a ruler over it, that your y values are going down and on the first one you can see that your y values were going up as your x values were increasing. So the first one was positive, so therefore our second one would be negative. So as the hours spent outside increase, the number of hours spent watching TV decrease. Now if you take a look at your third one on Siblings, your x axis is your Age in Years, and your y-axis is your Number of Siblings. As you can see you can’t really place a ruler anyway to get a nice line to describe it. So as the x values go from small to larger the y values do not go up or down, they are all over the place. So the type of correlation is, there is no correlation there is none, between the age and the number of siblings they have. So if you take a look at your three examples. Your first one you can see that the values went up from left to right, so we had a positive correlation. On the second one, you can see that the values went down from left to right, so we had a negative correlation. And on the third one we could not find a line, so there is no correlation. Now if you take a look at your scatter plot we have here on snakes. We have our length in feet, and our weight in pounds. So we want to answer some questions about it. How much does the snake that is 7 feet long weigh? Well, if you go over and look at your graph, you will see that you have it in increments of 5, so you have 0, 5 and 10. So 8 would fall a little bit closer to your 10, so if you went up to your point and you brought it over, it would be about 5 pounds. All we’re doing now is we’re reading and interpreting our scatter plot. So, how long are the snakes that weigh 3 pounds? So now we would look at where 3 pounds would be on our y axis because that’s our weight in pounds. So 3 would be in the middle between 2 and 4, so it looks like we have 2 points, so it would probably be 4 and 5 feet. Now if a snake had a length of 9 feet, about how much would you expect the snake to weight? Well we know we went over to 8 and it weighted 5 pounds. If we look at each time it looks like we had a positive correlation. So as your length increases, so did your weight. So we know that it would be more than 5 pounds, but not much more because it did not increase that much so we could say about 6 pounds. Now if a snake weighted 1 pound, about how many feet long would you expect the snake to be? Well if we go over to our 1 pound, on our y axis, we don’t have any length there, but we can see that we still have our positive correlation and if we went over with 2 pounds at probably about 2 or 3, so we could say it’s probably at 1 foot. Throughout the lesson you will now be taking charts and creating scatter plots, and answering questions based on your scatter plots. We’re now going to go back to the SOLVE problem from the beginning of the lesson. Jonathan just got back his Science test on weather. He scored an 86. He was curious to see how the amount of sleep a student got the night before affected their test score. He surveyed 10 of his friends, and the results are in the table below. Make a scatter plot of his data, and determine what type of correlation there is between the number of hours of sleep students got the night before and the test grade. We have already S our problem. So we had already underlined our question at the beginning of the lesson. And we already wrote in our own words what the problem is asking us to find. Which is, this problem is asking me to find the type of correlation between number of hours of sleep and test grades. The next thing we’re going to do is our O step. So we’re going to identify the facts. And eliminate the unnecessary facts. And list our necessary facts. So, Jonathan just got back his Science test on weather, that is a fact, but unnecessary, so we will cross it off. He scored an 86. That is also a fact. It is not necessary. So he was curious to see how the amount of sleep a student got the night before affected their test score. That is also a fact, but it is not a fact that we’ll need to answer our question. He surveyed 10 of his friends, and the results are in the table below. That is also a fact. So we’ll list our necessary facts which is the result of his 10 friends he surveyed. I wrote them as ordered pairs. (8, 85), (9, 95), (6, 75) and the rest of the chart. The next step in SOLVE is our L step. So we’ll need to choose an operation or operations. An operation is not available since we are going to be plotting points and making a scatter plot. The next part is to write in words what our plan of action will be. So we will make a scatter plot, and see if the points go up from left to right, down from left to right, or are scattered all over. The next step of SOLVE is our V step. The first thing we need to do is to estimate your answer. Well if you look at your points, I think it will be a positive correlation, because my teacher always tells me to get a good night’s sleep before a test. The next part is to carry out our plan. So we will need to graph all of our points, which I have done. If you use your ruler you will see that you could probably form a line that will go up from left to right. So it looks like there is a positive correlation. The next step of SOLVE is our E step. You’ll need to answer questions. Does your answer make sense? You want to compare our answer to the question. Yes, I told what the correlation is. The next question is, is your answer reasonable? Compare our answer to the estimate. Yes, I thought it would be positive, and it is. The next one is, is your answer accurate? You need to check your work. Go back and make sure you plotted your points correctly. And use your ruler to see if it is a positive, negative or no correlation. So yes. The last part is, write your answer in a complete sentence. So, there is a positive correlation between the number of hours of sleep the night before a quiz and the quiz grade. CREATING AND INTERPRETING SCATTER PLOTS ON THE GRAPHING CALCULATOR We are now going to create a scatter plot with our graphing calculator. The first thing you want to do is to clear your memory. We’ll hit second, plus, if you look at your screen you’ll hit 4, for clear all lists, and then you’ll hit enter and on your screen when you see the word done you know that you have cleared your lists. You look at your screen, you’ll now push 4, for clear all lists. And once you see clear all lists on your calculator on your screen you press enter twice, you will see, you’ll know you have cleared your list when you see on your screen the word done. Now we’ll begin entering our points. So you’ll hit stat and then you’ll hit enter, for the edit. Now you will arrow up, look at your screen, and over to L1, and down into the first spot. We will first enter our first coordinate, which is (4, 136), so you’ll press 4, enter, and you’ll see it goes down on your x values. So what you can do is you can actually put all your x values in and then put your y in to make sure. We’ll go ahead and do that. We’ll hit 10, enter, and if you watch your screen, you’ll see each one of the points entering in. So 5 enter, 5 enter, 7 enter, 6 enter, 8 enter, 9 enter, and 7 enter. Now if you look at your screen and you’ll see I’m just going to arrow up until I get to my first point of my x which was 4. And I will arrow over under the L2. So if you look at our table you’ll see it’s 4, 136. You’ll want to hit 136 and enter. You see on your screen, (4, 136). And we’ll just go down and enter the rest of them in. 187 enter, 127 enter, 141 enter, 138 enter, 151 enter, 146 enter, 179 enter, 185 enter, and 145 enter. You’ll want to go back up and verify that you have put all the coordinates in correctly. So you’ll see we have (10, 187), (4 and 127), (5, 141), (5, 138), (7, 151), (6, 146), (8, 179), (9, 185) and (7, at 145). It’s very important to make sure that you have entered the correct number in. Now to create our Scatter Plot, we will hit our second and our y equals. When you do that because if you look on your calculator the things that are in yellow by hitting your second key. Now if you look under type, you will see the first on your screen is a scatter plot. You can see if you wanted to do, the other ones you can arrow over to see the different types. So you can do line graphs, bar graphs and all the different types. So we see it’s already a highlighted scatter plot and if you arrow down you’ll see your x list which is our L1 which we entered them in, your L2 was our y list, and we can mark our preference. So you can see that you can have 3 different types points marked. Now what we’re going to do is set our window. We’ll hit window, now if you look at our screen there are already numbers in there. What we would want to do, we would want our x minimum below our x value. If you look at your chart you will see our lowest value is 4, so we could just do our lowest of 2, our x max above our highest one. So we have a highest one of 10, so we could do 12, we can do our x scale is set at 1. We can change that if we like. Then we have our y minimum or our lowest number you can see is 127, we can set that at 125, our y max the highest number is 187, so we can do that at 190. Our y scale we can keep at 1, so we’re all set. And now all we have to do is press graph, and now you’ll see your scatter plot all done for you. We’ll now go back and answer the essential questions from the beginning of the lesson. The first on is, when is it best to use a scatter plot? When you want to see if there is a relationship (correlation) between two pieces of data. The next question is, what does it mean if a scatter plot shows a positive correlation? It means as one value increases, the other value also increases. The last question was, how could scatter plots be used to predict what will happen? The scatter plot has a positive or negative correlation, you can use the trend to see what would happen if a point is outside of the points already plotted. If there is no correlation, you can not use a scatter plot to predict what will happen.