Scatter Graphs SUCCESS CRITERIA: Where are you now? Tick what you currently know about scatter graphs in the table below (one tick in each row please): Level Learning outcomes C3 Can I plot points on a scatter graph? C2 Can I describe the relationship between the data, including correlation? C1 Can I draw and use a "line of best fit" to estimate results? R A G What are scatter graphs? Scatter graphs show the relationship between two sets of data. Points are plotted very like co-ordinates. Below are the marks of eight students in their Maths and Science tests. Student A B C D E F G H Maths mark 56 73 51 62 24 67 94 35 Science mark 62 68 45 68 35 73 88 32 Draw a scatter graph of this information: Student A B C D E F G H Maths mark 56 73 51 62 24 67 94 35 Science mark 62 68 45 68 35 73 88 32 100 90 80 Science mark 70 60 50 40 30 20 10 0 10 20 30 40 50 60 Maths mark 70 80 90 100 Draw a scatter graph of this information: Student A B C D E F G H Maths mark 56 73 51 62 24 67 94 35 Science mark 62 68 45 68 35 73 88 32 What yours should look like: 100 90 80 Science mark 70 60 50 40 30 20 10 0 10 20 30 40 50 60 Maths mark 70 80 90 100 Plot these sets of data on scatter graphs: The data below shows the number of scarves sold by a shop in a week and the temperature that day: Day of the week M T W T F S S Sales of scarves 73 56 54 38 7 39 82 Temperature (oC) 9 13 15 19 25 12 5 The data below shows the amount of petrol used by a car and the distance driven on eight different journeys: Journey 1 2 3 4 5 6 7 8 Distance (km) 75 140 237 180 20 93 104 42 Petrol used (l) 7 12.5 25.3 16 3.5 8.9 9.5 4.1 How your scatter graph should look: Day of the week M T W T F S S Sales of scarves Temperature (oC) 20 73 56 54 38 7 39 82 9 13 15 19 20 12 5 Temperature (oC) 15 10 5 0 10 20 30 40 50 60 Sales of scarves 70 80 90 100 How your scatter graph should look: Journey 1 2 3 4 Distance (km) 75 140 197 Petrol used (l) 7 12.5 21.3 16 5 180 20 3.5 6 7 93 104 42 8.9 9.5 25 Petrol used (l) 20 15 10 5 0 20 40 60 80 100 120 140 160 180 200 Distance (km) 8 4.1 Scatter Graphs SUCCESS CRITERIA: Where are you now? Colour in where you now are with your understanding of plotting scatter graphs: Level Learning outcomes C3 Can I plot points on a scatter graph? C2 Can I describe the relationship between the data, including correlation? C1 Can I draw and use a "line of best fit" to estimate results? R A G What would you expect to happen? Look at the situations below and describe what you think might happen in each case: 1. The sales of ice creams as the temperature rises during the summer. 2. The value of a mobile phone as it gets older. 3. The amount you'll get in a maths test the further you live from school. What do scatter graphs tell us? Scatter graphs show the relationship between our two sets of data. We describe this relationship using correlation. There are basically 3 types of correlation: Positive, Negative and No Correlation The more in line the points, the stronger the correlation. What do you think the correlation might be in these situations? 1. The sales of ice creams as the temperature rises during the summer. 2. The value of a mobile phone as it gets older. 3. The amount you'll get in a maths test the further you live from school. Describe the correlation of these scatter graphs: Draw a scatter graph of this information and describe the correlation: Student A B C D E F G H Maths mark 56 73 51 62 24 67 94 35 Art mark 54 43 47 44 82 31 18 87 100 90 80 Art mark 70 60 50 40 30 20 10 0 10 20 30 40 50 60 Maths mark 70 80 90 100 Draw a scatter graph of this information and describe the correlation: Student A B C D E F G H Maths mark 56 73 51 62 24 67 94 35 Art mark 54 43 47 44 82 31 18 87 100 90 80 Art mark 70 Correlation: Negative(Moderate) 60 50 40 30 20 10 0 10 20 30 40 50 60 Maths mark 70 80 90 100 Scatter Graphs SUCCESS CRITERIA: Where are you now? Colour in where you now are with your understanding of describing correlation: Level Learning outcomes C3 Can I plot points on a scatter graph? C2 Can I describe the relationship between the data, including correlation? C1 Can I draw and use a "line of best fit" to estimate results? R A G How do we use scatter graphs? We can use scatter graphs to estimate results based upon other results. We do this by drawing a "line of best fit". A "line of best fit" is a straight line (drawn with a ruler) that goes through the middle of your points. This is an estimate, but try to get half of the points on either side of it. The "line of best fit" does not have to go through the origin! When doing an estimate from a scatter graph you must draw the "line of best fit" or you will get no marks! If there is no correlation, you cannot draw a "line of best fit". A typical exam question: Imogen missed the Science test because she was ill. She sat the Maths test and got 85. Use your scatter graph to estimate what Imogen would have achieved on the Science test. 100 90 80 Science mark 70 60 50 40 30 20 10 0 10 20 30 40 50 60 Maths mark 70 80 90 100 A typical exam question: Imogen missed the Science test because she was ill. She sat the Maths test and got 85. Use your scatter graph to estimate what Imogen would have achieved on the Science test. 100 90 80 Science mark 70 Imogen would have got 83. 60 50 40 30 20 10 0 10 20 30 40 50 60 Maths mark 70 80 90 100 Estimate, using your graph, how many scarves the shop would sell when the temperature was 7oC. Estimate, using your graph, how many litres of petrol the car would use on a journey of 160km. 20 25 20 Petrol used (l) 10 Temperature (oC) 15 15 10 5 5 0 10 20 30 40 50 60 Sales of scarves 70 80 90 100 0 20 40 60 80 100 120 140 160 180 200 Distance (km) Estimate, using your graph, how many scarves the shop would sell when the temperature was 7oC. Estimate, using your graph, how many litres of petrol the car would use on a journey of 160km. 20 25 20 Petrol used (l) 10 Temperature (oC) 15 15 10 5 5 0 10 20 30 40 50 60 70 Sales of scarves Answer: 80 scarves 80 90 100 0 20 40 60 80 100 120 140 160 180 200 Distance (km) Answer: 15 litres Scatter Graphs SUCCESS CRITERIA: Where are you now? Colour in where you now are with your understanding of using "lines of best fit" to estimate results: Level Learning outcomes C3 Can I plot points on a scatter graph? C2 Can I describe the relationship between the data, including correlation? C1 Can I draw and use a "line of best fit" to estimate results? R A G Now try some exam questions!