Gr 10 scatter graphs and lines of best fit

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Gr 10 scatter graphs and lines of best fit

  1. 1. Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1
  2. 2. 1. A positive correlation. As one quantity increases so does the other. 2. A negative correlation. As one quantity increases the other decreases . 3. No correlation. Both quantities vary with no clear relationship. Positive Correlation Negative correlation No correlation Scatter Graphs Scatter graphs are used to show whether there is a relationship between two sets of data. The relationship between the data can be described as either: Shoe Size Annual Income Height Shoe Size Soup Sales Temperature
  3. 3. Scatter Graphs A positive correlation is characterised by a straight line with a positive gradient . A negative correlation is characterised by a straight line with a negative gradient . 1. A positive correlation. As one quantity increases so does the other. 2. A negative correlation. As one quantity increases the other decreases . 3. No correlation. Both quantities vary with no clear relationship. Scatter graphs are used to show whether there is a relationship between two sets of data. The relationship between the data can be described as either: Shoe Size Annual Income Height Shoe Size Soup Sales Temperature
  4. 4. Positive Negative None Negative Positive Negative State the type of correlation for the scatter graphs below and write a sentence describing the relationship in each case. Height KS 3 Results Sales of Sun cream Maths test scores Heating bill (£) Car engine size (cc) Outside air temperature Daily hours of sunshine Physics test scores Age of car (years) Value of car (£) Petrol consumption (mpg) 1 2 3 4 5 6 People with higher maths scores tend to get higher physics scores. As the engine size of cars increase, they use more petrol. ( Less mpg) There is no relationship between KS 3 results and the height of students. As the outside air temperature increases, heating bills will be lower. People tend to buy more sun cream when the weather is sunnier. The older the car the less its value.
  5. 5. Weak Positive Moderate Positive Strong Positive Weak negative Moderate Negative Strong negative A positive or negative correlation is characterised by a straight line with a positive /negative gradient . The strength of the correlation depends on the spread of points around the imagined line.
  6. 6. Lobf A line of best fit can be drawn to data that shows a correlation. The stronger the correlation between the data, the easier it is to draw the line. The line can be drawn by eye and should have roughly the same number of data points on either side. The sum of the vertical distances above the line should be roughly the same as those below. Drawing a Line of Best Fit
  7. 7. Question 1 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size Plotting the data points/Drawing a line of best fit/Answering questions.
  8. 8. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  9. 9. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  10. 10. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  11. 11. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  12. 12. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  13. 13. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  14. 14. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  15. 15. 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  16. 16. <ul><li>(c) Use your line of best fit to estimate: </li></ul><ul><li>The mass of a man with shoe size 10½. </li></ul><ul><li>(ii) The shoe size of a man with a mass of 69 kg. </li></ul>Positive 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size 87 kg Size 6 (b) Draw a line of best fit and comment on the correlation.
  17. 17. Question2 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  18. 18. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  19. 19. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  20. 20. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  21. 21. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  22. 22. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  23. 23. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  24. 24. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  25. 25. 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  26. 26. <ul><li>(c) Use your line of best fit to estimate: </li></ul><ul><li>The number of visitors for 4 hours of sunshine . </li></ul><ul><li>(ii) The hours of sunshine when 250 people visit. </li></ul>Negative 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0 (b) Draw a line of best fit and comment on the correlation. 310 5 ½
  27. 27. Means 1 (b ) Draw a line of best fit and comment on the correlation. If you have a calculator you can find the mean of each set of data and plot this point to help you draw the line of best fit. Ideally all lines of best fit should pass through: (mean data 1, mean data 2) In this case: (8.6, 79.6) 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1). The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  28. 28. Means 2 (b) Draw a line of best fit and comment on the correlation. If you have a calculator you can find the mean of each set of data and plot this point to help you draw the line of best fit. Ideally all lines of best fit should pass through co-ordinates: (mean data 1, mean data 2) In this case: (5.2, 258)) Mean 2 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0
  29. 29. Worksheet 1 4 5 6 7 8 9 10 11 12 13 Shoe Size 60 65 70 75 80 85 90 95 100 Mass (kg) (1.) The table below shows the shoe size and mass of 10 men. (a) Plot a scatter graph for this data and draw a line of best fit. 80 74 88 76 78 78 92 68 97 65 Mass 8 6 11 8 9 10 10 7 12 5 Size
  30. 30. Worksheet 2 1 2 3 4 5 6 7 8 9 10 Hours of Sunshine 100 150 200 250 300 350 400 450 500 Number of Visitors (2). The table below shows the number of people who visited a museum over a 10 day period last summer together with the daily sunshine totals. (a) Plot a scatter graph for this data and draw a line of best fit. 320 350 220 175 50 200 390 100 475 300 Visitors 2 3 5 7 10 8 3 8 0.5 6 Hours Sunshine 0

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