Cumulative Frequency Curves

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Cumulative Frequency Curves

  1. 1. Cumulative Frequency Curves
  2. 2. Outcomes… <ul><li>Calculate the cumulative frequency </li></ul><ul><li>Write down the upper class boundaries </li></ul><ul><li>Plot the cumulative frequency curve </li></ul><ul><li>Find the median value </li></ul><ul><li>Find the upper and lower quartiles </li></ul><ul><li>Find the inter-quartile range </li></ul>
  3. 3. Cumulative Frequency
  4. 4. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3
  5. 5. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency
  6. 6. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7
  7. 7. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19
  8. 8. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34
  9. 9. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34 37
  10. 10. Upper Class Boundary
  11. 11. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34 37 Upper class boundary
  12. 12. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45
  13. 13. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50
  14. 14. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55
  15. 15. Height (mm) Frequency F 40  X  45 45  X  50 7 12 50  X  55 15 55  X  60 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55 60
  16. 16. Plot the curve
  17. 17. Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55 60
  18. 18. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  19. 19. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  20. 20. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  21. 21. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  22. 22. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  23. 23. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  24. 24. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  25. 25. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  26. 26. Median
  27. 27. Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55 60
  28. 28. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  29. 29. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  30. 30. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  31. 31. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency Median ≈ 49mm
  32. 32. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency Median ≈ 49mm
  33. 33. Quartiles
  34. 34. The lower quartile tells us what value 25% of the sample are less than
  35. 35. The upper quartile tells us what value 75% of the sample are less than
  36. 36. 37 cress seeds in total
  37. 37. A quarter of 37 is 9.25 Three quarters is 27.75
  38. 38. We use the graph to find what lengths correspond to cumulative frequencies of 9.25 and 27.75
  39. 39. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  40. 40. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  41. 41. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  42. 42. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency LQ ≈ 45mm
  43. 43. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  44. 44. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  45. 45. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency
  46. 46. Cress seedling height 0 10 20 30 40 35 40 45 50 55 60 Height (mm) Cumulative frequency UQ ≈ 52mm
  47. 47. Inter-quartile range
  48. 48. The difference between the upper and lower quartile
  49. 49. Median ≈ 49mm LQ ≈ 45mm UQ ≈ 52mm IQR ≈ UQ – LQ ≈ 7mm
  50. 50. Tells you the range of values occupied by the middle 50% of your sample
  51. 51. Summary
  52. 52. Cumulative frequency <ul><li>Running total of the frequencies </li></ul><ul><li>Plot against the upper class boundaries </li></ul><ul><li>Draw a smooth curve thru’ the points </li></ul><ul><li>Take half the total frequency and use that to read off a value of the median </li></ul><ul><li>Find the Lower Quartile and the Upper Quartile </li></ul><ul><li>Find the Inter-quartile range by subtracting </li></ul>
  53. 53. Your turn

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