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Cumulative Frequency Curves

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