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Cumulative Frequency Curves

Cumulative Frequency Curves. 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. Cumulative Frequency. Height (mm). 40  X 45.

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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) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3

  5. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency

  6. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7

  7. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19

  8. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34

  9. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34 37

  10. Upper Class Boundary

  11. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary

  12. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45

  13. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50

  14. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55

  15. Height (mm) 40X45 45X50 50X55 55X60 7 12 Frequency F 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55 60

  16. Plot the curve

  17. Upper class boundary 45 50 55 60 Cumulative Frequency 7 19 34 37

  18. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  19. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  20. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  21. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  22. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  23. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  24. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  25. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  26. Median

  27. Upper class boundary 45 50 55 60 Cumulative Frequency 7 19 34 37

  28. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  29. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  30. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  31. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm) Median ≈ 49mm

  32. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm) 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 9.25Three 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 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  40. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  41. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  42. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm) LQ ≈ 45mm

  43. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  44. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  45. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm)

  46. Cress seedling height 40 30 Cumulative frequency 20 10 0 35 40 45 50 55 60 Height (mm) 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

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