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# 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>