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1. Cumulative Frequency Curves

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

53. Your turn