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  4545  X  50 712 50  X  55 15 55  X  60 3

5. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency

6. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 7

7. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719

8. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 34

9. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 3437

10. Upper Class Boundary

11. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 3437 Upper class boundary

12. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 3437 Upper class boundary 45

13. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 3437 Upper class boundary 4550

14. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 3437 Upper class boundary 4550 55

15. Height (mm) Frequency F 40  X  4545  X  50 712 50  X  55 15 55  X  60 3 Cumulative Frequency 719 3437 Upper class boundary 4550 5560

16. Plot the curve

17. Cumulative Frequency 719 3437 Upper class boundary 4550 5560

18. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

19. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

20. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

21. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

22. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

23. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

24. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

25. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

26. Median

27. Cumulative Frequency 719 3437 Upper class boundary 4550 5560

28. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

29. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

30. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

31. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency Median ≈ 49mm

32. Cress seedling height 0 10 20 30 40 354045505560 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 354045505560 Height (mm) Cumulative frequency

40. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

41. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

42. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency LQ ≈ 45mm

43. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

44. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

45. Cress seedling height 0 10 20 30 40 354045505560 Height (mm) Cumulative frequency

46. Cress seedling height 0 10 20 30 40 354045505560 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