Cumulative Frequency Curves Outcomes Calculate the cumulative frequency
- Slides: 53
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) Frequency F 40 X 45 45 X 50 50 X 55 55 X 60 7 12 15 3
Height (mm) Frequency F Cumulative Frequency 40 X 45 45 X 50 50 X 55 7 12 15 55 X 60 3
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 Cumulative Frequency 7 12 15 3
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 Cumulative Frequency 7 19 15 3
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 Cumulative Frequency 7 19 34 3
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 3 Cumulative Frequency 7 19 34 37
Upper Class Boundary
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55
Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60 Frequency F 7 12 15 3 Cumulative Frequency 7 19 34 37 Upper class boundary 45 50 55 60
Plot the curve
Upper class boundary 45 50 55 60 Cumulative Frequency 7 19 34 37
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Median
Upper class boundary 45 50 55 60 Cumulative Frequency 7 19 34 37
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 Median ≈ 49 mm 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 Median ≈ 49 mm 45 50 Height (mm) 55 60
Quartiles
The lower quartile tells us what value 25% of the sample are less than
The upper quartile tells us what value 75% of the sample are less than
37 cress seeds in total
A quarter of 37 is 9. 25 Three quarters is 27. 75
We use the graph to find what lengths correspond to cumulative frequencies of 9. 25 and 27. 75
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 LQ ≈ 45 mm 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 45 50 Height (mm) 55 60
Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 UQ ≈ 52 mm 45 50 Height (mm) 55 60
Inter-quartile range
The difference between the upper and lower quartile
Median ≈ 49 mm LQ ≈ 45 mm UQ ≈ 52 mm IQR ≈ UQ – LQ ≈ 7 mm
Tells you the range of values occupied by the middle 50% of your sample
Summary
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
Your turn
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