Cumulative Frequency Curves Outcomes Calculate the cumulative frequency

Outcomes… • • • Calculate the cumulative frequency Write down the upper class boundaries

Height (mm) Frequency F 40 X 45 45 X 50 50 X 55 55

Height (mm) Frequency F Cumulative Frequency 40 X 45 45 X 50 50 X

Height (mm) 40 X 45 45 X 50 50 X 55 55 X 60

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

Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 Median ≈

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

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.

Cress seedling height Cumulative frequency 40 30 20 10 0 35 LQ ≈ 45

Cress seedling height Cumulative frequency 40 30 20 10 0 35 40 UQ ≈

The difference between the upper and lower quartile

Median ≈ 49 mm LQ ≈ 45 mm UQ ≈ 52 mm IQR ≈

Tells you the range of values occupied by the middle 50% of your sample

Cumulative frequency • • Running total of the frequencies Plot against the upper class

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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

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 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 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 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

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