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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
40X45 45X50
7 12
50X55
15
55X60
3
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34 37
Upper Class Boundary
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34 37
Upper class boundary
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34 37
Upper class boundary 45
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34 37
Upper class boundary 45 50
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34 37
Upper class boundary 45 50 55
Height (mm)
Frequency F
40X45 45X50
7 12
50X55
15
55X60
3
Cumulative Frequency 7 19 34 37
Upper class boundary 45 50 55 60
Plot the curve
Cumulative Frequency 7 19 34 37
Upper class boundary 45 50 55 60
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Median
Cumulative Frequency 7 19 34 37
Upper class boundary 45 50 55 60
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Median ≈ 49mm
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Median ≈ 49mm
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 9.25Three 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
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
LQ ≈ 45mm
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cu
mu
lati
ve
freq
uen
cy
UQ ≈ 52mm
Inter-quartile range
The difference between the upper and lower quartile
Median ≈ 49mm
LQ ≈ 45mm
UQ ≈ 52mm
IQR ≈ UQ – LQ ≈ 7mm
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
