cumulative frequency curves
DESCRIPTION
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). 40 X 45. - PowerPoint PPT PresentationTRANSCRIPT
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)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
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)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Median ≈ 49mm
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
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)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
LQ ≈ 45mm
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
Cress seedling height
0
10
20
30
40
35 40 45 50 55 60
Height (mm)
Cum
ulat
ive
freq
uenc
y
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