Cumulative Frequency Curves

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)
40?X?45
45?X?50
50?X?55
55?X?60
Frequency F
7
12
15
3
5
Height (mm)
40?X?45
45?X?50
50?X?55
55?X?60
Frequency F
7
12
15
3
Cumulative Frequency
6
Height (mm)
40?X?45
45?X?50
50?X?55
55?X?60
Frequency F
7
12
15
3
Cumulative Frequency
7
7
Height (mm)
40?X?45
45?X?50
50?X?55
55?X?60
Frequency F
7
12
15
3
Cumulative Frequency
7
19
8
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
9
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
10
Upper Class Boundary
11
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
12
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
13
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
14
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
15
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
16
Plot the curve
17
Upper class boundary
45
50
55
60
Cumulative Frequency
7
19
34
37
18
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
19
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
20
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
21
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
22
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
23
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
24
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
25
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
26
Median
27
Upper class boundary
45
50
55
60
Cumulative Frequency
7
19
34
37
28
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
29
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
30
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
31
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
Median 49mm
32
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
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 9.25Three 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
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
40
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
41
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
42
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
LQ 45mm
43
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
44
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
45
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
46
Cress seedling height
40
30
Cumulative
frequency
20
10
0
35
40
45
50
55
60
Height (mm)
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