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Tables to compare the wingspan of male and female butterflies.
Wing Span (mm)
30-31
32-33
34-36
37-39
Male Frequency
2
25
30
13
Wing Span (mm)
30-31
32-33
34-36
37-39
Female Frequency
0
15
45
0
What can you say?
Finding the mean
1070, 1080, 1120
0 Distance20 40 60 80 100 120 140 160 1800
020 40 60 80 100 120 140 160 1800 Distance
Graph to compare the distances that males and females travel in the car per week.
10
20
30
40
50
10
20
30
40
50
Distance Frequency
0<d<40 5
40<d<60 20
60<d<80 20
80 < d < 100 40
100 < d < 120 50
120 < d < 180 10
Distance Frequency
0<d<40 5
40<d<80 20
80<d<100 40
100 < d < 180 50
0 Distance20 40 60 80 100 120 140 160 1800
020 40 60 80 100 120 140 160 1800 Distance
Graph to compare the distances that males and females travel in the car per week.
0
0
0
0
0
0
0
0
0
0
Histograms
The difference is that you get the frequencies from the area of the rectangles and not the height.
Frequency Frequency Density
Frequency Diagram
Histogram
Histograms look like frequency diagrams.
Histograms can be used when the class intervals are unequal.
Time
0 < t < 10
10 < t < 20
20 < t < 30
30 < t < 40
40 < t < 50
Frequency
20
15
10
9
6
Time
0 < t < 10
10 < t < 15
15 < t < 20
20 < t < 25
25 < t < 40
Frequency
20
15
10
9
6
Equal Class Intervals Unequal Class Intervals
Frequency Density is equal to the Height of the Bar.
Frequency is equal to the Area of the Bar.
With a histogram you cant not get the frequency from the height of the bar.
Instead you get the frequency from the area of the bar.
Frequency density =frequency
width of interval
Width of interval =
Area (Frequency) =
Height (Frequency density) =
0.4
95 10511010
0.4
4
10
5
20
0.5
2
1.2
?
?
? 2 8
?
Width of interval =
Frequency =
Frequency density =
10
0.5
5
Width of interval =
Frequency =
Frequency density =
20
1.2
24
Width of interval =
Frequency =
Frequency density =
5
0.4
2
Width of interval =
Frequency =
Frequency density =
4
2
8
Find the relevant information for each bar.
Time
0 < t < 10
10 < t < 15
15 < t < 20
20 < t < 25
25 < t < 40
Frequency
20
15
10
9
6
Frequency Density
Frequency Density =
Frequency Class width
20 ÷ 10
15 ÷ 5
10 ÷ 5
9 ÷ 5
6 ÷ 15
2
3
2
1.8
0.4
Frequency Density
0
0.5
1.0
1.5
2.0
2.5
3.0
Time
5 10 15 20 25 30 35 400
Distance0 < t < 20
20 < t < 40
40 < t < 50
50 < t < 70
70 < t < 100
Frequency
2
4
5
12
9
Frequency Density
2 ÷ 20
4 ÷ 20
5 ÷ 10
12 ÷ 20
9 ÷ 30
0.1
0.2
0.5
0.6
0.3
Frequency Density
0
0.1
0.2
0.3
0.4
0.5
0.6
Distance10 20 30 40 50 60 70 80 90 100
Remember for a histogram the:
Frequency is equal to the Area of the bar.
Frequency Density is equal to the Height of the bar.
15
8 20
0.5 1.25 0.8? ? ?
Area = 15 x 0.5 = 7.5 Area = 1.25 x 8 = 10 Area = 20 x 0.8 = 16
Frequency = frequency density × width of intervalFrequency = frequency density × width of interval
0.4 × 15
2.2 × 5
1.4 × 5
1.2 × 5
0.4 × 10
7
11
6
6
4
Frequency
density × width
110 ≤ t < 115
115 ≤ t < 120
105 ≤ t < 110
120 ≤ t < 135
95 ≤ t < 105
Time in seconds
Area
(frequency)
Fre
qu
en
cy d
en
sity
0
0.4
0.8
1.2
1.6
2.0
2.4
Time in seconds95 100 105 110 115 120 125 130 135
Copy and complete the table.
Length 0 < t < 40
40 < t < 80
80 < t < 100
100 < t < 120
120 < t < 200
Frequency
4
8
16
12
12
40 x 0.1
20 x 0.4
20 x 0.8
20 x 1.0
60 x 0.2
Frequency Density
0
0.2
0.4
0.6
0.8
1.0
Distance20 40 60 80 100 120 140 160 1800
Write a definition of each word below.
Data set
Class interval
Midpoint
Range
Frequency diagram
Review
Frequency
Frequency polygon
Class interval
Histogram
Frequency density
Include methods for calculating.
