Tables to compare the wingspan of male and female
butterflies.
Wing Span (mm)

Male Frequency

Wing Span (mm)

Female Freq...
Finding the mean
1070, 1080, 1120
Graph to compare the distances that males and females travel in the car per week.
50
40
30
20
10
0

Distance

0

20

40

6...
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...
Graph to compare the distances that males and females travel in the car per week.
0
0
0
0
0
0

Distance

0

20

40

60

80...
Histograms
Histograms look like frequency diagrams.
The difference is that you get the frequencies from the area
of the re...
Histograms can be used when
the class intervals are unequal.
Time
Frequency
0 < t < 10
20
10 < t < 20
15
20 < t < 30
10
30...
With a histogram you cant not get the
frequency from the height of the bar.
Instead you get the frequency from the area of...
Find the relevant information for each bar.
0.5

?

10
Width of interval = 10
Frequency density = 0.5
Frequency = 5

1.2

...
Time
Frequency
0 < t < 10
20
10 < t < 15
15
15 < t < 20
10
20 < t < 25
9
25 < t < 40
6

Frequency
Frequency
=
Density
Clas...
Distance

Frequency
0 < t < 20
2
20 < t < 40
4
40 < t < 50
5
50 < t < 70
12
70 < t < 100
9

Frequency
Density

0.1
0.2
0.5...
Remember for a histogram the:
Frequency is equal to the Area of the bar.
Frequency Density is equal to the Height of the b...
Copy and complete the table.
Frequency = frequency density × width of interval

Frequency density

2.4
2.0

Time in
second...
1.0
0.8
Frequency
Density 0.6

0.4
0.2
0

0

20

40

60

80

100

120

Frequency
0 < t < 40
4
40 < t < 80
8
80 < t < 100
1...
Review
Write a definition of each word below.
Include methods for calculating.
Data set

Frequency

Class interval

Freque...
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    Male Mean = 34.53
    Female Mean = 34.375
    Range - 10 for males
    Range – 5 for females
    LQ Male – 32.7
    UQ Male – 36.1
    LQ Female – 33.5
    UQ Female 35.5
  • Introduce the concept of coding.
  • Who travels further? Is this graph misleading?
  • Who travels further? Is this graph misleading?
  • The results obtained should be compared with the original graph.
  • S1 starting points

    1. 1. Tables to compare the wingspan of male and female butterflies. Wing Span (mm) Male Frequency Wing Span (mm) Female Frequency 30-31 32-33 34-36 37-39 2 25 30 13 30-31 32-33 34-36 37-39 0 15 45 0 What can you say?
    2. 2. Finding the mean 1070, 1080, 1120
    3. 3. Graph to compare the distances that males and females travel in the car per week. 50 40 30 20 10 0 Distance 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Distance 50 40 30 20 10 0
    4. 4. 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
    5. 5. Graph to compare the distances that males and females travel in the car per week. 0 0 0 0 0 0 Distance 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Distance 0 0 0 0 0 0
    6. 6. Histograms Histograms look like frequency diagrams. The difference is that you get the frequencies from the area of the rectangles and not the height. Frequency Frequency Density Frequency Diagram Histogram
    7. 7. Histograms can be used when the class intervals are unequal. Time Frequency 0 < t < 10 20 10 < t < 20 15 20 < t < 30 10 30 < t < 40 9 40 < t < 50 6 Time Frequency 0 < t < 10 20 10 < t < 15 15 15 < t < 20 10 20 < t < 25 9 25 < t < 40 6 Equal Class Intervals Unequal Class Intervals
    8. 8. 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 is equal to the Area of the Bar. Frequency Density is equal to the Height of the Bar. frequency Frequency density = width of interval 0.4 95 110 105 Width of interval = 10 Height (Frequency density) = 0.4 Area (Frequency) = 4
    9. 9. Find the relevant information for each bar. 0.5 ? 10 Width of interval = 10 Frequency density = 0.5 Frequency = 5 1.2 ? ? 2 Width of interval = 5 Frequency = 2 Frequency density = 0.4 5 2 8 ? 20 Width of interval = 20 Frequency density = 1.2 Frequency = 24 Frequency = 8 Frequency density = 2 Width of interval = 4
    10. 10. Time Frequency 0 < t < 10 20 10 < t < 15 15 15 < t < 20 10 20 < t < 25 9 25 < t < 40 6 Frequency Frequency = Density Class width Frequency Density 2 3 2 1.8 0.4 20 ÷ 10 15 ÷ 5 10 ÷ 5 9÷5 6 ÷ 15 3.0 2.5 Frequency 2.0 Density 1.5 1.0 0.5 0 Time 0 5 10 15 20 25 30 35 40
    11. 11. Distance Frequency 0 < t < 20 2 20 < t < 40 4 40 < t < 50 5 50 < t < 70 12 70 < t < 100 9 Frequency Density 0.1 0.2 0.5 0.6 0.3 2 ÷ 20 4 ÷ 20 5 ÷ 10 12 ÷ 20 9 ÷ 30 0.6 0.5 Frequency Density 0.4 0.3 0.2 0.1 0 10 20 30 40 50 Distance 60 70 80 90 100
    12. 12. Remember for a histogram the: Frequency is equal to the Area of the bar. Frequency Density is equal to the Height of the bar. 0.5 ? 1.25 ? 0.8 ? 15 8 Area = 15 x 0.5 = 7.5 Area = 1.25 x 8 = 10 20 Area = 20 x 0.8 = 16
    13. 13. Copy and complete the table. Frequency = frequency density × width of interval Frequency density 2.4 2.0 Time in seconds 1.6 Frequency Area density × (frequency) width 1.2 95 ≤ t < 105 0.4 × 10 4 0.8 105 ≤ t < 110 1.2 × 5 6 0.4 110 ≤ t < 115 1.4 × 5 7 115 ≤ t < 120 2.2 × 5 11 120 ≤ t < 135 0.4 × 15 6 0 95 100 105 110 115 120 125 130 135 Time in seconds
    14. 14. 1.0 0.8 Frequency Density 0.6 0.4 0.2 0 0 20 40 60 80 100 120 Frequency 0 < t < 40 4 40 < t < 80 8 80 < t < 100 16 100 < t < 12 120 120 < t < 12 140 160 Length 200 40 x 0.1 20 x 0.4 20 x 0.8 20 x 1.0 60 x 0.2 180 Distance
    15. 15. Review Write a definition of each word below. Include methods for calculating. Data set Frequency Class interval Frequency polygon Midpoint Class interval Range Histogram Frequency diagram Frequency density
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