histograms

Starter
In the back of your book, draw a Bar Chart to show the following information;

Starter
Height (cm)
Frequency
0
5
20
15
10
100
25
120
180
160
140
200

Starter
Problems
1) The data is continuous so there should be no gaps
2) 150 – 160 has the same height as 120 – 140, even though it represents a smaller range
A Histogram will correct both of these problems!
Height (cm)
Frequency
0
5
20
15
10
100
25
120
180
160
140
200

Histograms
20
25
30
25
20
Frequency
0.5
160 < x ≤ 200
2.5
150 < x ≤ 160
3
140 < x ≤ 150
1.25
120 < x ≤ 140
1
100 < x ≤ 120
Frequency Density
Height (cm)
To take into account the size of the group, we calculate ‘Frequency Density’
Frequency Density
Frequency
Classwidth
=
Frequency Density
20
20
=
1
=
30
10
3
=
25
20
1.25
=
20
40
0.5
=
25
10
2.5
=

Histograms
100
140
130
120
150
160
180
170
110
200
190
1
2
3
0
Frequency Density
Height (cm)

Histograms
With a Histogram, area represents Frequency, not the height
eg) The first group is a rectangle measuring 20 by 1
20 x 1 = 20 so there were 20 people in the group
eg) The fifth group is a rectangle measuring 40 by 0.5
40 x 0.5 = 20 so there were 20 people in the group

Histograms
To take into account the size of the group, we calculate ‘Frequency Density’
Frequency Density
Frequency
Classwidth
=
Frequency Density
=
10
40
0.25
=
2
20
70 < x ≤ 80
7
35
65 < x ≤ 70
4
20
60 < x ≤ 65
1.8
18
50 < x ≤ 60
1.5
15
40 < x ≤ 50
0.25
10
0 < x ≤ 40
Frequency Density
Frequency
Speed (mph)
18
10
1.8
=
35
5
7
=
20
5
4
=
15
10
1.5
=
20
10
2
=

Histograms
0
80
40
30
20
10
60
50
70
10
2
8
6
4
0
Frequency Density
Speed (mph)

Histograms
0
80
40
30
20
10
60
50
70
10
2
8
6
4
0
Frequency Density
Speed (mph)
Group 1 is a 40 by 0.25 rectangle
40 x 0.25 = 10
So 10 people in the group
Remember that Area represents Frequency!
Group 5 is a 5 by 7 rectangle
5 x 7 = 35
So 35 people in the group

Plenary
(4)
33g
103g
Frequency Density
0.5
2.2
5.3
0.5

Plenary
1
Frequency Density
6
5
4
3
2
Egg Weight (g)