1. Unequal Class Intervals
Histograms
Unequal Class Intervals

2. Constructing a histogram from a frequency table
Example Question 1: The frequency table gives information on the speeds (mph) of a sample of drivers using a motorway. Construct a Histogram for this data. 10 20 30 40 50 60 80 70 90
100
frequency density
Speed
freq
0 - 30
240
320
500
780
960
820
640 fd
240 30 ? 8 32 50
240/30 = 8 78
320/10 = 32 96
500/10 = 50 82
780/10 = 78 16
960/10 = 96
1. The class intervals are unequal so a frequency density column is needed.
820/10 = 82
640/40 = 16
2. Scale the horizontal axis.
3. Calculate frequency densities and scale the vertical axis.
Cars 10 20 30 40 50 60 70 80 90
100
110
120
Speed mph

3. Constructing a histogram from a frequency table
Example Question 1: The frequency table gives information on the speeds (mph) of a sample of drivers using a motorway. Construct a Histogram for this data. 10 20 30 40 50 60 80 70 90
100
frequency density
Speed
freq
0 - 30
240
320
500
780
960
820
640 fd
Recorded Speeds of Cars on a Motorway 8 32 50 78 96 82 16
4. Draw the bars and title. 10 20 30 40 50 60 70 80 90
100
110
120
Speed mph

4. Ramblers 1 2 3 4 5 frequency density 5 1 ? 5 2 5  1 = 5 4 2  1 = 2 3
Example Question 2: The table shows the distance walked in miles by some ramblers on the Lincolnshire Wolds at the weekend. Draw a histogram for the data. 1 2 3 4 5
frequency density 5 1 ?
Distance
frequency fd
0  d < 1 5
1  d < 2 2
2  d < 5 12
5  d < 6 3
6  d < 10 5 2
5  1 = 5 4
2  1 = 2 3
12  3 = 4
1.25
3  1 = 3
1. The class intervals are unequal so a frequency density column is needed.
5  4 = 1.25
2. Scale the horizontal axis.
3. Calculate frequency densities and scale the vertical axis.
Ramblers 1 2 3 4 5 6 7 8 9 10
Distance (Miles)

5. Distance Walked by Ramblers
Example Question 2 The table shows the distance walked in miles by some ramblers on the Lincolnshire Wolds at the weekend. Draw a histogram for the data. 1 2 3 4 5
frequency density
Distance Walked by Ramblers
Distance
frequency fd
0  d < 1 5
1  d < 2 2
2  d < 5 12
5  d < 6 3
6  d < 10 5 2 4 3
1.25
4.Draw in the bars and title. 1 2 3 4 5 6 7 8 9 10
Distance (Miles)

6. Plants 0.1 frequency density 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 4 10
Question 3: Robert sowed some seeds in his greenhouse and measured the heights of the plants 3 months later. The results are shown in the table. Draw a histogram for this data.
0.1
frequency density
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0 4 10 ?
height (cm)
frequency fd
0  h < 10 4
10  h < 30 20
30  h < 45 9
45  h < 70 8
70  h < 100 15
0.4 1
4  10 = 0.4
0.6
20  20 = 1
0.32
9  15 = 0.6
0.5
8  25 = 0.32
1. The class intervals are unequal so a frequency density column is needed.
15  30 = 0.5
2. Scale the horizontal axis.
Plants
3. Calculate frequency densities and scale the vertical axis. 10 20 30 40 50 60 70 80 90
100
height (cm)

7. 4.Draw in the bars and title.
Question 3: Robert sowed some seeds in his greenhouse and measured the heights of the plants 3 months later. The results are shown in the table. Draw a histogram for this data.
0.1
frequency density
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Heights of Plants
height (cm)
frequency fd
0  h < 10 4
10  h < 30 20
30  h < 45 9
45  h < 70 8
70  h < 100 15
0.4 1
0.6
0.32
0.5
4.Draw in the bars and title. 10 20 30 40 50 60 70 80 90
100
height (cm)

8. Constructing a histogram from a frequency table.
Example Question 1: The frequency table gives information on the speeds (mph) of a sample of drivers using a motorway. Construct a Histogram for this data.
Speed f
0 - 30
240
320
500
780
960
820
640 fd
Worksheet 1

9. Example Question 2 The table shows the distance walked in miles by some ramblers on the Lincolnshire Wolds at the weekend. Draw a histogram for the data.
Distance
frequency fd
0  d < 1 5
1  d < 2 7
2  d < 5 12
5  d < 6 3
6  d < 10
Worksheet 2

10. Question 3. Robert sowed some seeds in his greenhouse and measured the heights of the plants 3 months later. The results are shown in the table. Draw a histogram for this data.
height (cm)
frequency fd
0  h < 10 4
10  h < 30 20
30  h < 45 9
45  h < 70 8
70  h < 100 15
Worksheet 3