6.3 Histograms
(A) Draw a histogram based on the frequency table of a grouped data
1. A histogram is a graphical representation of a frequency distribution.
2. A histogram consists of vertical rectangular bars without any spacing between them.
3. Steps for drawing a histogram
(a) Determine the lower boundaries and upper boundaries for each class interval.
(b) Choose suitable scales for the horizontal axis (x-axis) to represent class interval and the vertical axis (y-axis) to represent frequency.
Example:
The following frequency table shows the radii, in cm, of different types of trees in a garden.
Radii (cm) |
Frequency |
2.0 – 2.4 |
7 |
2.5 – 2.9 |
5 |
3.0 – 3.4 |
10 |
3.5 – 3.9 |
2 |
4.0 – 4.4 |
6 |
4.5 – 4.9 |
4 |
Draw a histogram to represent the above information.
Solution:
Solution:
Radii (cm) |
Frequency |
Lower boundary |
Upper boundary |
2.0 – 2.4 |
7 |
1.95 |
2.45 |
2.5 – 2.9 |
5 |
2.45 |
2.95 |
3.0 – 3.4 |
10 |
2.95 |
3.45 |
3.5 – 3.9 |
2 |
3.45 |
3.95 |
4.0 – 4.4 |
6 |
3.95 |
4.45 |
4.5 – 4.9 |
4 |
4.45 |
4.95 |