Histograms
A histogram looks like a A type of graph showing values that are represented by rectangular bars., except the area of the bar, and not the height, shows the frequency of the Values, typically letters or numbers.. Histograms are typically used when the data is in groups of unequal width.
The table shows the ages of 25 children on a school trip.
| Age | Frequency |
| 5-10 | 6 |
| 11-15 | 15 |
| 16-17 | 4 |
| Age | 5-10 |
|---|---|
| Frequency | 6 |
| Age | 11-15 |
|---|---|
| Frequency | 15 |
| Age | 16-17 |
|---|---|
| Frequency | 4 |
Each class, or category, is not equally sized, which is typical in a histogram question. This is called unequal class intervals.
To draw a histogram for this information, first find the class width of each category.
| Age | Frequency | Class width |
| 5-10 | 6 | 6 (5, 6, 7, 8, 9 and 10 are in this category) |
| 11-15 | 15 | 5 |
| 16-17 | 4 | 2 |
| Age | 5-10 |
|---|---|
| Frequency | 6 |
| Class width | 6 (5, 6, 7, 8, 9 and 10 are in this category) |
| Age | 11-15 |
|---|---|
| Frequency | 15 |
| Class width | 5 |
| Age | 16-17 |
|---|---|
| Frequency | 4 |
| Class width | 2 |
The area of the bar represents the frequency, so to find the height of the bar, divide frequency by the class width. This is called frequency density.
| Age | Frequency | Class width | Frequency density |
| 5-10 | 6 | 6 (5, 6, 7, 8, 9 and 10 are in this category) | \(6 \div 6 = 1\) |
| 11-15 | 15 | 5 | \(15 \div 5 = 3\) |
| 16-17 | 4 | 2 | \(4 \div 2 = 2\) |
| Age | 5-10 |
|---|---|
| Frequency | 6 |
| Class width | 6 (5, 6, 7, 8, 9 and 10 are in this category) |
| Frequency density | \(6 \div 6 = 1\) |
| Age | 11-15 |
|---|---|
| Frequency | 15 |
| Class width | 5 |
| Frequency density | \(15 \div 5 = 3\) |
| Age | 16-17 |
|---|---|
| Frequency | 4 |
| Class width | 2 |
| Frequency density | \(4 \div 2 = 2\) |
Once the frequency densities of the numbers are known, the histogram can be drawn.