Histograms
On a histogram, the area of the bar, and not the height, represents the frequency of the Values, typically letters or numbers.. Histograms are typically used when the data is in groups.
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 |
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 |
When class widths are not equally sized, they are called unequal class intervals.
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.