Histograms
- Histograms show grouped continuous data. There are no gaps between the bars.
- When classes have different widths, the vertical axis shows frequency density, not frequency.
- Frequency density = frequency ÷ class width. The area of each bar is proportional to the frequency.
- Example: the class 10 ≤ t < 30 has frequency 16. Its width is 20, so its frequency density is 16 ÷ 20 = 0.8.
Reading histograms
- Frequency = frequency density × class width. A bar 5 wide with frequency density 3.2 has frequency 16.
- To estimate how many values lie in part of a class, assume the data is spread evenly across the class and take the matching fraction of the bar's area.
- Example: 20 ≤ x < 30 has frequency density 1.6 and 30 ≤ x < 50 has frequency density 2. The estimated number between 25 and 40 is 5 × 1.6 + 10 × 2 = 8 + 20 = 28.
Frequency polygons
- A frequency polygon plots the frequency of each class at its midpoint, joined with straight lines.
- Two frequency polygons on the same axes make it easy to compare distributions, such as the heights of Year 7 and Year 11 students.
Key terms
- Histogram
- A diagram for grouped continuous data where bar area shows frequency.
- Frequency density
- Frequency divided by class width.
- Class width
- The difference between the upper and lower class boundaries.
- Frequency polygon
- Frequencies plotted at class midpoints and joined with straight lines.
- Midpoint
- The value halfway between the class boundaries.