Histograms
Histograms (Extended)
- A histogram looks like a bar chart, but bars can have different widths, and the area of each bar (not its height) gives the frequency.
Practice
On a histogram, the frequency is shown by each bar's:
With unequal widths, area (not height) represents frequency.
Frequency density
- The vertical axis is the frequency density:
$$\text{frequency density} = \frac{\text{frequency}}{\text{class width}}$$
- Worked example: frequency $25$, class width $10$ → density $= \dfrac{25}{10} = 2.5$.
Practice
A class has frequency 25 and class width 10. Find the frequency density.
25 ÷ 10 = 2.5.
Practice
A class has frequency 30 and class width 5. Find the frequency density.
30 ÷ 5 = 6.
You've got it
Key idea
- in a histogram the area of a bar = frequency (widths can differ)
- vertical axis = frequency density $= \dfrac{\text{frequency}}{\text{class width}}$
- frequency $25$, width $10$ → density $2.5$