Histograms
Frequency density (Higher tier only)
A is like a bar chart for continuous data, but the classes can have different widths. The height of each bar is the :
Frequency density = frequency ÷ class width (learn this)
The of each bar is the frequency.
Example: find the frequency density for each class.
| Mass (m kg) | Frequency | Class width | Frequency density |
|---|---|---|---|
| 0 < m ≤ 10 | 5 | 10 | 0.5 |
| 10 < m ≤ 15 | 10 | 5 | 2 |
| 15 < m ≤ 20 | 12 | 5 | 2.4 |
| 20 < m ≤ 40 | 8 | 20 | 0.4 |
- 0 < m ≤ 10: 5 ÷ 10 = 0.5
- 10 < m ≤ 15: 10 ÷ 5 = 2
Key terms
Drawing a histogram (Higher tier only)
- Work out the frequency density for each class.
- Label the vertical axis "frequency density" and the horizontal axis with the data, using a continuous scale.
- Draw each bar from the start to the end of its class, with no gaps, up to its frequency density.
Example: describe the bars for the masses table.
- From 0 to 10, height 0.5
- From 10 to 15, height 2; from 15 to 20, height 2.4
- From 20 to 40, height 0.4
- The two narrow middle bars are the tallest, even though the 20 to 40 class is the widest
Common mistake
Don't plot the frequency: the 0 < m ≤ 10 bar has a frequency of 5 but a height of only 0.5.
Key terms
Finding frequencies from a histogram (Higher tier only)
The area of a bar is its frequency, so:
Example: a histogram bar goes from 30 to 50 with a height of 1.5. Find its frequency.
- Class width: 50 − 30 = 20
- Frequency = 1.5 × 20 = 30
Example: using the masses table, estimate how many masses are between 12 kg and 15 kg.
- The 10 < m ≤ 15 bar has a frequency density of 2
- The part from 12 to 15 is 3 wide
- 2 × 3 = about 6 masses
This is an estimate, because it assumes the values are spread evenly across the class.