Histograms · Year 11
In Year 11 you learn: histograms and estimating frequencies from histograms.
A histogram shows grouped continuous data in bars with no gaps. The classes can have different widths, so the height of each bar is the frequency density, and the area of each bar is the frequency.
Key facts
- Frequency density = frequency ÷ class width. So frequency = frequency density × class width.
- The area of a bar is its frequency; the bars touch because the data are continuous.
- The modal class has the highest frequency density, which is not always the highest frequency.
Worked examples
Example 1
In a histogram, the bar for 20 < a ≤ 40 has a frequency density of 1.5. How many values are in that class? Estimate how many are between 25 and 40.
Answer: 30; about 22.5
Example 2
The class 0 < t ≤ 10 has a frequency of 20 and the class 10 < t ≤ 40 has a frequency of 30. Find the frequency density of each class.
Answer: 2 and 1
Example 3
Which is the modal class: 0 < x ≤ 10 with a frequency of 12, or 10 < x ≤ 30 with a frequency of 18?
Answer: 0 < x ≤ 10 (frequency density 1.2, not 0.9)
Example 4
A histogram has a bar from 0 to 10 with a frequency density of 3 and a bar from 10 to 25 with a frequency density of 2. How many values are there altogether?
Answer: 60