Using frequency for the height instead of frequency density H
"The Height Mistake"
The Mistake in Action
Draw a histogram for this data:
| Height (cm) | Frequency |
|---|---|
| 140-150 | 12 |
| 150-160 | 18 |
| 160-180 | 24 |
Wrong: Student draws bars with heights 12, 18, and 24.
Why It Happens
Students treat histograms like bar charts, using frequency directly for height.
The Fix
In a histogram, area = frequency, not height.
Calculate frequency density: $$\text{FD} = \frac{\text{Frequency}}{\text{Class Width}}$$
| Height | Width | Frequency | FD |
|---|---|---|---|
| 140-150 | 10 | 12 | $12 ÷ 10 = 1.2$ |
| 150-160 | 10 | 18 | $18 ÷ 10 = 1.8$ |
| 160-180 | 20 | 24 | $24 ÷ 20 = 1.2$ |
The third bar should be the same height as the first (both 1.2), but twice as wide.
If you used frequency for height, the 160-180 bar would look like it represents more data, when actually 140-150 and 160-180 have the same frequency density!
Spot the Mistake
Can you identify where this student went wrong?
Drawing bars with heights 12, 18, and 24
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: