Skill: Identify misleading graph scales

First, inspect the axis before comparing the bars or points.

1. Read the labels and tick marks. Check what each interval represents.
2. Look for a missing zero. If the axis starts above $0$, the graph is truncated.
3. Compare the actual numbers. Do not judge the difference only by the visual lengths.
4. Explain the distortion. A truncated axis can make a small difference look large.

Worked example

A bar graph compares two students’ scores:

• Mia: $(48)$ points
• Leo: $(50)$ points

The vertical axis is labeled $(45, 46, 47, 48, 49, 50)$, so it starts at $(45)$, not $0$.

The actual difference is

$$50-48=2$$

So, Leo scored only $2$ more points than Mia.

However, because the bars begin at $(45)$, Mia’s bar rises $3$ units above the bottom of the graph, while Leo’s rises $5$ units. The graph may make Leo’s score look much greater, even though the actual scores are close.

The scale is misleading because the axis is truncated. A less misleading graph would begin at $0$, or it would clearly show that the axis begins at $(45)$. Always use the labeled values to find the real difference.