Although we said before that an axis has to start from zero in order for a graph to not be misleading, sometimes the scale needed to achieve this would be so small that it make it very hard for the reader to notice small but important differences between the bars. To get around this problem, we can use a broken axis. This basically involves cutting off sections of the graph (i.e. breaking the axis). But unlike the cropped graphs before, these ones are not misleading if they follow two basic rules. Rule number one is that they must clearly indicate the point where the axis is broken and rule number two is that a large part of the original scale should be shown to avoid over-emphasising the differences between bars. A good example of the use of a broken axis is the graph to the right. Here the scale break is clearly indicated to be above 0 and below 60 on the vertical axis, and the sections of the bars between 60 and 68 have been included so that the difference between the bars do not appear exaggerated.

Source: Statistics New Zealand

The graph to the left, in contrast, is a poor example of the use of a broken axis. Here it is not clear where the axis is actually broken. There appears to be a break at a level near the top of the Mar-95 bar, but this leaves more questions than answers. What is the height of this bar? It could be anything between $0 and $35 million. For the broken axis to have been clear, the scale break should have been at a level well below the top of the lowest bar (i.e. the Mar-95 bar).

Outcomes

12C.D.2.3

Interpret statistics presented in the media, and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view

12C.D.2.4

Assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, a bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

Graphs with Broken Axes (Investigation)