A broken line graph is useful when there is a large gap between the values of one of the variables.
In the context of graphs over time, this may happen for many reasons. Possible causes are that the data were not available for a period (eg during war), or the method of collection was changed. Nevertheless, if these breaks are explained, the graph can provide indications of long term trends.
The disadvantage is that data on either side of the break, may not be comparable, even with the explanations, and the naive or careless user may be misled.
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