According to Wikipedia, only about 15–25% of actual sentences contain a discontinuity, and the percentage of discontinuous dependencies is even much less, approximately 1–2%. What confuses me is that sentences containing a discontinuity do not equal to discontinuous dependencies based on this explanation. Can somebody list a example to clarify the situation that can differ the situation between the two?
The next two trees are taken from the article in Wikipedia on discontinuities in syntax.
The parse on the left is a phrase structure analysis. The parse on the right is a dependency structure analysis. Both parses show a projectivity violation (= a discontinuity), as there are crossing lines. According to the numbers cited in the question, this sentence is therefore one of the 15-25% of the sentences in natural language that contain a discontinuity. Topicalization, wh-fronting, scrambing, extraposition are all mechanisms of syntax that can or must result in such discontinuities.
Now look at the dependency tree on the right more closely. That tree contains four dependency edges. Only one of those dependency edges extends across the dotted vertical projection lines. Hence there is only one dependency out of four that is discontinuous. Thus, only 25% of the dependencies in the tree are discontinuous. Taking 25% of 10-25%, one arrives at a much lower number for the overall percentage of discontinuous dependencies in the sentences of natural language. Note that the sentence here contains only 4 dependency edges and is thus a rather short sentence. Most sentences contain more dependencies, which means that the percentage of discontinuous dependencies in those sentences that contain a discontinuity comes down to a smaller number (smaller than 25%). Put all this together, and I think one can now see how Wikipedia arrives at the number of just 1-2% discontinuous dependencies altogether.