Predicting product ratio by rearrangement in Dehydration Reactions
The reaction pathway I would propose for the obtained products is as below:

Coming to the percentage of each product obtained, I would defer from the data provided in the question. I would believe that V would be the major product because it is both thermodynamically and kinetically the best possible product.
I would be the next best as it is formed from the best intermediate.
Than II and IV would be the next major products as they are formed from the second best intermediate. Actually I would assume that IV would have a slight higher percentage due to the fact that it is thermodynamically more stable.
III and VI are produced in very less quantities because to form the carbocation required to form these products it has to undergo a very unfavourable rearrangement which would happen only in very less proportion.
So according to me the order should be V&gt;I&gt;IV≥II and very minor quantities of III and VI.