grammaticality - Correct vs. incorrect usage of "there were + [number] noun + verb" patterns

I am having a problem figuring out what exactly makes the following sentences incorrect, and what is different in comparison with the correct sentences below. (I am not a native English speaker, but I believe these are incorrect. Correct me if I'm wrong.)

Incorrect:

• There were two data prepared


• There was a big group of people stayed
  for chatting


• There were four types of behavior prepared as follows


• There were XX% of visitors who did not comment

Correct:

• There were 10 sensors attached on ceiling


• There were typically multiple shops associated with the keyword

I live in Asia and I am often checking scientific papers for my colleagues, and I find them making this type of mistake very often. The above are all examples taken from papers I checked. I would like to explain the correct usage to my colleagues but I could not find an easy way to do it (besides simply saying something like "avoid using there were whenever you have a verb after the noun").

Can someone provide an explanation or point me to some page which explains the rules concerning this?

---

[An edit, proposed by the OP, but which was rejected in the review queue.]

EDIT: I am late to reply but many thanks to everyone who answered or commented! @FumbleFingers: Yes, I know there are other errors in the sentences, which are seemingly not relevant to my question. I had copied the examples exactly as they appeared in the papers before correcting them. But it is exactly some of these errors that could give an idea on how people misunderstand the usage of "there is/was" and what makes it hard to explain what is the correct usage. For example, sentence 3 can be changed to: 1. There were four types of behavior, which were prepared as follows, or 2. Four types of behavior were prepared as follows. But I couldn't come up with an easy to understand explanation why this is so. I think Jim's answer gives a simple way to explain the usage to my colleagues. So @Jim, thank you! (I would vote you up but don't have enough privileges...).