The context I have in mind, which is not particularly special though, is that there is a database storing school teacher(s') data and by using a device such as a PC, you can retrieve necessary pieces of information from it.
Ah, OK! You can use both - it really depends on the sentence.
The teachers' data as in "data about teachers" is tricky to pinpoint which one is better. I feel that "teacher data" will be used more, if I really had to say. "This database stores all sorts of teacher data, including income, class size, and even whether they have tenure or not."
The teachers' data as in "data from teachers" can more easily use both: "According to teacher(s') data, a lot of students have been absent recently." "The teachers' data has taught me a lot about the student body."