There is now well established practices associated with doing an analysis of data collected by other people, know as secondary analysis. In some respects there is a family resemblance to this kind of analysis and systematic reviews.
Ashley Crossman has a useful account of the approach.
Janet Heaton also offers a useful overview of the issues associated with secondary analysis. There is a more recent version of the overview here1.
There is also a useful chapter on secondary analysis in an ebook2 that be borrowed from the library.
Sociological Research Online published a special issue concerned with Reusing Qualitative data.
There is a large number of research data sets in education that are publicly available.