When you're looking for statistics, it is helpful to ask "who cares about this information?" Look for organizations concerned with your topic and see if any of them have published data relevant to your research. For example:
Statistics about job losses in the US --> US Department of Labor
Data about the global spread of AIDS --> World Health Organization
California high school graduation rate --> California Department of Education
Pay attention to the methodology used to collect the statistics. If you decide to compare data from different sources, you want to be sure you are not comparing apples to oranges!
Remember: it is entirely possible that the statistics you're looking for have never been collected and/or published.