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You might have to brush up your Excel skills, since the data is only available in database or CSV form. The project has been collecting user data for years, and gwern has graciously agreed to freely host the data for a few months. Lending Club: Lending Club provides data about loan applications it has rejected as well as the performance of loans that it issued. How about an analysis of how math levels correlate with number of cigarettes smoked? The economic incentives for predicting the weather are absurd. Publishing raw data and real time statistical analysis on e-journals. For instance, you can search for NBA players born in the 80s, in cities with more than 1M inhabitants.

You can use and analyse this machine learning dataset on your local computer or cloud services provided with AWS. Today, people rarely have that level of control and visceral experience of the finished product of their work.

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Bureau of Labor Statistics: Many important economic indicators for the United States like unemployment and inflation can be found on the Bureau of Labor Statistics website.

How about fraternity members or HAM radio operators?

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Publishing raw data and real time statistical analysis on e-journals. If you need economic census data on any industry, check out census.

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Look at a billboard and instead see a virtual extension of the natural landscape. Actually, all the StackExchange data is freely available, so you could feed it more math information from both MathOverflow and the other math stackexchange.

Free your inner child social scientist. European Statistics.

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19 Free Public Data Sets for Your Data Science Project