A good idea for a statistics project would be to investigate the distributions of returns for different investments, and then construct and manage a model portfolio. Different asset classes such as money markets, bonds, equities and commodities could be compared.
Two very different distributions may have the same mean or standard deviation. Investors have been concerned with owning investments that possess "fat tails," or higher than normal frequencies of outcome at both ends of an investment's distribution. Constructing a model portfolio based on distributions that complement each and observing the portfolio's performance in real markets are excellent ways to practice methods for building and analyzing statistical distributions of different asset returns. Adjusting the portfolio as distributions change over time provides insight into the mechanics of financial markets and the relation of different asset classes. Finally, a distribution of returns for the model portfolio itself may be constructed and analyzed.