Some good statistics projects for high school students are analyzing the patterns of word use in State of the Union speeches, evaluating characteristics of Donors Choose projects that get funded, and identifying the best and words neighborhoods to live in a particular city. These projects use free data available online.
One statistics project for high school students uses open data from a city's official website, such as the City of Boston. Use this data to identify several metrics for analysis, such as crime statistics and the number of parks, and calculate the best and worst neighborhoods based on these variables.
Another project uses data from several State of the Union speeches. Students use this data to identify certain words and graph the trends over time.