OpenRefine (previously Google Refine) is a powerful tool for working with messy data: cleaning it; transforming it from one format into another; and extending it with web services and external data.
Weka is a collection of machine learning algorithms for data mining tasks. It contains tools for data preparation, classification, regression, clustering, association rules mining, and visualization.
Using the United States economy as an example, this video discusses all of statistical analysis in 3 minutes using the following questions: 1) How big is it? 2) What difference does it make? 3) Are you sure it’s not just dumb luck?