When people are talking about Six Sigma you often hear statements like Six Sigma is complicated, Six Sigma is for professors and statistic gurus, Six Sigma is hard to learn and so on. The reason behind this is that people often focus on tools that might be used in Six Sigma projects. Actually, Six Sigma is a company philosophy and project management methodology. The goal is to reduce variation in your processes and keep your products or services in specification as required by your customers.
Typically, when Six Sigma is installed in proper way your company has something like a Six Sigma infrastructure that massively supports your improvement strategy. One way to implement a basic Six Sigma infrastructure is shown in the picture below.
Without having installed such an infrastructure and having clearly defined the roles and responsibilities your Six Sigma approach will fail. For these basics no statistics are needed.
But yes, the Six Sigma tool box also contains a lot of statistical tools that might be used while applying the scientific problem solving approach DEFINE, MEASURE, ANALYZE, IMPROVE and CONTROL (DMAIC). As a prerequisite for using statistical tools a lot of valid (e.g. normal distributed) data are required which are often not available. Instead you will use all the other easy to learn tools like Ishikawa Diagram, Pareto Chart, FMEA, C&E Matrix, Interrelation Diagram and so on. These tools are especially useful when you want to improve transactional processes where statistical data are not available in general.
If you want to go beyond 4 Sigma and the right data are available, just consult a statistic expert who will assist you with the right selection, application and interpretation of statistical tools and results. Do not make it more complicated as it is.