Develop your statistical competence
There have been several occassions in my work history when something out of the world of applied statistics struck me as being rather insightful. There was the time when a customer told us he knew our data was suspect because there were no tails in the distribution. At a different company we discovered cheating by simply plotting measured data. And my first formal designed experiment revealed something new about a process and about a technology that was not known in the industry. I was a junior employee at this point and I recognized that here was a body of knowledge, a discipline that was well worth knowing.
Most of my work has been in manufacturing and in this industry we tend to have a lot of data about our products and about our processes. Many companies also have Quality Engineers and Six Sigma Black Belts who are skilled in statistical methods and data analysis. But you don't need to have such qualifications to get started. You simply need to be curious enough about why a process performs the way it does, why defects show up in the manner in which they do, why some products perform better than others. This curiosity will drive you to look at the right data and this is the beginning of learning insights about your work processes.
If you want to develop your statistical competence but don't know where to begin, start with a key problem and work forward from there.