Spot on! I agree that paying extra attention to data analysis is important, especially for people who are not coming from STEM fields (where it’s often a part of the curriculum). More specifically, I’ve found that having a good grasp of statistics has been very valuable in both designing and evaluating product metrics and working with DevOps on SLAs.
Becoming a better writer is something everyone should focus on, but it’s definitely critical for product managers. Early in my career my desk neighbor and I would check each other’s emails before sending them out, but even today I often ask someone to give important emails a quick gander.
My favorite book to improve one’s writing is “How to Write” by Herbert and Jill Meyer. I would buy it for our interns and new PMs and can’t recommend it enough.