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I came across this thread while trying to answer the same question for the leadership at my company. I lead a team of statisticians and the execs constantly lump us in with the analysts. What I see the analysts doing (and this is my perception, not necessarily reality) is a lot of SQL, Excel pivot tables, PHP generated web pages based on the SQL and Excel tables to put data in front of whoever is asking for it.
My position is that you don't need a statistician for that. I have my team focused on root cause analysis, process control, designing experiments, defining sampling methods for A|B testing, and producing BI tools that fill the needs of different members of the business.
Am I being an intellectual snob?
Also read our discussion Can data scientists replace business analysts?.