How do you handle a request for analysis when the requirements are vague?

Show that you interrogate the request rather than guessing and producing something unusable.

• Ask what decision it will inform. This single question resolves most vagueness. If the answer is "nothing specific", the request may not be worth doing, and saying so politely saves everyone time.
• Ask what they expect to see, and what they would do if the answer were the opposite. It reveals the real question, which is often narrower than what was asked.
• Agree definitions explicitly. "Active user", "revenue", and "customer" mean different things to different teams, and a disagreement discovered after presenting destroys the work.
• Confirm scope and timeframe — which period, which segment, which markets.
• Show something rough early. People cannot specify an analysis in the abstract but react immediately to a draft. A quick first cut with caveats surfaces the misunderstanding while it is cheap to fix.

Note: Mentioning that you write the agreed question back to the requester in one sentence before starting is a simple, concrete practice that prevents most rework — and demonstrates that you have been burned by this before.