Practice — Product Analytics, Metrics & LTV (6 questions)

You join a grocery-delivery company that sells a monthly membership (flat fee, free delivery above a minimum basket). Leadership says "our metric is total orders". Growth is strong, but finance reports that membership churn is rising and support tickets per order are up. You are asked to propose how the product will be steered.

1. Propose a north-star metric and justify it against "total orders". State its exact definition (grain, window, what counts as active).
2. Draw the metric tree one level down: name 4 to 5 driver metrics and the team that would own each.
3. List 4 guardrail metrics and say which gaming move each one catches.
4. Orders per member is hard to move within a quarter and 12-month retention takes a year. Propose a proxy for the experiment OEC and describe how you would validate it before trusting it.

Six users all signed up on day 0. The table lists the days (since signup) on which each user performed the core action; 20 event rows in total.

1. Compute Day-1, Day-3 and Day-7 retention under the exact (classic) definition.
2. Compute Day-3 and Day-7 retention under the unbounded (rolling) definition, and bracketed retention for days 4 to 7.
3. Explain why the exact curve is not monotone here, what that says about the product, and which definition you would use for a product people are expected to use roughly weekly.
4. A teammate reports "Day-7 retention is 50 percent" in a deck that earlier showed Day-7 retention of 20 percent. List what you would check before celebrating.