A trading firm observes daily profit values `X_1` through `X_n` and wants a metric for average performance. In an interview, you must choose between mean and median, explain the trade-offs, and discuss how you would validate the choice with simulations or historical data. ### Constraints & Assumptions - Profit distributions may be heavy-tailed. - The firm cares about both typical days and total expected profit. - Only mean and median are allowed for the initial answer. - You can ask about risk and outliers before choosing. ### Clarifying Questions to Ask - Is the objective expected profit, robustness, or risk control? - Are losses and gains symmetric? - How often do extreme outlier days occur? - Will the metric drive trading decisions or performance reporting? - Do we compare strategies with different tail risks? ### What a Strong Answer Covers ```premium-lock What a Strong Answer Covers ``` ### Follow-up Questions - When would median be misleading? - When would mean be too unstable? - What metric would you prefer if not restricted? - How would you compare two strategies with equal mean but different tail risk?