Choose Mean or Median for Trading Profit Metrics
A trading firm observes daily profit values X_1 through X_n and wants a metric for average performance. You must choose between the mean and the median to represent this average, explain the trade-offs of each choice, and discuss how you would validate your selection using 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.
AI interview prep
Core dilemma
Balancing the sensitivity of the mean to extreme outliers (which can represent significant profit/loss events) against the robustness of the median to those same outliers (which might obscure important tail behavior).
2 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Choose Mean or Median for Trading Profit Metrics
A trading firm observes daily profit values X_1 through X_n and wants a metric for average performance. You must choose between the mean and the median to represent this average, explain the trade-offs of each choice, and discuss how you would validate your selection using 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.