Find constant minimizing absolute error
Company: Citadel
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Technical Screen
You have a dataset of real-valued targets \(y_1, y_2, \dots, y_n\). You want to fit a **constant** predictor (no features):
- Prediction: \(\hat y_i = c\) for all \(i\)
- Objective (L1 loss):
\[
E(c) = \sum_{i=1}^n |y_i - c|
\]
**Task:** Find the value(s) of \(c\) that minimize \(E(c)\). Describe what happens when \(n\) is odd vs. even, and how to compute \(c\) from the data.
Quick Answer: This question evaluates understanding of L1 loss minimization, robust central-tendency estimators, and order-statistics reasoning for point estimation from real-valued samples.