Find constant minimizing absolute error

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.