K-Fold Cross-Validation

Problem

You are evaluating a model using $K$-fold cross-validation on $N$ data points. Each fold produces a test error $e_k$.

Compute:

1. The mean CV error: $\text{CV} = \frac{1}{K}\sum_{k=1}^{K} e_k$

2. The standard error: $\text{SE} = \sqrt{\frac{s^2}{K}}$ where $s^2 = \frac{1}{K-1}\sum_{k=1}^{K}(e_k - \text{CV})^2$

Input Format

• Line 1: Two space-separated integers N K
• Line 2: $K$ space-separated floats (the fold errors)

Output Format

Two space-separated values: mean_error standard_error, each to 4 decimal places.