This is K-Nearest Neighbors (KNN) -- classify by majority vote of the $k$ closest training points. With $k=3$, you likely get "Low." With $k=7$, you include more distant points -- the decision may change. The choice of $k$ is critical: small $k$ = sensitive to noise, large $k$ = smoother boundaries.

Raw differences: |50-80|=30, |30-45|=15, |0.4-0.2|=0.2. But income dominates just because of scale! Feature scaling (standardizing to mean=0, std=1) ensures all features contribute equally. Without scaling, KNN essentially ignores low-magnitude features.

KNN creates piecewise boundaries that trace around training points. Small $k$ = jagged, complex boundaries (high variance). Large $k$ = smoother boundaries (high bias). As $k \to n$, the model just predicts the overall majority class.

You just did clustering -- grouping similar items without labels. K-Means does this automatically: (1) pick $k$ random centers, (2) assign each point to the nearest center, (3) recompute centers, (4) repeat until stable. Your groups likely match: Young/Low, Middle/Medium, Older/High.

Each iteration: reassign points to nearest centroid, then recompute centroids. It stops when assignments no longer change (convergence). Different starting centroids can yield different results -- this is initialization sensitivity. Solutions: run multiple times (K-Means++) or use smart initialization.

More clusters always reduce within-cluster error, but at a cost of complexity. The elbow method looks for where adding another cluster stops helping much. Using $k = n$ gives zero error but zero insight -- every point is its own cluster. The elbow balances fit vs. parsimony.

Round 1: Cluster1={A,B,C} with new centroid=(1.5,1.5). Cluster2={D,E,F} with new centroid=(6.5,5.5). Round 2: all assignments stay the same, so the algorithm converges in 2 iterations! This is K-Means in action.