Mapping and Clustering of Educational Facility Coverage across Regencies and Municipalities in North Sumatra Province Using K-Means in 2025

Abstract

This study aims to identify the characteristics and cluster regencies and municipalities in North
Sumatra Province based on educational facility coverage in 2025. The study uses secondary
data from Statistics Indonesia (BPS), covering 33 regencies and municipalities and four
variables: Elementary School (SD), Junior High School (SMP), Senior High School (SMA),
and Vocational High School (SMK) facility coverage. The research applies the K-Means
algorithm through several stages, including calculating educational facility coverage
percentages, data standardization using Z-Score, determining the optimal number of clusters
through the Elbow Method and Silhouette Score, and evaluating clustering performance using
Inertia, Silhouette Score, Davies-Bouldin Index, and Calinski-Harabasz Score. The evaluation
results indicate that K=2 is the optimal number of clusters, achieving a Silhouette Score of
0.4987. The clustering process produces Cluster 1, consisting of 22 regencies and municipalities
(66.67%), and Cluster 2, consisting of 11 regions (33.33%). Cluster 2 demonstrates higher
average educational facility coverage than Cluster 1 across all education levels. These findings
indicate that K-Means can identify differences in educational facility coverage among regions.
The results are expected to provide useful information for supporting educational facility
distribution planning and promoting more equitable access to education in North Sumatra
Province.