Curriculum Performance Analytics Dashboard with Complex Aggregations

Design a PostgreSQL query that generates a comprehensive curriculum performance dashboard tracking student engagement, grade distributions, and learning trajectory across multiple courses. The dashboard must include: 1) Aggregate course completion rates by subject, 2) Median grade progression, 3) Time-to-completion metrics, and 4) Skill mastery percentiles. Implement window functions to compare student performance against institutional benchmarks, ensuring the query can handle datasets with 50,000+ student records efficiently.