The core objective of Jenks is simple: minimize within-class variance while maximizing between-class differences.
Imagine plotting your exam scores on a single number line. Jenks looks for natural "gaps" or dips in the frequency of the data.
It groups similar values together.
It maximizes the distance between the boundaries of different classes.
It functions similarly to the ANOVA (Analysis of Variance) statistical test, running iterations to find the exact cutoffs (breaks) that create the most distinct groupings possible for your chosen number of classes ($K$).
Why It’s Great for Exam Scores
If you want to grade a sorted list of exam scores, Jenks is often a much better choice than GMM or K-Means because:
It respects 1D ordering: It inherently understands that numbers are on a linear scale, preventing weird anomalies like the high and low ends grouping together.
It highlights natural clusters: If there is a distinct gap between passing and failing students, or between B-grade and A-grade students, Jenks will place the class boundaries directly inside those natural gaps.
No distribution assumptions: Unlike GMM, it doesn't assume your data follows a normal (bell-curve) distribution. Real-world exam scores are frequently skewed or multi-modal, which Jenks handles effortlessly.
