About Jenks' natural breaks
The Jenks' natural breaks classification scheme determines the best arrangement of values into classes by iteratively comparing sums of the squared difference between observed values within each class and class means. The "best" classification identifies breaks in the ordered distribution of values that minimizes within-class sum of squared differences. For datasets with many values, such as counties across the United State, the iterative nature of Jenks' natural breaks method can lead to long calculation times.
which can be substituted to
A is the set of values that have been ordered from 1 to N.
1 ≤ i < j < N
Meani..j is the mean of the class bounded by i and j.