Definition:Class Interval/Integer Data

Definition
Let $D$ be a finite collection of $n$ data regarding some quantitative variable. Let the data in $D$ be described by natural numbers or by integers.

Let $d_{\min}$ be the value of the smallest datum in $D$.

Let $d_{\max}$ be the value of the largest datum in $D$. Let $P = \set {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n} \subseteq \Z$ be a subdivision of $\closedint a b$, where $a \le x_0 \le x_n \le b$.

The integer interval $\closedint a b$, where $a \le d_{\min} \le d_\max \le b$, is said to be divided into classes of integer intervals of the forms $\closedint {x_i} {x_{i + 1} }$ or $\closedint {x_i} {x_i}$ :


 * Every datum is assigned into exactly one class


 * Every class is disjoint from every other


 * The union of all classes contains the entire integer interval $\closedint {x_0} {x_n}$

By convention, the first and last classes are not empty classes.