\begin{definition}[Definition:Class (Descriptive Statistics)/Integer Data]
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 $P = \left\{{x_0, x_1, x_2, \ldots, x_{n-1}, x_n}\right\} \subseteq \Z$ be a subdivision of $\left[{a \,.\,.\, b}\right]$, where $a \le x_0 \le x_n \le b$.
The integer interval $\left[{a \,.\,.\, b}\right]$, where $a \le d_{\min} \le d_\max \le b$, is said to be divided into '''classes''' of integer intervals of the forms $\left[{x_i \,.\,.\, x_{i+1}}\right]$ or $\left[{x_i \,.\,.\, x_i}\right]$ {{iff}}:
: 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 $\left[{x_0 \,.\,.\, x_n}\right]$
By convention, the first and last classes are not empty classes.
\end{definition}