Definition:Class Interval/Real Data
Definition
Let $D$ be a finite collection of $n$ data regarding some quantitative variable.
Let the data in $D$ be described by rational numbers or by real numbers.
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 $P = \set {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n} \subseteq \R$ be a subdivision of $\closedint a b$, where $a \le x_0 \le x_n \le b$.
The closed real interval $\closedint a b$, where $a \le d_{\text {min}} \le d_{\text {max}} \le b$, is said to be divided into class intervals of real intervals with endpoints $x_i$ and $x_{i + 1}$ if and only if:
- Every datum is assigned into exactly one class interval
- Every class interval is disjoint from every other class interval
- The union of all class intervals contains the entire real interval $\closedint {x_0} {x_n}$
The class intervals may be any combination of open, closed, or half-open intervals that fulfill the above criteria, but usually:
- Every class interval except the last is of the form $\closedint {x_i} {x_{i + 1} }$
- The last class interval is of the form $\closedint {x_{n - 1} } {x_n}$
By convention, the first and last class intervals are not empty class intervals.
Sources
- 2011: Charles Henry Brase and Corrinne Pellillo Brase: Understandable Statistics (10th ed.): $\S 2.1$