\begin{definition}[Definition:Cumulative Rounding Error]
Let $S$ be a set of continuous data which is to be rounded to the nearest $n$th power of $10$.
The '''cumulative rounding error''' of $S$ is defined as:
:$R = \ds \sum_{x \mathop \in S} \paren {x - \overline x}$
where $\overline x$ denotes the rounded value of a given $x$.
\end{definition}