Definition:Cumulative Rounding Error

Definition
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:


 * $R = \displaystyle \sum_{x \mathop \in S} \paren {x - \overline x}$

where $\overline x$ denotes the rounded value of a given $x$.