Which of the following would be classified as a derivation business rule?

The derivation business rule is characterized by its reliance on calculations or formulas that help in deriving new data from existing data elements. In the given context, option B outlines a specific method to calculate the average length of stay by dividing the sum of inpatient days by the number of discharges within a defined timeframe. This clearly demonstrates how derived metrics are generated from collected data, which aligns with the definition of a derivation business rule.

In contrast, the other options represent different types of business rules. For instance, assigning a clinical service upon a patient's admission is an established procedure but does not derive a new metric from existing data, rather it sets a requirement for patient processing. The documentation format for date of birth serves as a standardization rule, guiding how information should be recorded. Similarly, taking the hospital census at midnight outlines a procedural timeframe for data collection rather than deriving new information. These types of rules are essential, but they do not fit the criteria of a derivation business rule, making option B the clear choice for this classification.