Final answer:
The seriousness of the offense is considered the most influential factor in determining the disposition of juvenile cases.
Step-by-step explanation:
The factor considered the most influential in determining the disposition of juvenile cases is the seriousness of the offense. When determining how to handle a juvenile case, the seriousness of the offense is taken into account and may influence the type of punishment or intervention that is recommended. For example, a more serious offense may result in probation, counseling, or even placement in a juvenile detention center.