Soft real-time streaming applications often process input data that evoke varying workloads for their tasks. This may lead to high energy consumption or deadline misses in case their mapping onto a heterogeneous MPSoC target architecture is not adapted, e.g., when tasks with high execution times for the current input are assigned to resources of low computational power. To handle the vast variety of different input data, we propose to cluster data with similar execution characteristics into so-called data scenarios for which we determine specialized mappings by performing a scenario-aware design space exploration (DSE). A runtime manager (RTM) uses these mappings to adapt the execution of the running applications to their upcoming input by first identifying their best-suited scenarios. Subsequently, the RTM selects mappings considering their identified scenarios, which minimize the total number of deadline misses and the consumed energy. We embed the RTM into hybrid application mapping (HAM); ergo, performing time-consuming optimizations offline. In this article, we propose a novel data-scenario-aware HAM methodology that can cope with multiple applications and comprises two novel scenario-based mapping selection algorithms: Inter-Application Resource Mediation Mapping introduces barely any runtime overhead. Adaptive multi-app mapping selection is highly adaptive to changes in the application workload but imposes a small runtime overhead. Our HAM approach is fully automated and uses machine-learning techniques to learn the selection of suitable mappings from training data sequences at design time. Experiments on three differently complex target architectures show that our proposed approach consistently outperforms existing state-of-the-art solutions regarding the number of deadline misses and consumed energy.