We are seeing an explosion of uncertain data—i.e., data that is more properly represented by probability distributions or estimated values with error bounds rather than exact values—from sensors in IoT, sampling-based approximate computations and machine learning algorithms. In many cases, performing computations on uncertain data as if it were exact leads to incorrect results. Unfortunately, developing applications for processing uncertain data is a major challenge from both the mathematical and performance perspectives. This paper proposes and evaluates an approach for tackling this challenge in DAG-based data processing systems. We present a framework for uncertainty propagation (UP) that allows developers to modify precise implementations of DAG nodes to process uncertain inputs with modest effort. We implement this framework in a system called UP-MapReduce, and use it to modify ten applications, including AI/ML, image processing and trend analysis applications to process uncertain data. Our evaluation shows that UP-MapReduce propagates uncertainties with high accuracy and, in many cases, low performance overheads. For example, a social network trend analysis application that combines data sampling with UP can reduce execution time by 2.3x when the user can tolerate a maximum relative error of 5% in the final answer. These results demonstrate that our UP framework presents a compelling approach for handling uncertain data in DAG processing.