The emergence of dockless shared e-scooters as a new form of shared micromobility offers a viable solution to specific urban transportation problems, including the first-mile-last-mile issue, parking constraints, and environmental emissions. However, this sharing service faces several challenges in daily operation, particularly related to demand volatility, battery recharging, maintenance, and regulation, owing to their trip and physical characteristics. Therefore, this study proposed a new data-driven rebalancing framework for dockless shared e-scooters that incorporates demand and variance prediction and uses Monte Carlo sampling to represent stochastic demand. Thus, demand uncertainty and the collection of low-battery and broken e-scooters were included in the rebalancing formulation to minimize user dissatisfaction and operating costs. Rebalancing optimization is an NP-hard problem, so small-size problems were solved using the integer linear programming (ILP) solver GNU Linear Programming Kit, and large-size problems were solved using a hybrid ant colony optimization-ILP algorithm (ACO-ILP). This framework was evaluated on a real-world dataset from Minneapolis, Minnesota, which demonstrated that the demand and variance prediction efficiently allocated the uncertainty while reducing the overall uncertainty, leading to shorter driving distances and lower rebalancing costs relative to baseline cases.