A scalable analysis system is described herein that performs common data analysis operations such as distinct counts and data grouping in a more scalable and efficient manner. The system allows distinct counts and data grouping to be applied to large datasets with predictable growth in the cost of the operation. The system dynamically partitions data based on the actual data distribution, which provides both scalability and uncompromised performance. The system sets a budget of available memory or other resources to use for the operation. As the operation progresses, the system determines whether the budget of memory is nearing exhaustion. Upon detecting that the memory used is near the limit, the system dynamically partitions the data. If the system still detects memory pressure, then the system partitions again, until a partition level is identified that fits within the memory budget.