Minimizing data-to-analysis time while enabling real-time interaction and efficient analytical computations on large datasets are fundamental objectives of contemporary exploratory systems. Although some of the recent adaptive indexing and on-the-fly processing approaches address most of these needs, there are cases, where they do not always guarantee reliable performance. Some examples of such cases include: exploring areas with a high density of objects; executing the first exploratory queries or exploring previously unseen areas (where the index has not yet adapted sufficiently); and working with very large data files on commodity hardware, such as low-specification laptops. In such demanding cases, approximate and incremental techniques can be exploited to ensure efficiency and scalability by allowing users to prioritize response time over result accuracy, acknowledging that exact results are not always necessary. Therefore, approximation mechanisms that enable smooth user interaction by defining the trade-off between accuracy and performance based on vital factors (e.g., task, preferences, available resources) are of great importance. Considering the aforementioned, in this work, we present an adaptive approximate query processing framework for interactive on-the-fly analysis (with out a preprocessing phase) over large raw data. The core component of the framework is a main-memory adaptive indexing scheme (VALINOR-A) that interoperates with user-driven sampling and incremental aggregation computations. Additionally, an effective error-bounded approximation strategy is designed and integrated in the query processing process. We conduct extensive experiments using both real and synthetic datasets, demonstrating the efficiency and effectiveness of the proposed framework.