ApproxIoT is a stream analytics system that leverages approximate computing to efficiently analyze data across edge and cloud resources. It employs a weighted hierarchical sampling algorithm to sample data streams across multiple levels in a distributed edge-cloud environment. This allows ApproxIoT to provide approximate analytics results within a given error bound while maximizing resource utilization and throughput. Evaluation shows ApproxIoT achieves over 2600x higher accuracy than simple random sampling, with throughput similar to non-approximate analytics.