With the development of the Internet of Things (IoT) technology, the current amount of data generated by the IoT system is increasing, and the data is continuously transmitted to the data center. The traditional IoT data processing and analysis system is inefficient and cannot handle such a large number of data streams. In addition, IoT smart devices have a resource-limited feature, which cannot be ignored during data analysis. This study proposes a new architecture ApproxECIoT (approximate edge computing IoT) suitable for real-time data stream processing of the IoT. It realizes a self-adjusting stratified sampling algorithm to process real-time data streams. The method adjusts the size of the sample strata according to the variance of each stratum while maintaining the given memory budget. This is beneficial to improving the accuracy of the calculation results when resources are limited. Finally, the experimental analysis is performed using simulated datasets and real-world datasets. The results show that ApproxECIoT can still obtain high-accuracy calculation results even with limited resources of the edge nodes.