Currently, the applications of the Internet of Things (IoT) generate a large amount of sensor data at a very high pace, making it a challenge to collect and store the data. This scenario brings about the need for effective data compression algorithms to make the data manageable among tiny and battery-powered devices and, more importantly, shareable across the network. Additionally, considering that, very often, wireless communications (e.g., low-power wide-area networks) are adopted to connect field devices, user payload compression can also provide benefits derived from better spectrum usage, which in turn can result in advantages for high-density application scenarios. As a result of this increase in the number of connected devices, a new concept has emerged, called TinyML. It enables the use of machine learning on tiny, computationally restrained devices. This allows intelligent devices to analyze and interpret data locally and in real time. Therefore, this work presents a new data compression solution (algorithm) for the IoT that leverages the TinyML perspective. The new approach is called the Tiny Anomaly Compressor (TAC) and is based on data eccentricity. TAC does not require previously established mathematical models or any assumptions about the underlying data distribution. In order to test the effectiveness of the proposed solution and validate it, a comparative analysis was performed on two real-world datasets with two other algorithms from the literature (namely Swing Door Trending (SDT) and the Discrete Cosine Transform (DCT)). It was found that the TAC algorithm showed promising results, achieving a maximum compression rate of 98.33%. Additionally, it also surpassed the two other models regarding the compression error and peak signal-to-noise ratio in all cases.