On-device machine learning is often constrained by limited storage, particularly in continuous data collection scenarios. This paper presents an empirical study on storage-aware learning, focusing on the trade-off between data quantity and quality via compression. We demonstrate that naive strategies, such as uniform data dropping or one-size-fits-all compression, are suboptimal. Our findings further reveal that data samples exhibit varying sensitivities to compression, supporting the feasibility of a sample-wise adaptive compression strategy. These insights provide a foundation for developing a new class of storage-aware learning systems. The primary contribution of this work is the systematic characterization of this under-explored challenge, offering valuable insights that advance the understanding of storage-aware learning.