This paper aims to provide understandings for the effect of an over-parameterized model, e.g. a deep neural network, memorizing instance-dependent noisy labels. We first quantify the harms caused by memorizing noisy instances, and show the disparate impacts of noisy labels for sample instances with different representation frequencies. We then analyze how several popular solutions for learning with noisy labels mitigate this harm at the instance level. Our analysis reveals that existing approaches lead to disparate treatments when handling noisy instances. While higher-frequency instances often enjoy a high probability of an improvement by applying these solutions, lower-frequency instances do not. Our analysis reveals new understandings for when these approaches work, and provides theoretical justifications for previously reported empirical observations. This observation requires us to rethink the distribution of label noise across instances and calls for different treatments for instances in different regimes.