It is well-known that deep neural networks generate different predictions even given the same model configuration and training dataset. It thus becomes more and more important to study prediction variation, the variation of the predictions on a given input example, in neural network models. Dropout has been commonly used in various applications to quantify prediction variations. However, using dropout in practice can be expensive as it requires running dropout inferences many times to estimate prediction variation. We study how to estimate dropout prediction variation in a resource-efficient manner. We demonstrate that we can use neuron activation strengths to estimate dropout prediction variation under different dropout settings and on a variety of tasks using three large datasets, MovieLens, Criteo, and EMNIST. Our approach provides an inference-once alternative to estimate dropout prediction variation as an auxiliary task. Moreover, we demonstrate that using activation features from a subset of the neural network layers can be sufficient to achieve variation estimation performance almost comparable to that of using activation features from all layers, thus reducing resources even further for variation estimation.