Dictionary of Applied Machine Learning
The mean of a random variable (RV) is its expectation, defined as the Lebesgue integral of the RV with respect to its probability distribution. The term also refers to the sample mean, i.e., the average of the data points in a dataset. The two usages are consistent: the sample mean is the mean of the RV obtained by drawing a data point uniformly at random from the dataset. For an RV with a finite second-order moment, the mean is the unique solution of a risk minimization problem under the squared error loss. For the RV associated with a dataset, this optimization problem reduces to empirical risk minimization (ERM) in the simplest regression setting: predicting a numeric label without any features, for which the learned hypothesis is the sample mean of the labels.
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@misc{dictml_mean,
author = {Jung, Alexander},
title = {mean},
howpublished = {Dictionary of Applied Machine Learning (course edition)},
year = {2026},
doi = {10.5281/zenodo.21569296},
note = {ISBN 978-952-64-3013-3, CC BY 4.0, retrieved 2026-08-06},
url = {https://dictionaryofml.org/terms/mean.html}
}