  The increasing need to analyse large volumes of data has led to the
development of Symbolic Data Analysis as a promising field to tackle the data
challenges of our time. New data types, such as interval-valued data, have
brought fresh theoretical and methodological problems to be solved. In this
paper, we derive explicit formulas for computing the Mallows' distance, also
known as $L_2$ Wasserstein distance, between two \textit{p}-dimensional
intervals, using information regarding the distribution of the microdata. We
establish this distance as a Mahalanobis' distance between two
2\textit{p}-dimensional vectors. Our comprehensive analysis leads to the
generalisation of the definitions of the expected value and covariance matrix
of an interval-valued random vector. These novel results bring theoretical
support and interpretability to state-of-the-art contributions. Additionally,
we discuss real examples that illustrate how we can model different levels of
available information on the microdata, leading to proper estimates of the
measures of location and association.
