soft question - Use of the word "data" not in the statistical sense

This use seems in line -- although perhaps not identical -- with the following dictionary definition:

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Data:

1. Factual information, especially information organized for analysis or used to reason or make decisions.




2. Computer Science Numerical or other information represented in a form suitable for processing by computer.




3. Values derived from scientific experiments.

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It is often used in mathematics in the way you have identified above. Namely, when defining a mathematical structure, it gives the reader a heads up as to the fact that that the structure is "multi-sorted" and involves more than one object. In more formal language, one might say "tuple", e.g.,

"A topological group is a triple $(G,m,tau)$, where G is a set, $m: G times G rightarrow G$ is a binary operation, and $tau$ is a family of subsets of $G$, such that...."

One could also have said "A topological group is given by the data G,m,$tau$..."