How Was Cumulative Locomotive Mileage Calculated ?

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In the statistical reports of railroads (including the N&W et al,) one frequently reads statements like this: Engine XXX ran 1,050-337 miles during its career. Or: In 1891, Passenger Egines made 2,093,544 miles, Freight Engines made 5,228,364 miles, Shifting Engines made 1,032,677 miles, and Distributing Engines made 274,942 miles.

These are very precise numbers. How were they derrived? Who curated them? From what reports were the mileage numbers taken? And, when an engine was used in yard service for a day, how many miles was it credited with having made?

Surely there is someone left who understands how the numbers were crunched in those days. After all, we are not talking about ancient Rome !

Bonus Question: What service was covered by "Distributing Engines" ?

      -- abram burnett,
On Line Supply-Chain E-Turnips