By "range of operation" of the transporter, I mean "distance up to which it could transport" or "distance from which it could transport something to its own location".
The range of operation would have increased with time without a doubt but I want to know the average range at any period. It'll be better if you provide full stats of all times.
Answer
From Memory Alpha's page on Transporters:
During the 22nd century, standard Earth transporter systems had a range of 10,000 kilometers; however, by the 24th century, standard transporter systems maximum range was about 40,000 kilometers, though a special type of transport, called subspace transport could beam over several light years. [...] Many 24th century starships were equipped with an emergency transporter system, but these only had a range of at best ten kilometers.
[...]
The maximum range of a transporter differs per species, depending on what kind of technologies they've used to build it. The transporter with the longest known range is that of the Sikarians, with a range of about 40,000 light years; however this was due to their planet's large quartz mantle which amplifies their transporter signal. Because of this, Sikarian transporter technology works only on their planet.
[...]
Gary Seven's mysterious sponsors on the Assigners' planet possessed transporter technology with a range of at least a thousand light years according to Spock. Scotty later noted that Seven's beam was so powerful it fused all of recording circuits, and therefore he could not say exactly how far it transported Seven, or even whether it transported him through time. Exactly how they achieved this effect remains unknown, since there has been no subsequent contact with them, and they hide their entire homeworld in some fashion.
[...]
The Vedala, one of the oldest space-faring races, also possessed transporter technology capable of beaming people and equipment to and from other planets (presumably in different star systems.) (TAS: "The Jihad") Dominion transporter technology, enhanced with a homing transponder, was said to have a range of at least three light years.
(Emphasis added)
Note; Gary Seven's people are identified as the 'Aegis' in several books & comics.
As Wikis mentioned, local factors can influence range, usually reducing it. (An exception being the Sikarians, who's planet's environment actually helps it.)
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