Average dataset with many repetitions?

Stealing Pickett's example:

Values @ GroupBy[res, Query[{"p1", "p2"}], Merge@Mean] 

{
 <|"p1" -> 1, "p2" -> 1, "r1" -> 64/5, "r2" -> 20|>, 
 <|"p1" -> 1, "p2" -> 2, "r1" -> 64/5, "r2" -> 156/5|>
}

And if m keys are required:

<|KeyDrop[#, {"r1", "r2"}], "m1" -> #r1, "m2" -> #r2|> & /@ %

One way:

gathered = GatherBy[res, {#p1, #p2} &]

<| "p1" -> First[#]["p1"],
   "p2" -> First[#]["p2"],
   Merge[#[[All, {Key["r1"], Key["r2"]}]], Mean]
   |> & /@ gathered

Test:

res = {
   <|"p1" -> 1, "p2" -> 1, "r1" -> 10, "r2" -> 20|>,
   <|"p1" -> 1, "p2" -> 1, "r1" -> 15, "r2" -> 20|>,
   <|"p1" -> 1, "p2" -> 1, "r1" -> 12, "r2" -> 20|>,
   <|"p1" -> 1, "p2" -> 1, "r1" -> 13, "r2" -> 20|>,
   <|"p1" -> 1, "p2" -> 1, "r1" -> 14, "r2" -> 20|>,
   <|"p1" -> 1, "p2" -> 2, "r1" -> 10, "r2" -> 20|>,
   <|"p1" -> 1, "p2" -> 2, "r1" -> 15, "r2" -> 30|>,
   <|"p1" -> 1, "p2" -> 2, "r1" -> 12, "r2" -> 34|>,
   <|"p1" -> 1, "p2" -> 2, "r1" -> 13, "r2" -> 32|>,
   <|"p1" -> 1, "p2" -> 2, "r1" -> 14, "r2" -> 40|>
   };

gathered = GatherBy[res, {#p1, #p2} &]
<| "p1" -> First[#]["p1"],
   "p2" -> First[#]["p2"],
   Merge[#[[All, {Key["r1"], Key["r2"]}]], Mean]
   |> & /@ gathered

(* Out: {<|"p1" -> 1, "p2" -> 1, "r1" -> 64/5, "r2" -> 20|>, <|"p1" -> 1, 
  "p2" -> 2, "r1" -> 64/5, "r2" -> 156/5|>} *)

Update borrowing from Kuba.

Join @@@ Normal@GroupBy[dat, Query[{"p1", "p2"}],
   KeyMap[StringReplace[#, "r" -> "m"] &]@*Mean@*Query[All, {"r1", "r2"}]]

---

Original post

Generate some data:

SeedRandom[123];
dat = Join[#, <|"r1" -> RandomReal[10], "r2" -> RandomReal[20]|>] & /@ 
   Flatten@ConstantArray[Table[<|"p1" -> i, "p2" -> j|>, {i, 2}, {j, 2}], 4];

Use GroupBy and a few Association related functions.

KeyValueMap[
  Join[
    AssociationThread[{"p1", "p2"} -> #1],
    AssociationThread[{"m1", "m2"} -> Mean@Query[All, {"r1", "r2"} /* Values]@#2]
    ] &
  ]@GroupBy[Lookup[{"p1", "p2"}]]@dat

(*
{<|"p1" -> 1, "p2" -> 1, "m1" -> 3.19274, "m2" -> 14.7372|>, 
 <|"p1" -> 1, "p2" -> 2, "m1" -> 4.41867, "m2" -> 11.8091|>, 
 <|"p1" -> 2, "p2" -> 1, "m1" -> 3.23234, "m2" -> 7.25984|>, 
 <|"p1" -> 2, "p2" -> 2, "m1" -> 6.18188, "m2" -> 6.79438|>}
*)

Hope this helps.