Average length (in words) of paragraphs in document

How picky are you about what counts as a word?:

ExampleData[{"Text", "PrideAndPrejudice"}];
assoc = Association@MapIndexed[First@#2 -> # &, StringSplit[%, "."]];

WordCount /@ assoc // Total // AbsoluteTiming
(*  {7.93687, 121851}  *)

Length@*StringSplit /@ assoc // Total // AbsoluteTiming
(*  {0.102869, 122541}  *)

Divide by Length@assoc to get the average (adds negligible time).

No need for averegL[#] & and WordCount[#] &. averegL and WordCount are already functions. (Not pure functions, though, but this is not of interest for Map.)

Here, I construct a pure function with \[Function], the infix form of Function.

ParallelMap[
 text \[Function] Total[WordCount /@ text]/N[Length[text]], 
 data
]

{0.015057, <|923 -> 40., 924 -> 52., 925 -> 32.|>}