So if you couldn't figure out the question from the title, does the subordinating conjunction (the word "that") precede or succeed the extra information between the commas?
1 Answer
The first version is the correct one. On average relates to the information you found out, not to your finding it.
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I think the principle here can be clearly illustrated with something like He knew that tomorrow he would die - where if we move the word that to after "adverbial" tomorrow, we end up with something that's clearly nonsense: He knew tomorrow that he would die. But in OP's exact context it's not that obvious to me that every native speaker would particularly notice and/or interpret the two versions differently. And that's even more the case if we replace on average by, say, obviously (in which case both versions mean "more or less" the same to me). Commented Dec 9, 2020 at 13:36
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Yes, I agree that many native speakers might not notice. Commented Dec 9, 2020 at 19:49
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Actually, I think there are potentially three possible parsings for such constructions, even if they net down to only one or two possible meanings. The flexibly interpreted adverbial element might attach to the verb in the "lead-in clause" (I found, He knew) or to the following "that-clause", but it could ALSO sometimes be seen as a "whole sentence adverb". Which in practice would normally carry one or other of the previous two senses, but I'm guessing you could contrive examples where it really does have a third meaning. Commented Dec 10, 2020 at 12:12