“ShadyJ did provide actual example of this math which clearly illustrates his point.”
He provided an uncited quote to reference his own claim. Considering his well documented bias against PSA, I’d like some citation. He also stated that “there is some real industry disagreement about averaging in Pa” so it shouldn’t be hard to provide a proper citation in context of his claim.
“To whatever if that math is right or not, I don't know as I didn't check (but you're welcome to),”
He provided the claim HE should provide the evidence and citation. His claim as stated begs the question that there is a potential and valuable reason for averaging in Pa. If he claims that we shouldn’t because he says so, fine. However, if he could cite some evidence supporting his claims, that would be ideal
Now that I have permission to quote an authority on the subject from what was said in private conversation, here is what Don Keele has to say about the subject:
"I don’t agree with using Pascals to calculate the CEA-2010 average SPL one bit!!! The CEA number is a simple figure of merit and is no way based on the averages of the powers in the three bands.
The differences between the two methods are very large if extreme values in the three dB values exist! If one or two bands essentially have no power at all (like in the following example), averaging the Pascal numbers always yields a relatively bogus high value which is essentially based on the results of only one or two bands! The band(s) with no output is given no weight at all in the rating!!"
Josh Ricci also seems to have a problem with averaging in pascals,
per this post: "We will be removing the averaged output data from DB entirely at some point, due to the numerous discussions over Pa conversion vs simple averaging and some differing of opinions on what this data is supposed to be conveying to the person reviewing it."
Btw, the first person I quoted in the prior post was not Keele or Ricci but someone else in the industry who is very knowledgeable, and just because it is an uncited quote does not change the math. I have not seen a good argument for averaging in pascals. The only reason which I can see why it is being done is so CEA averages can be inflated. If the Consumer Electronics Association wanted to use Pa to represent passing output levels, the individual frequency measurements should have been represented in Pa as well.