# If we have a 3x3 matrix of information where the row totals describe the total goods produced by a particular company and the column totals provide the total for a particular type of good for all companies how would I create a weighted average that tells me the average percentage Good A takes up, out of all production, for all companies? Is it necessary to weigh by company if the total number of products produced is, say, 10, 50, and 20?

If we have a $3×3$ matrix of information where the row totals describe the total goods produced by a particular company and the column totals provide the total for a particular type of good for all companies how would I create a weighted average that tells me the average percentage Good A takes up, out of all production, for all companies? Is it necessary to weigh by company if the total number of products produced is, say, $10,50$, and $20$?
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Marcel Mccullough
You will need to weight by total production. The reason being consistency: Imagine you are only told that the total production of each company. Then the total amount of A produced must equal the average fraction of A produced times the total production, which is equivalent to the average fraction of a per company.