Weighted average of weights themselves

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The discussion centers on calculating the weighted average market capitalization of a group of 50 companies using their market caps as weights. The proposed formula involves squaring each market cap, summing these squares, and dividing by the total market cap. While this method is mathematically valid, it does not reflect the central tendency of the market caps. A suggestion is made to test the formula with a smaller sample to verify its correctness. The approach may yield interesting insights, but it is important to understand its limitations.
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Hi,

I have a list of 50 companies and their market capitalizations. (The market cap of a company is the collective value of all the shares of the company. So if a company’s share price is $10 and there exists 200 shares of the company, then the market cap of the company is $2000.)

My question is about calculating the weighted average market cap of the group. The weights I want use are the market caps themselves. So basically I am squaring each market cap value then adding them and then dividing the result with the sum of the market caps of the 50 companies.

Wt. Avg Mkt. Cap = ( M1 * M1 + M2*M2 +…………M50* M50 ) / (M1 + M2 +…..M50)

Can I do that ? I mean is it correct technically? Of course I understand that it doesn't give the central tendency of the group.

Thanks,

MG.
 
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Simplest way to check whether this makes sense is to take a small sample (say 2 or 3) out of your list, and use your formula for them.
 
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