## Weighted average of weights themselves

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 tendancy of the group.

Thanks,

MG.
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