Morningstar defines the overall size of a stock fund's portfolio as the geometric mean of the market capitalization for all of the stocks it owns. It's calculated by raising the market capitalization of each stock to a power equal to that stock's stake in the portfolio. The resulting numbers are multiplied together to produce the geometric mean of the market caps of the stocks in the portfolio, which is reported as geometric average cap.
Benefit
This number is different from the fund's median market cap—the capitalization of the median stock in its portfolio. The geometric average cap better identifies the portfolio's "center of gravity." That is, it provides more accurate insight into how market trends (as defined by capitalization) might affect the portfolio.
Example
If a fund currently held equal stakes in three stocks, with market capitalizations of $2 billion, $10 billion, and $25 billion, the geometric average cap would equal:
($2 billion1/3) * ($10 billion1/3) * ($25 billion1/3) = $7.94 billion