What is the average daily opening auction volume of stocks in the Dow
Jones Industrial Average and how does this compare with their total
daily volumes?

Background: An opening "auction" is held for stocks trading on the
NYSE and AMEX to determine the price at which each day's general
trading session will open.

I would like to know the average volume (by number of shares or by
dollar value) of the opening auction as well as average total trading
volume per day.  (The latter is fairly easy to find.)

A great answer will list specific avearage opening and daily volumes
for each stock for say a month or year for the 30 stocks in the DJIA. 
A good answer will list an average of all DJIA stocks.  I am most
interested in DJIA stock, but more general information (e.g., S&P 500
stocks) would also be very helpful.