How can I access certain information from YQL?
From reading the YQL Documentation and viewing the data sources it appears that while the yahoo.finance.quote does provide data on all the stock data, running a query on a large data set make take some time and the data may be returned in multiple pages which means that your application will have to handle the pages. It also appears that the YQL data requires a where clause in order to run so you would need to know the symbols for all of the stocks.

There is a YQL Console which allows you to access the YQL data and run queries, view the output etc. I would suggest reading the YQL documentation and running some sample queries in the YQL Console to see if the data you require is available.

To access the YQL Console you can 


Start at the YQL Console
In the top left hand corner under Datatables ensure you tick the Show Community Tables
In the search box type Finance. This should display all of the Finance tables (approx 31)
In the "Your YQL Statement" window type your YQL statment. 
In order to get the average daily volume for Yahoo you could use the following YQL:


select symbol,AverageDailyVolume from yahoo.finance.quote where symbol in ("YHOO")