Sort of. Create a view, make sure the column  to be averaged is included.
At the bottom of the view definition, in the Totals section, select the
column, and select the Average option.

The view will display the average, but the caveat is that it will only
display the average of the items displayed on the page. So if you have
1000 items in your list, and the view only displays 100 items at a time,
the average will be for those 100 items.

Thanks for your answer, but I forgot to mention that I also wish to
graph the averages of the columns if possible. Sorry I didn't mention
it earlier. Your solution doesn't allow me to graph them.

I'm trying to use the PivotChart graph webpart, but it won't work.
Does anyone know of a graphing webpart that would graph the average
values of columns in a table?

I found out how to do what I wanted. I did not know about the Office
Spreadsheet web part, and I found using that in conjunction with the
PivotChart works nicely.

Look at the Totals section of any List View. It provides aggregates like
Count, Min, Max, Avg, etc. based upon the datatype of each column  in the
view.