I believe that the Grand Total uses the aggregation defined on the measure. So, if your measure is defined to aggregate as SUM, then the Grand Total would also be calculated as a SUM as described here.
Would it work if you had a duplicate copy of the measure to show the average across the set?
So how do you "create a duplicate copy of the measure and get it to average across the set"?
Right click on the measure and select 'Duplicate', which will now create a measure with a suffix of (Copy).
On the new measure, right click and select Field Propertieis > Aggregation > Average.
Does that help?