Trying to get the average of a count resultset

You just can put your query as a subquery:

SELECT avg(count)
  FROM 
    (
    SELECT COUNT (*) AS Count
      FROM Table T
     WHERE T.Update_time =
               (SELECT MAX (B.Update_time )
                  FROM Table B
                 WHERE (B.Id = T.Id))
    GROUP BY T.Grouping
    ) as counts

Edit: I think this should be the same:

SELECT count(*) / count(distinct T.Grouping)
  FROM Table T
 WHERE T.Update_time =
           (SELECT MAX (B.Update_time)
              FROM Table B
             WHERE (B.Id = T.Id))