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))