SQL Average Time from timestamp stored as string

Question

I have two columns called date and starthour in a Microsoft SQL Server table.

Both columns are char; Another guy make it and I don't know why it was built in this way. :)

date                     starthour

20/01/2011               8:10:00
20/01/2011               8:20:00
20/01/2011               8:30:00
20/01/2011               8:40:00
21/01/2011               8:10:00
21/01/2011               8:20:00
21/01/2011               8:30:00

I want to determine the average starthour for each date.

date                     starthour
20/01/2011               8:25:00
21/01/2011               8:20:00

I tried the following:

SELECT date, Avg(cast(starhour as datetime())) AS starhour
FROM table
GROUP BY date

but it doesn't work.

Answer 1

SELECT [date], 
  CAST(DATEADD(second, AVG(DATEDIFF(second, 0 , starhour)), '00:00:00') AS time)
FROM dbo.test17
GROUP BY [date]

Demo on SQLFiddle