select time, coalesce(count(case when activities = 3 then 1 end), 0) as count
from MyTable
group by time
SQL Fiddle Example
Output:
| TIME | COUNT |
-----------------
| 13:00 | 2 |
| 13:15 | 2 |
| 13:30 | 0 |
| 13:45 | 1 |
If you want to count all the activities in one query, you can do:
select time,
coalesce(count(case when activities = 1 then 1 end), 0) as count1,
coalesce(count(case when activities = 2 then 1 end), 0) as count2,
coalesce(count(case when activities = 3 then 1 end), 0) as count3,
coalesce(count(case when activities = 4 then 1 end), 0) as count4,
coalesce(count(case when activities = 5 then 1 end), 0) as count5
from MyTable
group by time
The advantage of this over grouping by activities, is that it will return a count of 0 even if there are no activites of that type for that time segment.
Of course, this will not return rows for time segments with no activities of any type. If you need that, you'll need to use a left join with table that lists all the possible time segments.
