In SQL, how can I count the number of values in a column and then pivot it so the column becomes the row?

I have a survey database with one column for each question and one row for each person who responds. Each question is answered with a value from 1 to 3.

Id    Quality?  Speed?
--    -------   -----
1     3         1
2     2         1
3     2         3
4     3         2

Now, I need to display the results as one row per question, with a column for each response number, and the value in each column being the number of responses that used that answer. Finally, I need to calculate the total score, which is the number of 1's plus two times the number of 2's plus three times the number of threes.

Question  1    2    3    Total
--------  --   --   --   -----
Quality?  0    2    2    10
Speed?    2    1    1    7

Is there a way to do this in set-based SQL? I know how to do it using loops in C# or cursors in SQL, but I'm trying to make it work in a reporting tool that doesn't support cursors.

Solution

This will give you what you're asking for:

SELECT
    'quality' AS question,
    SUM(CASE WHEN quality = 1 THEN 1 ELSE 0 END) AS [1],
    SUM(CASE WHEN quality = 2 THEN 1 ELSE 0 END) AS [2],
    SUM(CASE WHEN quality = 3 THEN 1 ELSE 0 END) AS [3],
    SUM(quality)
FROM
    dbo.Answers
UNION ALL
SELECT
    'speed' AS question,
    SUM(CASE WHEN speed = 1 THEN 1 ELSE 0 END) AS [1],
    SUM(CASE WHEN speed = 2 THEN 1 ELSE 0 END) AS [2],
    SUM(CASE WHEN speed = 3 THEN 1 ELSE 0 END) AS [3],
    SUM(speed)
FROM
    dbo.Answers

Keep in mind though that this will quickly balloon as you add questions or even potential answers. You might be much better off if you normalized a bit and had an Answers table with a row for each answer with a question code or id, instead of putting them across as columns in one table. It starts to look a little bit like the entity-value pair design, but I think that it's different enough to be useful here.