Calculating percentile rankings in MS SQL

Question

What\'s the best way to calculate percentile rankings (e.g. the 90th percentile or the median score) in MSSQL 2005?

I\'d like to be able to select the 25th, median,

Answer 1

I've been working on this a little more, and here's what I've come up with so far:

CREATE PROCEDURE [dbo].[TestGetPercentile]

@percentile as float,
@resultval as float output

AS

BEGIN

WITH scores(score, prev_rank, curr_rank, next_rank) AS (
    SELECT dblScore,
        (ROW_NUMBER() OVER ( ORDER BY dblScore ) - 1.0) / ((SELECT COUNT(*) FROM TestScores) + 1)  [prev_rank],
        (ROW_NUMBER() OVER ( ORDER BY dblScore ) + 0.0) / ((SELECT COUNT(*) FROM TestScores) + 1)  [curr_rank],
        (ROW_NUMBER() OVER ( ORDER BY dblScore ) + 1.0) / ((SELECT COUNT(*) FROM TestScores) + 1)  [next_rank]
    FROM TestScores
)

SELECT @resultval = (
    SELECT TOP 1 
    CASE WHEN t1.score = t2.score
        THEN t1.score
    ELSE
        t1.score + (t2.score - t1.score) * ((@percentile - t1.curr_rank) / (t2.curr_rank - t1.curr_rank))
    END
    FROM scores t1, scores t2
    WHERE (t1.curr_rank = @percentile OR (t1.curr_rank < @percentile AND t1.next_rank > @percentile))
        AND (t2.curr_rank = @percentile OR (t2.curr_rank > @percentile AND t2.prev_rank < @percentile))
)

END

Then in another stored procedure I do this:

DECLARE @pct25 float;
DECLARE @pct50 float;
DECLARE @pct75 float;

exec SurveyGetPercentile .25, @pct25 output
exec SurveyGetPercentile .50, @pct50 output
exec SurveyGetPercentile .75, @pct75 output

Select
    min(dblScore) as minScore,
    max(dblScore) as maxScore,
    avg(dblScore) as avgScore,
    @pct25 as percentile25,
    @pct50 as percentile50,
    @pct75 as percentile75
From TestScores

It still doesn't do quite what I'm looking for. This will get the stats for all tests; whereas I would like to be able to select from a TestScores table that has multiple different tests in it and get back the same stats for each different test (like I have in my example table in my question).

Answer 2

The 50th percentile is same as the median. When computing other percentile, say the 80th, sort the data for the 80 percent of data in ascending order and the other 20 percent in descending order, and take the avg of the two middle value.

NB: The median query has been around for a long time, but cannot remember where exactly I got it from, I have only amended it to compute other percentiles.

DECLARE @Temp TABLE(Id INT IDENTITY(1,1), DATA DECIMAL(10,5))

INSERT INTO @Temp VALUES(0)
INSERT INTO @Temp VALUES(2)
INSERT INTO @Temp VALUES(8)
INSERT INTO @Temp VALUES(4)
INSERT INTO @Temp VALUES(3)
INSERT INTO @Temp VALUES(6)
INSERT INTO @Temp VALUES(6)
INSERT INTO @Temp VALUES(6) 
INSERT INTO @Temp VALUES(7)
INSERT INTO @Temp VALUES(0)
INSERT INTO @Temp VALUES(1)
INSERT INTO @Temp VALUES(NULL)


--50th percentile or median
SELECT ((
        SELECT TOP 1 DATA
        FROM   (
                SELECT  TOP 50 PERCENT DATA
                FROM    @Temp
                WHERE   DATA IS NOT NULL
                ORDER BY DATA
                ) AS A
        ORDER BY DATA DESC) + 
        (
        SELECT TOP 1 DATA
        FROM   (
                SELECT  TOP 50 PERCENT DATA
                FROM    @Temp
                WHERE   DATA IS NOT NULL
                ORDER BY DATA DESC
                ) AS A
        ORDER BY DATA ASC)) / 2.0


--90th percentile 
SELECT ((
        SELECT TOP 1 DATA
        FROM   (
                SELECT  TOP 90 PERCENT DATA
                FROM    @Temp
                WHERE   DATA IS NOT NULL
                ORDER BY DATA
                ) AS A
        ORDER BY DATA DESC) + 
        (
        SELECT TOP 1 DATA
        FROM   (
                SELECT  TOP 10 PERCENT DATA
                FROM    @Temp
                WHERE   DATA IS NOT NULL
                ORDER BY DATA DESC
                ) AS A
        ORDER BY DATA ASC)) / 2.0


--75th percentile
SELECT ((
        SELECT TOP 1 DATA
        FROM   (
                SELECT  TOP 75 PERCENT DATA
                FROM    @Temp
                WHERE   DATA IS NOT NULL
                ORDER BY DATA
                ) AS A
        ORDER BY DATA DESC) + 
        (
        SELECT TOP 1 DATA
        FROM   (
                SELECT  TOP 25 PERCENT DATA
                FROM    @Temp
                WHERE   DATA IS NOT NULL
                ORDER BY DATA DESC
                ) AS A
        ORDER BY DATA ASC)) / 2.0