Updated: 31 Oct 2012

Use RunningSTDEV to calculate the sample standard deviation of column values in an ordered resultant table, without the need for a self-join. The standard deviation is calculated over all the values from the first value to the last value in the ordered group or partition. If the column values are presented to the functions out of order, an error message will be generated.

SELECT [Example].[wct].[RunningSTDEV](

<@Val, float,>

,<@RowNum, int,>

,<@Id, tinyint,>)

GO

the value passed into the function. *@Val* is an expression of type **float** or of a type that can be implicitly converted to **float**.

the number of the row within the group for which the sum is being calculated. If *@RowNum* for the current row in a set is less than or equal to the previous *@RowNum* and *@RowNum* is not equal to 1, an error message will be generated.* @RowNum* is an expression of type **int** or of a type that can be implicitly converted to **int**.

a unique identifier for the RunningSTDEV calculation. *@Id* allows you to specify multiple RunningSTDEV calculations within a resultant table. *@Id* is an expression of type **tinyint** or of a type that can be implicitly converted to **tinyint**.

· If *@Id* is NULL then *@Id* = 0.

· To calculate moving standard deviations, use the MovingSTDEV function.

· If *@RowNum* is equal to 1, RunningSTDEV is equal to NULL

· *@RowNum* must be in ascending order.

· There may be cases where the order in which the data are returned to the function and the order in which the results are returned are different, generally due to parallelism. You can use OPTION(MAXDOP 1) or OPTION(MAXDOP 1,FORCE ORDER) to help eliminate this problem.

In this example, we have 20 rows of sample data from a population with a mean of 100 and a standard deviation of 15.

SELECT rn

,x

,wct.RunningSTDEV(x,rn,NULL) as [STDEV]

FROM (

SELECT 1,85.2968 UNION ALL

SELECT 2,88.2566 UNION ALL

SELECT 3,100.1934 UNION ALL

SELECT 4,116.3052 UNION ALL

SELECT 5,109.6867 UNION ALL

SELECT 6,130.3847 UNION ALL

SELECT 7,76.5458 UNION ALL

SELECT 8,99.5511 UNION ALL

SELECT 9,101.5546 UNION ALL

SELECT 10,114.318 UNION ALL

SELECT 11,100.2686 UNION ALL

SELECT 12,110.5982 UNION ALL

SELECT 13,91.4181 UNION ALL

SELECT 14,118.5804 UNION ALL

SELECT 15,126.6649 UNION ALL

SELECT 16,103.8977 UNION ALL

SELECT 17,82.2819 UNION ALL

SELECT 18,123.3369 UNION ALL

SELECT 19,98.9415 UNION ALL

SELECT 20,89.1731

) s(rn,x)

This produces the following result.

rn x STDEV

----------- --------------------------------------- ----------------------

1 85.2968 NULL

2 88.2566 2.09289465095594

3 100.1934 7.88623591920336

4 116.3052 14.086019172688

5 109.6867 13.3585832496564

6 130.3847 17.238411164915

7 76.5458 19.0647847280317

8 99.5511 17.6575161160451

9 101.5546 16.5191247575937

10 114.3180 16.1450505878186

11 100.2686 15.3277128598674

12 110.5982 14.8220936235839

13 91.4181 14.5347368987681

14 118.5804 14.6608663518127

15 126.6649 15.3853044419388

16 103.8977 14.8647794369106

17 82.2819 15.376554425524

18 123.3369 15.648435468131

19 98.9415 15.2589544074601

20 89.1731 15.2228784743608