# SQL Server sample standard deviation function

STDEV_S

Updated: 24 May 2013

Use the aggregate function STDEV_S to return the estimated standard deviation based on a sample. The standard deviation is a measure of how widely values are dispersed from the mean. STDEV_S is a numerically stable single-pass calculation of the sample standard deviation which will produce more reliable results under certain conditions than the built-in SQL Server function STDEV, without compromising performance.
The formula for the calculation of the sample standard deviation is:

Syntax
Arguments
@Known_x
the values to be used in the calculation. @Known_x must be of a type float or of a type that implicitly converts to float.
Return Types
float
Remarks
·         If you want measure the standard deviation for the entire population, then use the STDEV_P function.
·         To calculate the sample variance use the VAR_S function.
·         To calculate the population variance use the VAR_P function.
·         To calculate a running sample standard deviation use the RunningSTDEV function.
·         To calculate a moving sample standard deviation use the MovingSTDEV function.
Examples
SELECT wct.STDEV_S(x) as STDEV_S
FROM (
SELECT 30000.0000216303 UNION ALL
SELECT 30000.0000565854 UNION ALL
SELECT 30000.000038137 UNION ALL
SELECT 30000.0000495983 UNION ALL
SELECT 30000.0000185861 UNION ALL
SELECT 30000.0000863479 UNION ALL
SELECT 30000.0000776366 UNION ALL
SELECT 30000.0000637985 UNION ALL
SELECT 30000.0000939786 UNION ALL
SELECT 30000.000031191 UNION ALL
SELECT 30000.0000550457 UNION ALL
SELECT 30000.0000207558 UNION ALL
SELECT 30000.0000805531 UNION ALL
SELECT 30000.0000241287
)n(x)
This produces the following result
STDEV_S
----------------------
2.63111609950729E-05

In this example, using the same data, we compare the XLeratorDB value to the value returned by the native SQL Server function.
SELECT wct.STDEV_S(x) as XLeratorDB
,STDEV(x) as [SQL Server]
FROM (
SELECT 30000.0000216303 UNION ALL
SELECT 30000.0000565854 UNION ALL
SELECT 30000.000038137 UNION ALL
SELECT 30000.0000495983 UNION ALL
SELECT 30000.0000185861 UNION ALL
SELECT 30000.0000863479 UNION ALL
SELECT 30000.0000776366 UNION ALL
SELECT 30000.0000637985 UNION ALL
SELECT 30000.0000939786 UNION ALL
SELECT 30000.000031191 UNION ALL
SELECT 30000.0000550457 UNION ALL
SELECT 30000.0000207558 UNION ALL
SELECT 30000.0000805531 UNION ALL
SELECT 30000.0000241287
)n(x)
This produces the following result.
XLeratorDB             SQL Server
---------------------- ----------------------
2.63111609950729E-05                      0