# SQL Server population variance function

VAR_P

Updated: 24 May 2013

Use the aggregate function VAR_P to calculate the variance for an entire population. VAR_P is a numerically stable single-pass calculation of the population variance which will produce more reliable results under certain conditions than the built-in SQL Server function VARP, without compromising performance.
For a population N having a distribution where the mean is not known, the population variance is defined as:

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 variance for a sample, then use the VAR_S function.
·         To calculate the population standard deviation use the STDEV_P function.
·         To calculate the sample standard deviation use the STDEV_S function.
·         To calculate a running population variance use the RunningVARP function.
·         To calculate a moving population variance use the MovingVARP function.
Examples
SELECT wct.VAR_P(x) as VAR_P
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
VAR_P
----------------------
6.42828821986598E-10

In this example, using the same data, we compare the XLeratorDB value to the value returned by the native SQL Server function.
SELECT wct.VAR_P(x) as XLeratorDB
,VARP(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
---------------------- ----------------------
6.42828821986598E-10                      0