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XLeratorDB/statistics Documentation

SQL Server sample variance function


VAR_S

Updated: 24 May 2013


Use the aggregate function VAR_S to estimate variance based on a sample, or use VAR_S to estimate the population variance from a sample of N elements with an unknown mean (the mean being calculated from the sample itself). VAR_S is a numerically stable single-pass calculation of the sample variance which will produce more reliable results under certain conditions than the built-in SQL Server function VAR, without compromising performance.
The formula for the calculation of the sample variance is:

XLeratorDB Sample Variance formula for SQL Server
Syntax
Syntax for XLeratorDB Sample Variance function for SQL Server
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 the entire population, then use the VAR_P 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 sample variance use the RunningVAR function.
·         To calculate a moving sample variance use the MovingVAR function.
Examples
SELECT wct.VAR_S(x) as VAR_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
                 VAR_S
----------------------
 6.92277192908644E-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_S(x) as XLeratorDB
,VAR(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
---------------------- ----------------------
 6.92277192908644E-10                      0
 


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