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XLeratorDB/statistics Documentation

SQL Server sample variance function


VAR

Updated: 28 February 2011


Note: This documentation is for the SQL2008 (and later) version of this XLeratorDB function, it is not compatible with SQL Server 2005.
Click here for the SQL2005 version of the VAR function


Use VAR to estimate variance based on a sample, or use VAR to estimate the population variance from a sample of N elements with an unknown mean (the mean being calculated from the sample itself). This function differs from the built-in SQL Server VAR function in that it employs a two-pass and more numerically stable method for calculating the standard deviation and under certain conditions will return a different value than the built-in function.
 
The equation for VAR is:
 
VAR function for SQL Server 
Syntax
XLeratorDB syntax for VAR function for SQL Server
Arguments
@x
the values used in the variance calculation. @x is an expression of type float or of a type that can be implicitly converted to float.
Return Types
float
Remarks
·         If you want measure the population variance, then use the VARP function.
·         NULL values are not included in the standard deviation calculation.
·         VAR is an aggregate function and follows the same conventions as all other aggregate functions in SQL Server.
·         If you have previously used the VAR scalar function, the VAR aggregate has a different syntax. The VAR scalar function is no longer available in XLeratorDB/statistics2008, though you can still use the scalar VAR _q.
Examples
SELECT wct.VAR(x) as VAR
FROM (VALUES
 (91.3698),
 (76.3382),
 (74.5692),
 (85.2957),
 (99.0112),
 (86.99),
 (70.7837),
 (72.834),
 (78.1644),
 (77.7472),
 (66.0627),
 (59.781),
 (68.4793),
 (78.6103),
 (59.8621)
) n(x)
 

This produces the following result
                   VAR
----------------------
      121.668645804095
 
(1 row(s) affected)


In the following example, we will use demonstrate the difference between the SQL Server VAR calculation and XLeratorDB VAR calculation. Using the XLeratorDB/math SeriesFloat function to create a million rows of randomly generated values between 1,000,000,000 and 1,000,000,010
SELECT ROUND(SeriesValue * 10, 0) + 1000000000 as x
INTO #n
FROM wctMath.wct.SERIESFLOAT(0,1,'',1000000,'R')
 
SELECT VAR(x) as [SQL SERVER VAR]
,wct.VAR(x) as [XLDB VAR]
,VAR(x-1000000000) as [SQL SERVER VAR adjusted]
FROM #n
 
DROP TABLE #n

This produces the following result. Your results will vary, since the dataset is randomly generated. The first column shows the built-in SQL Server VAR calculation, the second shows the XLeratorDB calculation and the third column shows the built-in calculation for x minus 1,000,000,000.
        SQL SERVER VAR               XLDB VAR SQL SERVER VAR adjusted
---------------------- ---------------------- -----------------------
      277965.192653193       8.49671095762951        8.49671095774196
 

(1 row(s) affected)



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