VAR

Updated 2023-10-24 14:51:32.233000

Syntax

SELECT [westclintech].[wct].[VAR] (
  <@x, float,>)

Description

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:

\frac{1}{N-1} \sum_{j=0}^{N-1}(x_j-\bar{x})^2

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 Type

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.

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

{"columns":[{"field":"VAR","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"VAR":"121.668645804095"}]}

In the following example, we will use demonstrate the difference between the SQL Server VAR calculation and XLeratorDB VAR calculation. Using the 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 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.

{"columns":[{"field":"SQL SERVER VAR","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"XLDB VAR","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"SQL SERVER VAR adjusted","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"SQL SERVER VAR":"277965.192653193","XLDB VAR":"8.49671095762951","SQL SERVER VAR adjusted":"8.49671095774196"}]}