VARP

Updated 2023-10-24 14:58:57.743000

Syntax

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

Description

Use VARP to return the variance for an entire population. This function differs from the built-in SQL Server VARP 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.

For a population N having a distribution where the mean is not known, the population variance is defined as:

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

Arguments

@x

the values used in the standard deviation 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 to measure the variance for a sample, then use the VAR function.

NULL values are not included in the variance calculation.

VARP is an aggregate function and follows the same conventions as all other aggregate functions in SQL Server.

Examples

SELECT wct.VARP(x) as VARP

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":"VARP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"VARP":"113.557402750489"}]}

In the following example, we will use demonstrate the difference between the SQL Server VARP calculation and XLeratorDB VARP 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 wctMath.wct.SERIESFLOAT(0, 1, '', 1000000, 'R');

SELECT VARP(x) as [SQL SERVER VARP],

       wct.VARP(x) as [XLDB VARP],

       VARP(x - 1000000000) as [SQL SERVER VARP 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 VARP 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 VARP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"XLDB VARP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"SQL SERVER VARP adjusted","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"SQL SERVER VARP":"250181.844992","XLDB VARP":"8.49856400542397","SQL SERVER VARP adjusted":"8.498564005436"}]}