STDEVP

Updated 2023-10-24 14:39:47.310000

Syntax

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

Description

Use the aggregate function STDEVP to return the standard deviation for an entire population. This function differs from the built-in SQL Server STDEVP function in that it employs a two-pass and more numerically stable method for calculating the population standard deviation and under certain conditions will return a different value than the built-in function.

The standard deviation is a measure of how widely values are dispersed from the mean. The equation for STDEVP is:

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

Arguments

@x

the values used in the population 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 measure the standard deviation for a sample, then use the STDEV function.

NULL values are not included in the standard deviation calculation.

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

Examples

SELECT wct.STDEVP(x) as STDEVP

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":"STDEVP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"STDEVP":"10.6563315803558"}]}

In the following example, we will use demonstrate the difference between the SQL Server STDEVP calculation and XLeratorDB STDEVP 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 STDEVP(x) as [SQL SERVER STDEVP],

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

       STDEVP(x - 1000000000) as [SQL SERVER STDEVP 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 STDEVP 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 STDEVP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"XLDB STDEVP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"SQL SERVER STDEVP adjusted","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"SQL SERVER STDEVP":"513.945997848023","XLDB STDEVP":"2.91608615295645","SQL SERVER STDEVP adjusted":"2.91608615296582"}]}