STDEV_S

Updated 2024-02-13 19:43:21.250000

Syntax

SELECT [westclintech].[wct].[STDEV_S] (
  <@Known_x, float,>)

Description

Use the aggregate function STDEV_S to return the estimated standard deviation based on a sample. The standard deviation is a measure of how widely values are dispersed from the mean. STDEV_S is a numerically stable single-pass calculation of the sample standard deviation which will produce more reliable results under certain conditions than the built-in SQL Server function STDEV, without compromising performance.

The formula for the calculation of the sample standard deviation is:

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

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 Type

float

Remarks

If you want measure the standard deviation for the entire population, then use the STDEV_P function.

To calculate the sample variance use the VAR_S function.

To calculate the population variance use the VAR_P function.

To calculate a running sample standard deviation use the RunningSTDEV function.

To calculate a moving sample standard deviation use the MovingSTDEV function.

Examples

SELECT wct.STDEV_S(x) as STDEV_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

{"columns":[{"field":"STDEV_S","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"STDEV_S":"2.63111609950729E-05"}]}

In this example, using the same data, we compare the XLeratorDB value to the value returned by the native SQL Server function.

SELECT wct.STDEV_S(x) as XLeratorDB,

       STDEV(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.

{"columns":[{"field":"XLeratorDB","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"SQL Server","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"XLeratorDB":"2.63111609950729E-05","SQL Server":"0"}]}