VAR_P

Updated 2024-02-13 19:57:57.577000

Syntax

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

Description

Use the aggregate function VAR_P to calculate the variance for an entire population. VAR_P is a numerically stable single-pass calculation of the population variance which will produce more reliable results under certain conditions than the built-in SQL Server function VARP, without compromising performance.

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

@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 variance for a sample, then use the VAR_S function.

To calculate the population standard deviation use the STDEV_P function.

To calculate the sample standard deviation use the STDEV_S function.

To calculate a running population variance use the RunningVARP function.

To calculate a moving population variance use the MovingVARP function.

Examples

SELECT wct.VAR_P(x) as VAR_P
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":"VAR_P","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"VAR_P":"6.42828821986598E-10"}]}

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

SELECT wct.VAR_P(x) as XLeratorDB,
       VARP(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":"6.42828821986598E-10","SQL Server":"0"}]}