Variance

Variance ( series ) : Real

Parameter	Type		Description
series	Field, Array	→	Data for which to return the variance
Function result	Real	←	Variance of series

Description

Variance returns the variance for series. If series is an indexed field, the index is used to find the variance.

You can pass an array (one or two dimensions) in series. In this case, the array must be of the Integer, Longint or Real type.

The variance of a set of values is their average squared deviation from the mean. Its measures the dispersion of values around the mean. 4D uses the following variance formula:

Variance(x) = Sum (x-m)*(x-m)/(n-1)
m = Mean
n = Number of values

If the values considered are not a sample, multiple the value returned by Variance by (n-1)/n.

Example 1

The following example is an object method for the variable var. The object method assigns the sum of squares for a data series to var:

 var:=Variance(Students]Grades)

The following method is called to print the records in the selection and to activate break processing:

 ALL RECORDS([Students])
 ORDER BY([Students];[Students]Class;>)
 BREAK LEVEL(1)
 ACCUMULATE([Students]Grades)
 OUTPUT FORM([Students];"PrintForm")
 PRINT SELECTION([Students])

Note: The parameter to the BREAK LEVEL command should be equal to the number of breaks in your report. For more information about break processing, refer to the chapter Printing.

Example 2

This example gets the variance of the values placed in an array:

 ARRAY REAL($ArrGrades;0)
 QUERY([Exams];[Exams]Exam_Date=!01/07/11!)
 SELECTION TO ARRAY([Exams]Exam_Grade;$ArrGrades)
 vVariance:=Variance($ArrGrades)

See also

Average
Std deviation
Sum
Sum squares

Properties

Command number	27
Thread safe	✓