Building on Part 1 and Part 2, we continue extending the native 4D.Vector class with the lightweight utility class VectorUtility.
In this part we add two very practical functions:

calculateVariance
calculateStdDev

These functions let you quickly measure the dispersion or spread of any collection of numbers.

property defaultDimension : Integer Class constructor  This.defaultDimension:=3 ... Function calculateVariance($values : Collection) : Real   If ($values.length<2)     return 0   End if   var $average : Real   $average:=$values.average()   var $sumOfSquares : Real   $sumOfSquares:=0   var $value : Real   For each ($value; $values)     $sumOfSquares:=$sumOfSquares+(($value-$average)^2)   End for each   $values.length Function calculateStdDev($values : Collection) : Real   return Square root(This.calculateVariance($values))

Example: Measuring consistency of processing times

var $util : cs.VectorUtility $util:=cs.VectorUtility.new() //collection of numeric values: processing times in seconds var $values : Collection $values:=New collection(45; 52; 38; 61; 49; 55; 42; 58; 47; 50) var $variance : Real $variance:=$util.calculateVariance($values) var $standardDeviation : Real $standardDeviation:=$util.calculateStdDev($values)

• Average = 49.7 seconds


• Variance = 45.61 => It is the average of the squared differences between each processing time and the mean 49.7 seconds. In other words, it quantifies how spread out the values are, the higher the number, the greater the variation.


• Standard deviation = 6,753517601961 seconds =>most processing times differ by about 6.75 seconds above or below the average. A smaller standard deviation means more consistent results or data.