﻿ Measures.WeightedStandardDeviation Method (Double[][], Double[], Boolean)

Calculates the matrix Standard Deviations vector.

Namespace:  Accord.Statistics
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntax
```public static double[] WeightedStandardDeviation(
this double[][] matrix,
double[] weights,
bool unbiased = true
)```

#### Parameters

matrix
Type: SystemDouble
A matrix whose deviations will be calculated.
weights
Type: SystemDouble
The number of times each sample should be repeated.
unbiased (Optional)
Type: SystemBoolean
Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

#### Return Value

Type: Double
Returns a vector containing the standard deviations of the given matrix.

#### Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type . When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).
Remarks

Setting unbiased to true will make this method compute the standard deviation σ using the sample variance, which is an unbiased estimator of the true population variance. Setting this parameter to true will thus compute σ using the following formula:

```                   N
σ² = 1 / (N - 1)  ∑   (x_i − μ)²
i=1```

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

```                   N
σ² =   (1 / N)    ∑   (x_i − μ)²
i=1```