Function Repository Resource:

# SkewnessAround

Calculate the skewness of a list along with its uncertainty

Contributed by: Sander Huisman
 ResourceFunction["SkewnessAround"][{x1,x2,x3,…}] gives an Around object describing the skewness and corresponding uncertainty of the xi.

## Details

The standard error of the skewness is defined as: , where n is the number of samples.
The "Value" of the Around object is calculated using the built-in Skewness function.

## Examples

### Basic Examples (1)

Calculate the skewness of some numbers:

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### Scope (2)

SkewnessAround works with symbolic expressions:

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SkewnessAround also works with quantities with units, though the answer is dimensionless:

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The skewness is independent of the units of course:

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### Possible Issues (3)

SkewnessAround applied to symbolic expressions can get unwieldy fast:

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At least three value are needed to give a plausible error estimate:

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Try with 3 values:

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Skewness can give Indeterminate, in which case there will not be an Around result:

### Neat Examples (1)

Study the skewness and its uncertainty for a sequence of values and compare it to the theoretical value of the distribution (dashed):

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SHuisman

## Version History

• 1.0.0 – 21 November 2022