# QuartileSkewness

QuartileSkewness[list]

gives the coefficient of quartile skewness for the elements in list.

QuartileSkewness[dist]

gives the coefficient of quartile skewness for the distribution dist.

# Details • With {q1,q2,q3}=Quartiles[list], QuartileSkewness[list] is equivalent to .
• A positive value of quartile skewness indicates the median is closer to the lower quartile than the upper quartile .
• A negative value of quartile skewness indicates the median is closer to the upper quartile.
• QuartileSkewness[list,{{a,b},{c,d}}] uses the quantile definition specified by parameters a, b, c, d.

# Examples

open allclose all

## Basic Examples(2)

Quartile skewness for a list of exact numbers:

Quartile skewness of a parametric distribution:

## Scope(14)

### Data(11)

Exact input yields exact output:

Approximate input yields approximate output:

QuartileSkewness for a matrix gives column-wise ranges:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Compute results using other parametrizations:

Find the quartile skewness for WeightedData:

Find the quartile skewness for EventData:

Find the quartile skewness for TemporalData:

Find the quartile skewness of TimeSeries:

The quartile skewness depends only on the values:

Find the quartile skewness for data involving quantities:

### Distributions and Processes(3)

Find the quartile skewness for a parametric distribution:

Quartile skewness for a derived distribution:

Data distribution:

Quartile skewness for a time slice of a random process:

## Applications(6)

Zero QuartileSkewness indicates the median is equally distant from the remaining quartiles:

Positive QuartileSkewness indicates that the median is closer to the lower quartile:

Negative QuartileSkewness indicates that the median is closer to the upper quartile:

Obtain a robust estimate of asymmetry when extreme values are present:

Measures based on the Mean are heavily influenced by extreme values:

This time series contains the number of steps taken daily by a person during a period of five months:

Median number of steps:

Analyze whether the step distribution is skewed toward the lower or the upper quartile:

The histogram of the frequency of daily counts shows that the median is closer to the upper quartile:

Find the quartile skewness for the heights of children in a class:

Negative quartile skewness indicates that the median is closer to the lower quartile:

## Properties & Relations(3)

QuartileSkewness is a function of linearly interpolated Quantile values:

QuartileSkewness is a function of quartiles:

QuartileSkewness is a function of the median, first quartile and a dispersion measure:

## Possible Issues(1)

QuartileSkewness requires numeric values: ## Neat Examples(1)

The distribution of QuartileSkewness estimates for 50, 100 and 300 samples: