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 allBasic Examples (2)
Scope (14)
Data (11)
Exact input yields exact output:
Approximate input yields approximate output:
QuartileSkewness for a matrix gives column-wise ranges:
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:
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:
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:
Text
Wolfram Research (2007), QuartileSkewness, Wolfram Language function, https://reference.wolfram.com/language/ref/QuartileSkewness.html (updated 2017).
CMS
Wolfram Language. 2007. "QuartileSkewness." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/QuartileSkewness.html.
APA
Wolfram Language. (2007). QuartileSkewness. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuartileSkewness.html