SnDispersion
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SnDispersion

Details and Options

- SnDispersion is a robust measure of dispersion.
- SnDispersion is a rank-based estimator with its statistic based on absolute pairwise differences. The statistic does not require location estimation.
- For the list {x1,x2,…,xn}, the value of
estimator is given by the median of {zi,1≤i≤n} multiplied by a scaling factor c, where zi is the median of {xi– xj,1≤j≤n} over j.
- When c is not specified, a positive scaling factor c* that satisfies
is applied to make
statistic a consistent estimator of the scale parameter for normally distributed data. Also, a finite sample correction is used by default to make the estimator unbiased for small samples.
- SnDispersion[{{x1,y1,…},{x2,y2,…},…}] gives {SnDispersion[{x1,x2,…}],SnDispersion[{y1,y2,…}],…}.
- SnDispersion supports a Method option. The following explicit settings can be specified:
-
"FiniteSample" uses finite sample correction (default) "None" no correction - The option Method is ignored if the scaling factor c is specified in the input.
Examples
open allclose allBasic Examples (4)Summary of the most common use cases
SnDispersion of a list:

https://wolfram.com/xid/0n4ghdf4uju-wd9

SnDispersion of columns of a matrix:

https://wolfram.com/xid/0n4ghdf4uju-vu6sr

SnDispersion of a list with scaling factor 1:

https://wolfram.com/xid/0n4ghdf4uju-whtpl

SnDispersion of a list of dates:

https://wolfram.com/xid/0n4ghdf4uju-ziof1v

Scope (8)Survey of the scope of standard use cases
Exact input yields exact output when the scaling factor is exact:

https://wolfram.com/xid/0n4ghdf4uju-ug7y2


https://wolfram.com/xid/0n4ghdf4uju-bcry2t

SnDispersion with different scaling parameters:

https://wolfram.com/xid/0n4ghdf4uju-fgu628


https://wolfram.com/xid/0n4ghdf4uju-bdt2rg

SnDispersion for a matrix gives a columnwise estimate:

https://wolfram.com/xid/0n4ghdf4uju-jywoa6

SnDispersion of a large array:

https://wolfram.com/xid/0n4ghdf4uju-enve04


https://wolfram.com/xid/0n4ghdf4uju-if5yx4

Find the SnDispersion of a TimeSeries:

https://wolfram.com/xid/0n4ghdf4uju-tg8p6z

https://wolfram.com/xid/0n4ghdf4uju-ffhpdi

SnDispersion depends only on the values:

https://wolfram.com/xid/0n4ghdf4uju-fy9fte

SnDispersion works with data involving quantities:

https://wolfram.com/xid/0n4ghdf4uju-jopin9


https://wolfram.com/xid/0n4ghdf4uju-e8c21s

Compute SnDispersion of dates:

https://wolfram.com/xid/0n4ghdf4uju-b1smxx

https://wolfram.com/xid/0n4ghdf4uju-pa4nmn


https://wolfram.com/xid/0n4ghdf4uju-uok1il


https://wolfram.com/xid/0n4ghdf4uju-o9ersi

Compute SnDispersion of times:

https://wolfram.com/xid/0n4ghdf4uju-et9bla


https://wolfram.com/xid/0n4ghdf4uju-ztsexm

List of times with different time zone specifications:

https://wolfram.com/xid/0n4ghdf4uju-mrqghz


https://wolfram.com/xid/0n4ghdf4uju-ow7hca

Options (1)Common values & functionality for each option
Applications (6)Sample problems that can be solved with this function
Obtain a robust estimate of dispersion when extreme values are present:

https://wolfram.com/xid/0n4ghdf4uju-b99oaf

Sample standard deviation is heavily influenced by extreme values:

https://wolfram.com/xid/0n4ghdf4uju-3fz1a

Identify periods of high volatility in stock data using a five-year moving dispersion:

https://wolfram.com/xid/0n4ghdf4uju-nj16d1

https://wolfram.com/xid/0n4ghdf4uju-kfgcti

https://wolfram.com/xid/0n4ghdf4uju-bef0x

Compute dispersion for slices of a collection of paths of a random process:

https://wolfram.com/xid/0n4ghdf4uju-8se1zg

https://wolfram.com/xid/0n4ghdf4uju-52xxug

https://wolfram.com/xid/0n4ghdf4uju-iakfqb
Plot dispersion over these paths:

https://wolfram.com/xid/0n4ghdf4uju-tvmkqe

Find the dispersion of the heights for the children in a class:

https://wolfram.com/xid/0n4ghdf4uju-cevfij

https://wolfram.com/xid/0n4ghdf4uju-fllmtw


https://wolfram.com/xid/0n4ghdf4uju-celepo

Plot the dispersion with respect to the median:

https://wolfram.com/xid/0n4ghdf4uju-g98mgx

https://wolfram.com/xid/0n4ghdf4uju-7po36z

Consider data from standard normal distribution with outliers modeled by another normal distribution with large spread:

https://wolfram.com/xid/0n4ghdf4uju-hby4vw
Test the data against standard normal distribution:

https://wolfram.com/xid/0n4ghdf4uju-7wya5


https://wolfram.com/xid/0n4ghdf4uju-pszm77

Remove outliers by selecting data points that are within three times the dispersion from the sample median:

https://wolfram.com/xid/0n4ghdf4uju-bf1y7q

https://wolfram.com/xid/0n4ghdf4uju-ehmy0c
Test the new data against standard normal distribution:

https://wolfram.com/xid/0n4ghdf4uju-i4ekyf

Generate data from a Student t distribution:

https://wolfram.com/xid/0n4ghdf4uju-zqggj

https://wolfram.com/xid/0n4ghdf4uju-ihrckh

Compute the dispersion of the data with three measures: standard deviation, square root of trimmed variance and dispersion:

https://wolfram.com/xid/0n4ghdf4uju-3r1x1

https://wolfram.com/xid/0n4ghdf4uju-ita83i

Assess the accuracy of these three dispersion estimators via bootstrapping:

https://wolfram.com/xid/0n4ghdf4uju-c1py80
estimator gives the smallest spread with the given data:

https://wolfram.com/xid/0n4ghdf4uju-bxitpz

Properties & Relations (2)Properties of the function, and connections to other functions
SnDispersion is a rank-based dispersion estimator with its statistic based on pairwise absolute differences:

https://wolfram.com/xid/0n4ghdf4uju-o55m4v
Compute the low median of high medians using RankedMin:

https://wolfram.com/xid/0n4ghdf4uju-n2rpvg

Compare with SnDispersion with scaling factor equal to 1:

https://wolfram.com/xid/0n4ghdf4uju-foof01

QnDispersion, SnDispersion and StandardDeviation are estimators of the scale parameter of NormalDistribution:

https://wolfram.com/xid/0n4ghdf4uju-by15b

https://wolfram.com/xid/0n4ghdf4uju-cp1as4

Assess the accuracy of the estimators via bootstrapping:

https://wolfram.com/xid/0n4ghdf4uju-sep9r
Compute the relative efficiencies with respect to StandardDeviation using the estimated results:

https://wolfram.com/xid/0n4ghdf4uju-dy97cz

Wolfram Research (2017), SnDispersion, Wolfram Language function, https://reference.wolfram.com/language/ref/SnDispersion.html (updated 2024).
Text
Wolfram Research (2017), SnDispersion, Wolfram Language function, https://reference.wolfram.com/language/ref/SnDispersion.html (updated 2024).
Wolfram Research (2017), SnDispersion, Wolfram Language function, https://reference.wolfram.com/language/ref/SnDispersion.html (updated 2024).
CMS
Wolfram Language. 2017. "SnDispersion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/SnDispersion.html.
Wolfram Language. 2017. "SnDispersion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/SnDispersion.html.
APA
Wolfram Language. (2017). SnDispersion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SnDispersion.html
Wolfram Language. (2017). SnDispersion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SnDispersion.html
BibTeX
@misc{reference.wolfram_2025_sndispersion, author="Wolfram Research", title="{SnDispersion}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SnDispersion.html}", note=[Accessed: 06-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_sndispersion, organization={Wolfram Research}, title={SnDispersion}, year={2024}, url={https://reference.wolfram.com/language/ref/SnDispersion.html}, note=[Accessed: 06-June-2025
]}