gives the statistic of the elements in list.


gives the statistic with a scaling factor c.

Details and Options

  • QnDispersion is a robust measure of dispersion.
  • QnDispersion 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 the statistic is given by the first quartile of the set {xi xj,i<j} multiplied by a scaling factor c. »
  • When c is not specified, a scaling factor is applied to make the 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.
  • QnDispersion[{{x1,y1,},{x2,y2,},}] gives {QnDispersion[{x1,x2,}],QnDispersion[{y1,y2,}],}.
  • QnDispersion 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.


open allclose all

Basic Examples  (3)

QnDispersion of a list:

Click for copyable input

QnDispersion of columns of a matrix:

Click for copyable input

QnDispersion of a list with scaling factor 1:

Click for copyable input

Scope  (6)

Options  (1)

Applications  (6)

Properties & Relations  (2)

See Also

Variance  StandardDeviation  Covariance  MeanDeviation  MedianDeviation  InterquartileRange  QuartileDeviation  TrimmedVariance  WinsorizedVariance  SnDispersion  BiweightMidvariance

Introduced in 2017