查看“︁中值绝对离差”︁的源代码

在[[统计学]]中，'''中值绝对离差''' (MAD) 是衡量[[定量研究|定量数据]]{{tsl|en|univariate|单变量}}样本[[离散程度|变异性]]的[[稳健统计|稳健]]指标。 它也可以指通过从样本计算的 MAD [[估计理论|估计]]的[[总体]][[參數 (數學)|参数]]。<ref>{{cite book  | last = Hoaglin | first = David C. |author2=Frederick Mosteller |author3=John W. Tukey | title = Understanding Robust and Exploratory Data Analysis | url = https://archive.org/details/understandingrob0000unse | publisher = John Wiley & Sons| date = 1983 | pages = [https://archive.org/details/understandingrob0000unse/page/404 404]–414 | isbn = 978-0-471-09777-8 }}</ref>

对于单变量数据集''X''<sub>1</sub>,&nbsp;''X''<sub>2</sub>,&nbsp;...,&nbsp;''X<sub>n</sub>''，MAD定义为与数据[[中位数]]的[[离差]]的[[中位数]]： <math>\tilde{X}=\operatorname{median}(X)  </math>：<ref>{{cite book | last = Russell | first = Roberta S. | author2 = Bernard W. Taylor III | title = Operations Management | publisher = John Wiley & Sons | date = 2006 | pages = [https://archive.org/details/operationsmanage0005russ/page/497 497–498] | isbn = 978-0-471-69209-6 | url = https://archive.org/details/operationsmanage0005russ/page/497 }}</ref>
:<math>
\operatorname{MAD} = \operatorname{median}( |X_i - \tilde{X}|)
</math>
也就是说，从数据[[中位数]]的[[离差]]开始，MAD是其[[绝对值]]的[[中位數|中位数]]。<ref>{{cite book  | last = Venables | first = W. N. |author2=B. D. Ripley | title = Modern Applied Statistics with S-PLUS | publisher = Springer | date = 1999 | pages = 128 | isbn = 978-0-387-98825-2 }}</ref>
==参考文献==
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{{統計學}}

[[Category:统计偏差和离散度]]
[[Category:穩健統計學]]