October 2021
Intermediate to advanced
289 pages
8h 31m
Chinese
Content preview from 数据科学中的实用统计学(第2版)
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
14
｜
第
1
章
不管是方差、标准差，还是平均绝对偏差，它们对离群值和极端值都比较敏感（参见
1.3.2
节中对健壮位置估计的讨论）。方差和标准差对离群值尤其敏感，因为它们基于偏差的
平方。
变异性的一种健壮估计是
中位数绝对偏差
，或称
MAD
：
MAD
=
中位数
12
(| |, | |, , | |)
N
xm x m x m−− −
其中
m
表示中位数。和中位数一样，
MAD
也不受极端值的影响
。类似于截尾均值（参见
1.3.1
节）
，我们也可以计算出截尾标准差。
方差、标准差、平均绝对偏差和中位数绝对偏差互不等价，即使数据来自于
一个正态分布。实际上，标准差总是大于平均绝对偏差，而平均绝对偏差也
总是大于中位数绝对偏差。有时候，中位数绝对偏差会乘以一个固定的缩放
因子，使得
MAD
在
正态分布情况下与标准差具有相同的尺度。常用的缩放
因子是
1.4826
，它可以使
50%
的正态分布值落在
±
MAD
的范围内。
1.4.2
基于百分位数的估计
估计数据的离散度还有另外一种方法，它基于有序数据的分布情况。基于有序数据的统计
量称为
顺序统计量
。最基本的测量方式是
极差
：最大值与最小值之间的差异。最大值和最
小值本身就非常有用，了解它们有助于识别离群值，但极差对离群值非常敏感，作为一种
测量数据离散度的方式，它的作用有限。
为了避免对离群值的敏感性，我们可以看一下在两端各去掉一些值之后的数据范围。确切
地说，这种估计基于
百分位数
之间的差异。在一个数据集中，第
P
个百分位数是使得至少
百分之
P
个值小于等于它，至少百分之
(100 –
P
)
的值大于等于它的那个值。例如， ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.