October 2018
Beginner to intermediate
238 pages
6h 32m
Chinese
Content preview from 面向数据科学家的实用统计学
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探索性数据分析
｜
13
即使数据符合正态分布，方差、标准偏差、平均绝对偏差以及中位数绝对偏
差这四者也并非是等价的估计量。事实上，标准偏差总是大于平均绝对偏
差，而平均绝对偏差总是大于中位数绝对偏差。有时，中位数绝对偏差会乘
上一个常数比例因子（通常使用
1.4826
），使得在正态分布下，中位数绝对
偏差与标准偏差具有相同的尺度。
1.4.2
基于百分位数的估计量
另一种估计离差的方法基于对有序数据分布情况的查看。基于有序数据的统计量被称为
顺
序统计量
，其中最基本的测量是
极差
，即数据的最大值与最小值之间的差值。知道最大值
和最小值本身也是十分有用的，这有助于识别离群值。但是极差对离群值非常敏感，对于
测量数据的离差并非十分有用。
为避免对离群值敏感，我们可以删除有序数据两端的值，然后再查看数据的极差。正式表
述为，此估计量基于
百分位数
间的差异。在一个数据集中，第
P
百分位数表明，至少有
P
%
的值小于或等于该值，而
(100
-
P
)%
的值大于或等于该值。例如，如果要找到第
80
百
分位数，我们首先对数据进行排序，然后从最小值开始，按照从小到大的顺序数出其中
80%
的数值。注意，中位数等同于第
50
百分位数。百分位数在本质上等同于
四分位数
，
而四分位数是根据分数做索引的，因此
0.8
四分位数等同于第
80
百分位数。
变异性的一种常用测量方法第
25
百分位数和第
75
百分位数间的差值，称为
四分位距
（
IQR
）。下面给出一个例子，对于数据集
{3, 1, 5, 3, 6, 7, 2, 9}
，我们在排序后得到
{1, 2, 3, 3,
5, 6, ...
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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.