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晏晏 · 2020年03月08日

问一道题:NO.PZ2018103102000151 [ CFA II ]

问题如下:

Zhang remembers learning about the weighted harmonic mean. She decides to calculate the weighted harmonic mean for the index and makes the following statement to support her decision: 

“The harmonic mean can be used to mitigate the effects of both large and small outliers.”

Zhang’s statement to support using the harmonic mean is best described as: 

选项:

A.

incorrect with respect to large outliers 

B.

incorrect with respect to small outliners  

C.

correct 

解释:

Zhang’s statement is incorrect with respect to small outliers. The harmonic mean tends to mitigate the impact of large outliers. It may aggravate the impact of small outliers, but such outliers are bounded by zero on the downside.

A is incorrect. The harmonic mean may aggravate the impact of small outliers, but such outliers are bounded by zero on the downside.

C is incorrect. The harmonic mean may aggravate the impact of small outliers, but such outliers are bounded by zero on the downside. 

您好,可以解释下解析么,没有看明白答案。
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已采纳答案

袁园_品职助教 · 2020年03月09日

同学你好!

这道题主要是在考 调和平均数 的定义和性质。

调和平均数就是取倒数再加和取平均,而不是直接相加取平均。例如我有一组数字,1、2、3、4、500,直接求平均数并不能反映这组数的性质,因为有500这个 large outlier,但是如果我对他们先取倒数,那么500变成1/500,对计算结果的影响就很小了,即 harmonic mean tends to mitigate the impact of large outliers

同理,如果一组数里面有一个很小很接近零的数,例如0.01,他取倒数之后就变成了100,反而会对计算带来很大的影响,即 harmonic mean may aggravate the impact of small outliers

同学可以再去听一下R29课程的最后一个视频,讲义如下图:

Jody · 2020年03月19日

请问一下老师,bounded by zero on the downside是什么意思?

袁园_品职助教 · 2020年03月20日

同学你好!

bounded by zero 就是说一个很小很接近零的数取倒数之后就会反弹变得很大,例如0.01取倒数后反弹为100

on the downside 就是说这是 harmonic mean 的一个缺点

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2023-08-13 16:52 1 · 回答