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Nan🌞 · 2021年09月27日

课后题哪家企业的绝对离散度最大

NO.PZ2021061603000025

问题如下:

Annual returns and summary statistics for three funds are listed in the following exhibit:


The fund with the highest absolute dispersion is:

选项:

A. Fund PQR if the measure of dispersion is the range

B. Fund XYZ if the measure of dispersion is the variance

C. Fund ABC if the measure of dispersion is the mean absolute deviation

解释:

C is correct. The mean absolute deviation (MAD) of Fund ABC's returns is greater than the MAD of both of the other funds.

MDA=i=1nXiXˉnMDA = \frac{{\sum\limits_{i = 1}^n {\left| {{X_i} - \bar X} \right|} }}{n}, where Xˉ{\bar X} is the arithmetic mean of the series.

MAD for Fund ABC =

20(4)+34(4)+14(4)+5(4)+14(4)5=14.4%\frac{{\left| { - 20 - ( - 4)} \right| + \left| {34 - ( - 4)} \right| + \left| { - 14 - ( - 4)} \right| + \left| {5 - ( - 4)} \right| + \left| { - 14 - ( - 4)} \right|}}{5} = 14.4\%

MAD for Fund XYZ=

33(10.8)+12(10.8)+12(10.8)+8(10.8)+11(10.8)5=9.8%\frac{{\left| { - 33 - ( - 10.8)} \right| + \left| { - 12 - ( - 10.8)} \right| + \left| { - 12 - ( - 10.8)} \right| + \left| { - 8 - ( - 10.8)} \right| + \left| {11 - ( - 10.8)} \right|}}{5} = 9.8\%

MAD for Fund PQR=

14(5)+18(5)+6(5)+2(5)+3(5)5=8.8%\frac{{\left| { - 14 - ( - 5)} \right| + \left| { - 18 - ( - 5)} \right| + \left| {6 - ( - 5)} \right| + \left| { - 2 - ( - 5)} \right| + \left| {3 - ( - 5)} \right|}}{5} = 8.8\%

A and B are incorrect because the range and variance of the three funds are as follows:


The numbers shown for variance are understood to be in "percent squared" terms so that when taking the square root, the result is standard deviation in percentage terms. Alternatively, by expressing standard deviation and variance in decimal form, one can avoid the issue of units. In decimal form, the variances for Fund ABC, Fund XYZ, and Fund PQR are 0.0317, 0.0243, and 0.0110, respectively.

像给个表格和标准差让你判断哪家企业的绝对离散度最大这种题目是不是只要根据标准差判断谁的离散度最大就可以了,不需要再去计算其他像range,MAD等等参数?
2 个答案

星星_品职助教 · 2021年09月30日

对的

星星_品职助教 · 2021年09月27日

同学你好,

如果考试和本题一样,那么就先比较直接给出来的标准差。至少也能排除一个错误选项。

如果判断完标准差后无法直接得到答案,就需要计算比较另外两者。可以从比较容易的range入手做排除。


Nan🌞 · 2021年09月29日

我的问题是,是不是三个企业中标准差最大的那个,其他的指标也肯定最大?还是具体情况具体分析?

星星_品职助教 · 2021年09月30日

具体问题具体分析

Nan🌞 · 2021年09月30日

那就是说还是要分别去计算的是吧

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2024-08-06 10:23 1 · 回答

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2023-05-22 22:38 1 · 回答

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2023-04-22 23:57 1 · 回答

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2023-01-11 12:00 1 · 回答

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2022-09-12 15:52 2 · 回答