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yy1177 · 2023年04月22日

考试中碰到这种题目,有快速解题技巧么

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.

MAD=i=1nXiXˉnMAD = \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)+23(4)+14(4)+5(4)+14(4)5=14.4%\frac{{\left| { - 20 - ( - 4)} \right| + \left| {23 - ( - 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.

是不是只能把三个挨个算出来

1 个答案
已采纳答案

星星_品职助教 · 2023年04月23日

同学你好,

本题可以直接先看不需要计算的standard deviation,也就是B选项。就可以直接得出答案,不用计算另外两者。

如果standard deviation这个选项不对,那么再看关于range这个选项,找出最大最小值就可以判断,计算比MAD容易很多。

如果standard deviation和range的选项都不对,那么直接排除法选MAD那个就可以了。

但MAD的计算也是要掌握的,考试可能直接要求去计算MAD。

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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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2023-01-11 12:00 1 · 回答

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2022-09-12 15:52 2 · 回答