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Jusay · 2021年11月10日

为什么我直接没读懂题?

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.

MAD、方差这些都会算,但是没读懂题和答案,麻烦老师科普下?

1 个答案
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星星_品职助教 · 2021年11月11日

同学你好,

题目:“The fund with the highest absolute dispersion is:”指的是哪个fund收益的离散程度最大。

选项里给了三个衡量离散程度的标准(measure of dispersion):range;variance;和MAD。

所以根据这三个标准,逐一去判断在这个对应的标准下哪个fund的离散程度最大,然后对应选择即可。range和MAD需要计算后比较,variance直接比较表格中的standard deviation即可。

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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