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Metis李敏玲 · 2020年10月18日

问一道题：NO.PZ2017092702000051

问题如下：

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

The fund that shows the highest 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.

$MAD=\frac{\displaystyle\sum_i^n{\vert Xi-\overline X\vert}}n$

where \(\overline X\) is the arithmetic mean of the series.

MAD for Fund ABC =

$\frac{{\lbrack-20-{(-4)}\rbrack}+{\lbrack23-{(-4)}\rbrack}+{\lbrack-14-{(-4)}\rbrack}+{\lbrack5-{(-4)}\rbrack}+{\lbrack-14-{(-4)}\rbrack}}5=14.4\%$

MAD for Fund XYZ =

$\frac{{\lbrack-33-{(-10.8)}\rbrack}+{\lbrack\text{-12}-{(-10.8)}\rbrack}+{\lbrack-\text{12}-{(-10.8)}\rbrack}+{\lbrack\text{-8}-{(-10.8)}\rbrack}+{\lbrack\text{11}-{(-10.8)}\rbrack}}5=\text{9}\text{.8}\%$

MAD for Fund PQR =

$\frac{{\lbrack-\text{14}-{(-\text{5})}\rbrack}+{\lbrack\text{-18}-{(-\text{5})}\rbrack}+{\lbrack\text{6}-{(-\text{5})}\rbrack}+{\lbrack\text{-2}-{(-\text{5})}\rbrack}+{\lbrack\text{3}-{(-\text{5})}\rbrack}}5=\text{8}\text{.8}\%$

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.

根据基础班课程，对比两组或以上数据的离散程度，已知均值和标准差，则用CV就可以判断离散程度的大小？

Fund 1：17.8/4=4.45

Fund 2：15.6/10.8=1.44

Fund 3：10.5/5.0=2.1

所以Fund 1离散程度最大

所以在这里也可以基于CV判断，不是非要用十进制方差？

另外，老师可以把答案中的0.0317、0.0243、0.0110计算过程展示一下吗？

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星星_品职助教 · 2020年10月18日

同学你好，

如果题干要求比较CV，则需要根据CV来比较离散程度。但这道题的选项明显说明本题的衡量标准是range和MAD。

variance就是standard deviation的平方，以fund ABC为例，variance=17.8%的平方即0.031684。另外两个计算方法同理。

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2021-05-31 00:15 1 · 回答

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2021-02-16 13:55 1 · 回答

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2021-02-10 11:50 1 · 回答

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