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Jine · 2019年11月21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.

请教老师，Fund ABC if the measure of dispersion is the mean absolute deviation. 答案C这句话该如何理解？Q

其实我只是看ABC的标准差最大，我就选C了

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星星_品职助教 · 2019年11月21日

同学你好，

这道题是从三个不同的维度来衡量这三个fund离散程度的大小。A选项就是从Range的角度来看，B是方差的角度，C则是从MAD的角度。Mean Absolute Deviation就是MAD的全称。所以C选项的意思是如果从MAD的角度来看，fund ABC的离散程度最大。

这道题需要分别算出来三个fund各自的range，方差和MAD进行比较。逐项排除。由于Range很容易计算，方差只需要看已经给出的标准差就行，所以主要考察的还是MAD的计算。直接代入MAD公式即可。

我感觉这道题是不是没有反应过来mean absolute deviation就是MAD？如果能对应上，直接代数就行，加油~

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Jine · 2019年11月22日

哈哈哈，被你猜中了，明白了！谢谢解答！

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FunXYZ if the measure of spersion is the variance. FunAif the measure of spersion is the meabsolute viation. C is correct. The meabsolute viation (MA of FunABC’s returns is greater ththe Mof both of the other fun. MA∑in∣Xi−X‾∣nMA\frac{\splaystyle\sum_i^n{\vert Xi-\overline X\vert}}nMAni∑n∣Xi−X∣ where \(\overline X\) is the arithmetic meof the series. Mfor FunA= [−20−(−4)]+[23−(−4)]+[−14−(−4)]+[5−(−4)]+[−14−(−4)]5=14.4%\frac{{\lbrack-20-{(-4)}\rbrack}+{\lbrack23-{(-4)}\rbrack}+{\lbrack-14-{(-4)}\rbrack}+{\lbrack5-{(-4)}\rbrack}+{\lbrack-14-{(-4)}\rbrack}}5=14.4\%5[−20−(−4)]+[23−(−4)]+[−14−(−4)]+[5−(−4)]+[−14−(−4)]=14.4% Mfor FunXYZ = [−33−(−10.8)]+[-12−(−10.8)]+[−12−(−10.8)]+[-8−(−10.8)]+[11−(−10.8)]5=9.8%\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}\%5[−33−(−10.8)]+[-12−(−10.8)]+[−12−(−10.8)]+[-8−(−10.8)]+[11−(−10.8)]=9.8% Mfor FunPQR = [−14−(−5)]+[-18−(−5)]+[6−(−5)]+[-2−(−5)]+[3−(−5)]5=8.8%\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}\%5[−14−(−5)]+[-18−(−5)]+[6−(−5)]+[-2−(−5)]+[3−(−5)]=8.8% A anB are incorrebecause the range anvarianof the three fun are follows: The numbers shown for varianare unrstooto in \"percent square" terms so thwhen taking the square root, the result is stanrviation in percentage terms. Alternatively, expressing stanrviation anvarianin cimform, one cavoithe issue of units; in cimform, the variances for FunABFunXYZ, anFunPQR are 0.0317, 0.0243, an0.0110, respectively. 老师，我用计算器78键上面的数据功能算出的标准差B也对哦，这怎么回事。这个不能用计算器算吗

2021-05-31 00:15 1 · 回答

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2021-02-16 13:55 1 · 回答

NO.PZ2017092702000051 请问range是什么公式？

2021-02-10 11:50 1 · 回答

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2021-02-06 09:38 1 · 回答

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2020-10-18 12:11 1 · 回答