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闫旭 · 2022年03月19日

range的计算

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)+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.

答案中的range结果,为什么带百分号,怎么算的?

1 个答案

星星_品职助教 · 2022年03月20日

同学你好,

百分号是题干中给的单位。用最大的减最小的,然后加上单位(%)就可以了。

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NO.PZ2021061603000025 问题如下 Annureturns ansummary statistifor three fun are listein the following exhibit:The funwith the highest absolute spersion is: A.FunPQR if the measure of spersion is the range B.FunXYZ if the measure of spersion is the varian C.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∑i=1n∣Xi−Xˉ∣nM= \frac{{\sum\limits_{i = 1}^n {\left| {{X_i} - \bX} \right|} }}{n}MAni=1∑n​∣Xi​−Xˉ∣​, where Xˉ{\bX}Xˉ is the arithmetic meof the series.Mfor FunA=∣−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\% 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{{\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\%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{{\left| { - 14 - ( - 5)} \right| + \left| { - 18 - ( - 5)} \right| + \left| {6 - ( - 5)} \right| + \left| { - 2 - ( - 5)} \right| + \left| {3 - ( - 5)} \right|}}{5} =8.8\% 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. 不考虑实际意义的话,题目告诉3个数据集的标准差,要求3个数据集的MA大小,那么是否根据标准差和MA公式,直接通过n*S2=(MAn)^2即MA(S2/n)^1/2?如此,还可以推导出标准差更大的数据集其实MA更大?

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