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Weike · 2024年02月27日

什么时候用n-1 什么时候用n

  1. CFA I
  2. Portfolio

NO.PZ2015121802000021

问题如下：

Calculate the standard deviation of annual returns on an investment based on the following chart:

选项：

A.

1.2%.

B.

4.44%.

C.

19.7%.

解释：

B is correct.

Mean annual return = (4% - 3% - 4% + 3% + 6%) / 5 = 1.2%

Squared deviations from the mean:

4%-1.2%=2.8%      （2.8%）2= 7.84

-3% -1.2% = -4.2%   （-4.2%）2 = 17.64

-4% -1.2% = -5.2%   （-5.2%）2 = 27.04

3% -1.2% =1.8%    （1.8%）2= 3.24

6% -1.2% = 4.8%    （4.8%） 2= 23.04

Sum of squared deviations = 7.84 + 17.64 + 27.04 + 3.24+ 23.04 = 78.8

Sample variance = 78.8/(5 - 1) = 19.7

Sample standard deviation = 19.71/2= 4.44%

什么时候要除n-1 什么时候除n

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1 个答案

Kiko_品职助教 · 2024年02月27日

嗨，爱思考的PZer你好：


总体方差分母除以的是n，而样本除以的是n-1

通常情况下，一个投资的投资期远不止5年，所以这题中所列举的5年投资期只是总体投资时间中的一个样本而已。故题目要求的是样本方差。

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NO.PZ2015121802000021 问题如下 Calculate the stanrviation of annureturns on investment baseon the following chart: A.1.2%. B.4.44%. C.19.7%. B is correct.Meannureturn = (4% - 3% - 4% + 3% + 6%) / 5 = 1.2%Squareviations from the mean: 4%-1.2%=2.8% （2.8%）2= 7.84-3% -1.2% = -4.2% （-4.2%）2 = 17.64-4% -1.2% = -5.2% （-5.2%）2 = 27.043% -1.2% =1.8% （1.8%）2= 3.246% -1.2% = 4.8% （4.8%） 2= 23.04Sum of squareviations = 7.84 + 17.64 + 27.04 + 3.24+ 23.04 = 78.8Sample varian= 78.8/(5 - 1) = 19.7Sample stanrviation = 19.71/2= 4.44% 老师这道题用计算器好像很快？我直接按x1, x2, x3...计算器显示Sx=4.438468?

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NO.PZ2015121802000021 问题如下 Calculate the stanrviation of annureturns on investment baseon the following chart: A.1.2%. B.4.44%. C.19.7%. B is correct.Meannureturn = (4% - 3% - 4% + 3% + 6%) / 5 = 1.2%Squareviations from the mean: 4%-1.2%=2.8% （2.8%）2= 7.84-3% -1.2% = -4.2% （-4.2%）2 = 17.64-4% -1.2% = -5.2% （-5.2%）2 = 27.043% -1.2% =1.8% （1.8%）2= 3.246% -1.2% = 4.8% （4.8%） 2= 23.04Sum of squareviations = 7.84 + 17.64 + 27.04 + 3.24+ 23.04 = 78.8Sample varian= 78.8/(5 - 1) = 19.7Sample stanrviation = 19.71/2= 4.44% 第二个问题，为啥sample是除以n-1，数量学科有这个公式但太久了记不清了，谢谢老师

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