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lldyy · 2023年10月22日

可以解释下这道题目吗？

  1. Quantitative

NO.PZ2022123001000026

问题如下：

The following exhibit shows the annual MSCI World Index total returns for a 10-year period


The fourth quintile return for the MSCI World Index is closest to:

选项：

A.

20.65%

B.

26.03%

C.

27.37%

解释：

Quintiles divide a distribution into fifths, with the fourth quintile occurring at the point at which 80% of the observations lie below it. The fourth quintile is equivalent to the 80th percentile. To find the yth percentile (Py), we first must determine its location. The formula for the location (Ly) of a yth percentile in an array with n entries sorted in ascending order is Ly = (n + 1) × (y/100). In this case, n = 10 and y = 80%, so

L80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.

With the data arranged in ascending order (−40.33%, −5.02%, 9.57%, 10.02%, 12.34%, 15.25%, 16.54%, 20.65%, 27.37%, and 30.79%), the 8.8th position would be between the 8th and 9th entries, 20.65% and 27.37%, respectively. Using linear interpolation, P8.8 = X8 + (Ly − 8) × (X9 − X8),

P8.8 = 20.65 + (8.8 − 8) × (27.37 − 20.65) = 20.65 + (0.8 × 6.72) = 20.65 + 5.38 = 26.03%.

可以解释下这道题目吗？

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1 个答案

星星_品职助教 · 2023年10月23日

同学你好，

提问请具体标明具体不理解的地方。

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本题求fourth quintile，根据公式Ly = (n + 1) × (y/100)，可知该分位数在排序后的数字中，是第8.8个数。

将数字排序，可知第8个数是20.65%，第9个数是27.37%。

由于第8个第9两个数之间相当于1单位的差距，这1单位的差距是27.37%-20.65%=6.72%，所以0.8单位的差距就是6.72%×0.8=5.376%。

由此可知，第8.8个数是第8个数再加上0.8个单位，也就是20.65%+5.376%=26.026%

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NO.PZ2022123001000026 问题如下 The following exhibit shows the annuMSWorlInx totreturns for a 10-yeperiohe fourth quintile return for the MSWorlInx isclosest to: A.20.65% B.26.03% C.27.37% Quintiles vi a stribution into fifths, with the fourth quintile occurring the point whi80% of the observations lie below it. The fourth quintile is equivalent to the 80th percentile. To finthe yth percentile (Py), we first must termine its location. The formula for the location (Ly) of a yth percentile in arrwith n entries sortein ascenng orr is Ly = (n + 1) × (y/100). In this case, n = 10 any = 80%, soL80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.With the ta arrangein ascenng orr (−40.33%, −5.02%, 9.57%, 10.02%, 12.34%, 15.25%, 16.54%, 20.65%, 27.37%, an30.79%), the 8.8th position woulbetween the 8th an9th entries, 20.65% an27.37%, respectively. Using lineinterpolation, P8.8 = X8 + (Ly − 8) × (X9 − X8), P8.8 = 20.65 + (8.8 − 8) × (27.37 − 20.65) = 20.65 + (0.8 × 6.72) = 20.65 + 5.38 = 26.03%. 答案的公式怎么没见过？跟讲义的不一样，不理解是什么意思

2024-01-30 14:25 1 · 回答