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yumish7 · 2025年06月27日

第四个五分位数不是应该刚好是0.8，是第8个位置上的数吗，为什么是总数是11？

  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%.

第四个五分位数不是应该刚好是0.8，是第8个位置上的数吗，为什么是总数是11？

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1 个答案

品职助教_七七 · 2025年06月28日

嗨，爱思考的PZer你好：


第几个分位数需要通过公式Ly算出来。不能自己确定。

本题代入Ly的公式后，可得第四个五分位数为第8.8个数。不是第8个位置。

11为Ly公式的n+1所得到的结果。

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2024-01-30 14:25 1 · 回答

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%. 可以下这道题目吗？

2023-10-22 14:03 1 · 回答