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Cutie🍒 · 2020年10月28日

问一道题:NO.PZ2017092702000049

问题如下:

The following table shows the annual MSCI World Index total returns for 2004–2013.

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:

B is correct.

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, P80 = X8 + (Ly – 8) × (X9 X8), P80 = 20.65 + (8.8 – 8) × (27.37 – 20.65) = 20.65 + (0.8 × 6.72) = 20.65 + 5.38 = 26.03%

这题的fourth quintile不是五分之四吗?不就是十分之八的第八个数吗?我好像忘记知识点了

1 个答案
已采纳答案

星星_品职助教 · 2020年10月28日

同学你好,

fourth quintile数值等于8/10,但是不能直接认为是第八个数。将表格里的数字按从小到大的顺序排序后,运用公式:

Ly=(n+1)*(y/100)=(10+1)*(80/100)=8.8,所以可知其实要求的是第8.8个数。

所以需要在第八个数,20.65%的基础上,再加上用插值法求出0.8个数代表的数值。即0.8*(第九个数27.37%-第八个数20.65%)=5.38%。

所以第8.8个数就是20.65%+5.38%=26.03%,选择B选项。

Cutie🍒 · 2020年10月28日

get到了,非常感谢

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老师 forth quintile不就是第四个五分位数吗?就是十个数里第八个啊?

2020-10-31 20:32 1 · 回答

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2020-07-06 20:43 1 · 回答

26.03%. 27.37%. B is correct. 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%, so L80 = (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, P80 = X8 + (Ly – 8) × (X9 – X8), P80 = 20.65 + (8.8 – 8) × (27.37 – 20.65) = 20.65 + (0.8 × 6.72) = 20.65 + 5.38 = 26.03% ​就算按照偶数算,第八位数也是20.65A呀

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