题目
The following exhibit shows the annual MSCI World Index total returns for a 10-year period.「huixue_img/importSubject/1564548692608946176.jpeg」
The fourth quintile return for the MSCI World Index is closest to:
选项
A.20.65%.
B.26.03%.
C.27.37%.
答案
B
解析
B is correct. Quintiles divide a distribution intofifths, with the fourth quintile occurring at the point at which 80% of theobservations lie below it. The fourth quintile is equivalent to the 80thpercentile. To find the yth percentile (Py), we first must determine itslocation. The formula for the location (Ly) of a yth percentile in an arraywith 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%), the8.8th 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%. 五分位数把一个分布分成五分之三，而第四分位数出现在80%的观察值低于它的地方。第四个五分位数相当于第80个百分位数。要找到第yth百分位数(Py)，首先必须确定它的位置。按升序排列n个元素的数组中第y百分位的位置(Ly)公式为Ly = (n＋1)×(y/100)。此时，n = 10, y = 80%，所以L80 =(10＋1)×(80/100)= 11×0.8 = 8.8。 数据按升序排列(－40.33%、－5.02%、9.57%、10.02%、12.34%、15.25%、16.54%、20.65%、27.37%和30.79%)，8.8位分别位于第8和第9项之间，分别为20.65%和27.37%。采用线性插值，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%。