问一道题：NO.PZ2017092702000154

问题如下：

The third quartile percentage of total returns is closest to:

选项：

19.42%

20.43%

23.45%.

解释：

B is correct. Quartiles divide a distribution into quarters, with the third quartile occurring at the point at which 75% of the observations lie below it. The third quartile is equivalent to the 75th percentile. The formula for the location (Ly) of the 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 = 75, so L75 = (11) × (75/100) = 11 × 0.75 = 8.25. Rearranging the data in ascending order (i.e., with the lowest value at the top), the 8.25th position would be between the eighth and ninth rank order entries, 19.42% and 23.45%, respectively. Using linear interpolation, P75 = X8 + (L75 – 8) × (X9 – X8), so P75 = 19.42% + (8.25 – 8) × (23.45% – 19.42%) = 20.428%, or 20.43%.
A is incorrect because it is the non-interpolated value of the eighth observation without the adjustment for placement at the location of the third quartile.
C is incorrect because it is the non-interpolated value of the ninth observation without the adjustment for placement at the location of the third quartile.