I came across the following question, the answer to which I am confused by:

The following 10 observations are a sample drawn from a normal population: 25, 20, 18, –5, 35, 21, –11, 8, 20, and 9. The fourth quintile (80th percentile) of the sample is closest to:

ANSWER: The observations, when ranked from smallest to largest, are: –11, –5, 8, 9, 18, 20, 20, 21, 25, and 35. The fourth quintile (80th percentile) is the eighth largest of these ordered numbers. The eighth largest number is 21.

I thought the answer would be 24.2 (i.e. closer to 24) using the following logic:

If the formula for the position of a percentile in an array with n entries is

Ly = (n + 1)y/100

Then we get Ly = (10 + 1)80/100 = 8.8

So our fourth quintile (80^{th} percentile) is 8.8 or 0.8 between the 8^{th} and 9^{th} item in the array – then we use linear interpolation to calculate 0.8 between the 8^{th} and 9^{th} figures (0.8 * (25 – 21)) + 21 = 24.2

Is there any reason why the calculation stopped at the 8^{th} position and didn’t go on to use linear interpolation to calculate the difference between the 8^{th} and 9^{th} figures?