# Calculating percentiles - no linear interpolation?

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

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

I came to the same exact conclusion as you, and posted the same exact question in another forum. Unfortunately I didn’t get any good feedback.

If I get a similar question on the test though, I’m going to do the regular interpolation method.

Yeah I think I would also use the normal interpolation method for a non integer result. I’d be interested to hear anyone else’s thoughts on the matter too…

Up