Calculating percentiles -- misunderstanding

CFA Level I
#1

Came across a question today concerning calculating a percentile, here it was:

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:

While the answer was:

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.

Am I confusing two seperate formulas or do I remember having to take n+1 and multiply that by the percentile to find the appropriate number? So, in this case n = 10, therefore: 11 * .8 = 8.8, and figure out the number position that way…?

Am I completley confusing two seperate things?

#2

That’s what I though as well when I was taking the CFAI mock, but apparently not?

#3

Anyone have any feedback?

Thanks

#4

I would have calculated it the same way:

L§ = (n+1)*P/100 = 8.8 20th percentile = 21+ (25-21)*0,8 = 24.2

Maybe it’s an error in the solution. Or maybe the distributrion is intended to be discrete and only integer values are part of the distribution.

…just speculation

Regards,

Oscar

#5

The inconsistency in some of the formulas is pretty annoying (1/2 convexity or not?)

#6

Yes I agree, I would have also used: Ly = (n+1)*Y/100

#7

Okay, so not just me. Good to know

#8

Hey I don’t know if you guys found the solution, but it IS correct. It’s in the wording of the question. It asks for a percentile of a normal POPULATION and not a SAMPLE.

The percentile of a population is (n)*y/100, or in this case, 10*.8 = 8. The 8th number being 21.

The sample percentile would be of course (n+1)*y/100. tricky tricky.