Percentiles numbers, between, however, question, recently

simeezee

hi guys, hoping someone can clarify -- I thought that to calculate percentiles, you used the formula (n+1)*(y/100) where y is the percentile eg 50 for 50th percentile etc.

however i recently saw a question that seemed to contradict this.

so, to clarify. if you have 10 numbers in ascending order, is the 50th percentile:

a) the fifth biggest number

or

b) (10+1)*(50/100) ie 5.5, or the point that's halfway between number 5 and number 6 in your list.

this is such a simple topic so i can't understand why there seem to be contradictory ways of solving it. thanks much.

Micholien

The point halfway between number 5 and number 6 in your list.

Just the same as in sequence of 2 numbers, the middle point would neither be 1st nor 2nd number. It would be between 1st and 2nd number.

spartanag07

I know what you're talking about and I have the same confusion-- between the formula for L(y) in the ordered list of numbers in the set and what I saw on a mock exam and the explanation.

The question I think I recall described 10 items in a list and asked for the 80th percentile and the correct answer was the 8th number, not the interpolated number you would arrive at if you used the formula. I still remain confused. It seems like common sense that if you have a set with 10 numbers the 8th number would represent the 80th percentile... but obviously that's not what the formula produces and on that mock, the interpolated answer choice was not correct.

dontknow1987

Can you guys post the 10 values - or maybe the entire question here?

Matori

It doesn't matter, does it? Pick 10 numbers: -3, -1, 1, 3, 4, 5, 6, 7, 8, 9. I believe it may have been on the CFAI mock exam, and I don't want to reproduce any protected content.

Daniel1985

I am glad other people have the same issues with this!!

JPSem

Hopefully we can resolve the issue quickly...

btcapital

if an even # of numbers in your list - you need to find (10+1)/2 = 5.5th number

for 11 numbers => 6 ...

CP

Penny-wenny

I am quite certain it is incorrect in the mock solution. The CFA book explains it with examples that it is (n+1)y/100 and it makes sense too. Just like optiix noted above

"Just the same as in sequence of 2 numbers, the middle point would neither be 1st nor 2nd number. It would be between 1st and 2nd number."

If we have 2 numbers: 10 and 20, the 50th percentile is neither 10 nor 20. It is 15.

MythosHF

Can we put this one to rest with an example?

Returns for 10 years are (in percent): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

What is the 80th percentile? 8.8% is the 80th percentile. Yes? Using the formula above you get L(y) is 8.8, which means it is the 8th number (of the ordered set) plus .8 of the difference between the 8th and 9th numbers of the ordered set (the difference is 1, so .8 of 1 is .8)-- so 8 + .8 = 8.8%.

Correct/comment/add to the explanation. Thanks. It just seems odd that the 80th percentile isn't 8% though.