# Percentiles

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.

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.

Kiakaha Wrote: ------------------------------------------------------- > 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. I think we can up our scores by a point each!

When L(y) is not a whole number, you must use linear interpolation. Look at the example on page 376 L1V1R7. As a side note, L(y) = (n+1)*(y/100).

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.

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

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.

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

Hopefully we can resolve the issue quickly…

if an even # of numbers in your list - you need to find (10+1)/2 = 5.5th number for 11 numbers => 6 …

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.

Kia, why don’t u post this on the elan forum and see what they say?

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.

someone…?

L(80) = (n+1)*(y/100) = (10+1)*(80/100) = 8.8. Since L(80) is 8.8, you’d use interpolation: P(80) = X(8) + [L(80) - 8]*[X(9) - X(8)] = 8 + (8.8 - 8)*(9 - 8) = 8.8. Note that in this case L(80) = P(80) by mere coincidence - not always the case. As mentioned earlier, refer to the example on page 376 L1V1R7. Good luck remembering the formula. Haha.

Did someone find why the answer was the 8th largest number (on 10) for the 80th percentile?? The CFAI Mock was incorrect?

disiz64 Wrote: ------------------------------------------------------- > Did someone find why the answer was the 8th > largest number (on 10) for the 80th percentile?? > > The CFAI Mock was incorrect? I have written to CFA institute about it and they have forwarded it to their Education Department. Should hear back sometime soon. Will let you know what they say.

anish Wrote: ------------------------------------------------------- > disiz64 Wrote: > -------------------------------------------------- > ----- > > Did someone find why the answer was the 8th > > largest number (on 10) for the 80th > percentile?? > > > > The CFAI Mock was incorrect? > > > I have written to CFA institute about it and they > have forwarded it to their Education Department. > Should hear back sometime soon. Will let you know > what they say. Ok. Thank you.

disiz64 Wrote: > Ok. Thank you. So I heard back. The question and the answer are correct. When you have a sample from a population and you need fourth quintile of the POPULATION, you use (n+1)y/100 In case you have the sample and you need to find the fourth quintile of the SAMPLE, you use ny/100 (that’s what I understand)

Sorry but I dont understand what you really mean. Can you please repost their answer? I encouter the same difficulty in figuring out why they have that answer. Thanks