Quintile Question!

CFA Level I Quant
#1

Hello,

here is the question

the following ten observations are a sample drawn from a normal population 25,20,18,-5,35,21,-11,8,20and9. The fourth quintile (80th percentile) of the sample is closest to:

a. 8

b. 21

c. 24.2

i use Ly=(n+1)*(y/100). I think the answer is c. But the correct answer is b, because 80% means the eighth largest number which is 21. Can anyone help me with that?

Thanks so much

#2

I remember reading this question a while ago. there is a small trick:

-11, -5, 8, 9, 18, 20, 20, 21, 25, 35

Therefore n = 10 so Ly = (10+1)*80/100= 8.8

So obviously 8.8 would at first make you think it is 24.2, however since 24.2 is not an option in the set of numbers it does state that for Quantiles it is AT OR BELOW. since 24.2 is not in the set of numbers and the closest number below the 4th quintile is 21. the answer is B. does that make sense?

#3

First you place the numbers in order:

35, 25, 21, 20, 20, 18, 9, 8, -5, -11

Then you compute the formula: L80%=(10+1)*0,8 = 8,8.

Therefore the answer is 21 + 0,8*(25-21)=24.2

Correct answer is C), no doubt.

#4

Thanks for the reply. I kind of understand it. You mean we have to select the number among the ten samples, it that what you mean? If so, under what condition, the answer should be 24.2?

#5

If 24.2 is not a selectable answer, I understand the reason why 21 is correct. But now 24.2 is among the answers, then I am confused why 21 is right.

#6

EnricB is correct. 8.8 means that the percentile is between the 8th and 9th answer. You need to do linear interpolation to get the answer.

#7

if you do a linean interpolation, c is the correct answer

#8

Totally right

#9

I stand corrected, i just asked a guy i know who has the CFA charter and teaches a prep course for all levels. he says that the answer B is wrong. C is the correct answer

#10

Thanks for the help. If 24.2 is right, I am ok now. Thanks so much