Quintile/Quartile

[faptor]

For this question,

The following ten 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:
A. 8.0.
B. 21.0.
C. 24.2.
Answer = B



Ranking the sample from smallest to largest, we have -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.

Shouldn’t we use Ly= (n+1)(y/100) to calculate it, getting an answer of 24.2?

 

[glorysk87]

Ive asked this question many times, and have not gotten a good answer about it.
Someone get s2000 in here.

 

[faptor]

I think i got the answer, after some reference and thinking.
The Ly = (n+1) (y/100) formula is used if and only if could not get a whole number for a stated percentile in a data set
If we have a whole number, we use it. If not, we use that formula and linear interpolation.
Refer to CFAI Quan text, which I quote for convenience: “”“When dealing with actual data, we often find that we need to approximate the value of a percentile. For example, if we are interested in the value of the 75th percentile, we may find that no observation divides the sample such that exactly 75 percent of the observations lie at or below that value. The following procedure, however, can help us determine or estimate a percentile. The procedure involves first locating the position of the percentile within the set of observations and then determining (or estimating) the value associated with that position.””“
Hence, for the question in my first post, since there is a whole number for the stated percentile (80th is the 8th position of 10 numbers) then we use that number. If there were 11 numbers in the dataset, then the 80th percentile would not be a real value in the dataset (ie- it will fall in between 2 of the numbers) then we apply the formula.

 

[S2000magician]

Notice the three key words in the CFA Institute quote: “at or below”. Here, there is a value at the 80th percentile.

 

[Gurifissu]

How do you all get 24.2? (I know the answer is 21 by the way).
Hypothetically, if what you did was correct, (n+1)*0.8=8.8. This means the hypothetical value would be 21 + 0.8 = 21.8.
Say we needed the values below 75%.
11*0.75 = 8.25
The answer would be 21.25 right?

 

[S2000magician]

Gurifissu wrote:How do you all get 24.2? (I know the answer is 21 by the way).
Hypothetically, if what you did was correct, (n+1)*0.8=8.8. This means the hypothetical value would be 21 + 0.8 = 21.8.

That’s incorrect. 8.8 is the position: the 8/10 of the way between the value in the 8th position and the value in the 9th position.