Question on Quantiles yesterday, provided, practice, following, companies

franzino

Was reviewing some practice questions yesterday and came across the following:

You're provided annual returns for 20 companies and asked to provide the lowest return within the top quartile. Since the top quartile would be the top 5 returns (20/4) you would just count down in reverse order until you find the 5th highest return.

Simple enough.

Now if you were asked to provide the 75th percentile for that same group of 20, you would use the (n+1)*75/100 formula which would leave you with a breakpoint somewhere between the 15th and 16th position.

Again, on its own, simple enough.

What I am having trouble reconciling in my mind is the relationship of the two results. I would have assumed they could be able to be added together since you're dealing with the top quartile and the bottom three to arrive at n but you can't.

I'm sure there is a simple piece of logic or reasoning that I am missing and would appreciate it if someone could point it out.

Thanks!

dotamasta

Top quartile is not the top 5 returns, but rather the top 5.25 returns.
2nd top quartile is the first 10.5 returns
3nd top quartile is the first 15.75 returns (where your 75th percentile starts)
4th quartile is the remaining 4.25 returns

ramdabom

[EDIT]

Top quartile is not the top 5 returns, but rather the top 5.25 returns.
2 top quartiles are the first 10.5 returns
3 top quartiles are the first 15.75 returns [where your 75th percentile (bottom)starts]
4th quartile is the remaining 4.25 returns

pogo

Thats what I had penciled out. I think the simplified answer from Schweser (below) sort of clouded my thought process for a moment and I disregarded the role of (n+1).

"With 20 datapoints, the top quartile (1/4) is the top 5. Count down from the greatest value to find the 5th from the top."

Thanks.