Percentile Jargon

[mohit.wrangler]

Please clarify following doubts:

1. I suppose the definition of percentiles which GRE uses is: If some value x in a data set is 30th percentile than 30 percent of values in data set are less than x and 70% percent of data values are equal or greater than x. Let me know if I am wrong here.

2. Given a data set: {3,5,7,8,9,11,13,15}. What method, according to GRE, is used to calculate 32nd percentile in this set?

3. Can we find each percentile i.e. 1st, 2nd, 3rd up to 99th percentile even if the values repeat in a data set? (consider data set {30,30,30...40 times, 70,70,70,70....60 times})

4. Consider following question:


I understand that by definition answer should be C. But what about following two cases:



Is there anything wrong with the 1st case?

[tommywallach]

1. Yep.

2. You can't.

3. Nope.

4. See above. Your example doesn't actually have those percentiles in it (there are not two scores that exist as 32nd percentile or 68th percentile, and if there were, to create it, you'd need to put the exact same number of testtakers on either side, so the answer would remain C). That said, I think this question is sorta unfair without saying that there are over 100 different scores, so we know that there are disparate score/percentiles.

-t

[mohit.wrangler]

Thanks, that was helpful.

Here are some follow-ups

2. But here, in data set: {3,5,7,8,9,11,13,15}, we can find 50th percentile = 9. Similarly, 25th = 7, and 75th = 13 and whichever percentile that satisfy the definition exactly, right?

Look at an answers explanation from 5lb book
(see question #25 at end of this post)

Notice in the 4rth line of the first paragraph in above picture: 151 is stated to be 0th and 1st percentile. But 1st percentile does not make sense according to the definition. Moreover, in the second paragraph, it is mentioned that if everyone gets 157 then it "corresponds to" all 100 percentile group.

How should I understand this?
Shouldn't then, following the same analogy, in data set {20,20,20...40 times, 80,80,80,80....60 times} the data 20 corresponds to all percentile from 0th to 39th percentile? hence, also to 32nd percentile? (refer to case 1st in the second image of original post)

Here is the question #25 from 5lb book

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Following is a new question
5. I've also read that median of a data set is 50th percentile. Also, the median of the first half of the data set is 25th percentile and of the second half is 75th percentile. Now, if we consider same data set as question #2 above: {3,5,7,8,9,11,13,15}, median =50th percentile = AVG(8,9) = 8.9. But we know that data 9 also fits in the definition of 50th percentile. So which one is correct if a question asks for 50th percentile in this set?

[tommywallach]

Here's what I can say. I have NEVER seen anything like this tested in my whole life on any major standardized tests. Yes, the median is the 50th percentile (technically), while the 25th percentile is the median of the first half of the data and the 75th is the median of the second half. But I've never seen that tested, because as you noted, it makes it impossible to solve ANY percentile but the specific ones at those landmarks...which is not very useful.

In your analogy example, that is definitely true. If there are 100 data points, each percentile corresponds to one of them (well, technically you could argue only 99 data points, because the 0th percentile is used so rarely). The point is that percentiles are taught and understood VERY loosely, so the GRE only questions them in the most basic way. Even the 5lb. book question that got us here is possibly TOO advanced for the real GRE.

-t