**Question:** Jane scored in the 68th percentile on a test, and John scored in the 32nd

percentile.

Quantity A

The proportion of the class that

received a score less than John’s

score

Quantity B

The proportion of the class that

scored equal to or greater than Jane’s

score

**Doubt:** The book states the answer as C, however I think it should be D because of the case where all the test scores are equal to each other. So quantity A should be zero, and Quantity B should be 1. And of course the other case where 32% of class score less than John and 32% score more than Jane.

Hey, thanks for the reply. I went through the post, however the question still remains: Does 32nd percentile mean 32% of class scored less than John or did 32 % of the class score less than or equal to John. (exclusive vs inclusive definition). Here’s the wiki definition for reference : In statistics, a **k-th** percentile, also known as **percentile score or centile**, is a score below which a given percentage k of scores in its frequency distribution falls (“**exclusive**” definition) or a score at or below which a given percentage falls (“**inclusive**” definition).

Being a QC question I’m thinking of boundary cases such as everybody in the class gets the same score. So as per the inclusive definition, it is not wrong to say that Jane scored in the 68th percentile ( or John scoring in the 32nd percentile). However, I am wrong to assume that if I consider the exclusive definition.

All I know for sure is that percentiles mean dividing the data into 100 groups, sorted from lowest to highest.

What concerns me is that ETS does not really mention which definition it follows (to my knowledge). I believe ETS will probably not ask questions like these if its kind of fuzzy. Or maybe its something along the lines of root of 4 being equal to 2 (only positive roots taken) on the GRE, and its a really straightforward thing where 32nd percentile means 32% of class scores **LESS** than John. I would really appreciate if you could enlighten me on the above.

if John is in the 32nd percentile, it means that 32% of the scores are equal to or less than John’s score. Similarly, if Jane is in the 68th percentile, it means that 68% of the scores are equal to or less than Jane’s score.

Now, considering the scenario where all students have the same score, percentile rankings can become less meaningful. If everyone scored the same, then technically everyone is in the 100th percentile (since no score is lower), and also in the 0th percentile (since no score is higher).

However, in most practical scenarios, test scores will have some variation, and percentile is a useful way to understand one’s relative standing in the distribution of scores.

As for the GRE and other standardized tests, they typically use the inclusive definition of percentile. That is, if a student’s score is in the 90th percentile, for example, it means that they scored higher than or equal to 90% of the test-takers.

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I think Tushar’s point is more of the fact that it is ambiguous, and unfortunately ETS doesn’t make it clear. I would say that option D is not incorrect as a result.

We try to avoid it by explicitly mentioning that the values are different (this doesn’t).

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Thank you for the assuring reply.

Completely agree with you there. Consequently, the question seems flawed by not mentioning the uniqueness of values. Thanks a lot!