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I am confused with the concept of percentile rank. I am in the top 7 of my class, how would I calculate my percentile rank?

Number of students 72 I am 7th rank in my class

Does this mean my percentile rank is 7?

Blue Hat
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2 Answers2

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You are in the top $\frac7{72}\times100\% \approx 10\%$ of your class. Since percentile rank is usually expressed in terms of "how many percent are worse or equal to the score in questions", that means your percentile rank is $90$.

Ingix
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  • Wouldn't it be more than 10% ? – Blue Hat Dec 10 '18 at 14:58
  • That's why I said "how many percent are worse or equal to the score in questions", based on https://en.wikipedia.org/wiki/Percentile_rank. Of course, it would be equally valid to say "top 10%", as I did initially. Generally, the question is what would be expected by a value of "percentile rank 10": top 10% or bottom 10%. – Ingix Dec 10 '18 at 15:03
  • I stand in top 10% of the class, so I would want to say that in percentile, how would I do that? -> Overall 90 percentile? – Blue Hat Dec 10 '18 at 15:04
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The $7^{th}$ best rank is the $\color{blue}{66}^{th}$ data item in the ordered $72$ scores.

So, this is the $\color{blue}{91^{st}}$ percentile as $\left \lceil 72\cdot \frac{\color{blue}{91}}{100} \right \rceil = \color{blue}{66}$.

Note, that it is not the $92^{th}$ percentile as $72\cdot \frac{92}{100} > 66$.

trancelocation
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  • So, If I have to state, I say that my score is overall 91st percentile? – Blue Hat Dec 10 '18 at 15:13
  • As the percentiles are often reported as 1%-ranges of data although they are "cut-offs", you can safely state that your score belongs to the 91st percentile. – trancelocation Dec 10 '18 at 15:36
  • Alright! Thank you for the explanation. To talk, which one, percentile or percentage is a proper way in formal language? – Blue Hat Dec 10 '18 at 16:01
  • @BlueHat : In the context of comparing performances on tests percentiles are very often used. Also when grades are assigned to scores and if highest scores (like above 90% can hardly be achieved) then often percentiles serve as the cut-offs for different grades like "scores not above the 40th percentile" (roughly: "those students with the lowest 40% of the overall achieved scores") get an F. – trancelocation Dec 10 '18 at 16:46
  • so a 91st percentile rank is good right? – Blue Hat Dec 10 '18 at 16:47
  • this is very good! :-) – trancelocation Dec 10 '18 at 16:54
  • So, if I say to someone that my overall score is 91st percentile, what exactly does that infer? How will they know the overall strength of the class, or my comparison to the entire class, there can be 10 students, in that case this would not be great!? – Blue Hat Dec 10 '18 at 19:25
  • @BlueHat: Without additional information about the unerlying data set, reporting a percentile is indeed not very meaningful. In your case there are $72$ data items. So, reporting a percentile can be meaningful and acceptable. Basically reporting a percentile makes sense, if the underlying data is large and relatively "dense" (many different data items with only small gaps between them). Then it reflects a ranking and you can say something like "I achieved a score in the $91^{st}$" percentile. This would be interpreted that you belong to the best $9%$ (of the course, on the test; ...) – trancelocation Dec 11 '18 at 05:05