5

I am confused by the term percentile. Once my teacher told me that percentile means the percentage with respect to the score of the highest achiever.

This means that if in a competition I got $80$ out of $100$ and the highest score in that competition was 90 out of 100 then my percentile would be $\frac{80}{90}*100=88.89$.

So I got $80\%$ and $88.89$ percentile.

I was believing that my above concept was right.

But when I see the definition of percentile on Wikipedia then I got something new (but I don't understand this definition) and then I thought that what my teacher told me was wrong.

Kindly tell me if my teacher right or wrong.

Nick
  • 7,014
Singh
  • 2,168
  • 3
    "When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean — neither more nor less." – Henry Sep 25 '14 at 11:25
  • 3
    "The percentage with respect to the score of the highest achiever" is perhaps not the most common way of defining it. I would rather use "The number of people that scored lower than you as a percentage of the total number of participants". – Arthur Sep 25 '14 at 11:35
  • 1
    Your teacher should call it Percentile Rank but then again, no one calls it that. We live in a mathematically challenged world. – Nick Sep 25 '14 at 12:35
  • @Arthur "not the most common way of defining it"? I would say the teacher is defining a totally different concept. If someone makes 10% of what Warren Buffett makes, are they in the 10th percentile of the income distribution? I'd say they are still far above the median (i.e. 50th percentile). – arne.b Sep 25 '14 at 13:02
  • @Henry: I thought a while about what you meant by that quote. Now, I agree. A percentile is a hippopotamus in a pink unitard. – Nick Sep 25 '14 at 13:10
  • @Arthur: Please Please Please explain why the latter is better than the former and whether or not they are equivalent! – Nick Sep 25 '14 at 13:52

3 Answers3

1

"It is an important and popular fact that things are not always what they seem."
- Hitchhiker's Guide to The Galaxy

Your teacher meant Percentile Rank. In the Wikipedia Article, it is verifiably stated that: "In test theory, the percentile rank of a raw score is interpreted as the percentages of examinees in the norm group who scored at or below the score of interest."

So, in mathematical layman's terms, for practical everyday examination purpouses,

"The $n^{\text{th}}$ Perecentile Rank in a group whose highest mark is $m$ is equivalent to $n\%$ of $m$
and vice-versa"

No one can be blamed. The terms Percentile and Percentile Rank are interchanged especially in schools and test centres where they conduct competitive examinations.

A percentile is a different concept similar to deciles in statistics.

Nick
  • 7,014
  • 1
    The explanation at your Percentile Rank link does not mention the highest score that the OP's teacher referred to. I do not see how the teacher could have meant what is explained at the link. – arne.b Sep 25 '14 at 12:55
  • 1
    Well, I'm sorry you didn't understand that what he said and what was stated in the link was equivalent. Maybe read the Wikipedia article. It's much clearer. :D Have a nice day. – Nick Sep 25 '14 at 13:06
  • I still do not think we have the same interpretation of what the teacher meant. The teacher references a single "highest achiever", not the number of 'lower' or 'higher achievers' (as in "examinees...who scored at or below..."). – arne.b Sep 25 '14 at 13:32
  • @arne.b: If two people share 1st prize/place, who is the single highest achiever? Also, please understand that teachers say a lot of things inorder to get concepts into student's heads. Arthur's definition is most apt. – Nick Sep 25 '14 at 13:49
  • Where is the part in grey quoted from? It is equivalent to what the OP's teacher said, and still in grave contradiction to what your links say. "n% of the highest mark" does not work for A-B-C-D-F grades, yet percentiles (and ranks) can be calculated. Also, by that logic, if the two richest persons somewhere own 3 and 1 bazillion, respectively, one is in the 100th percentile and everyone else in the 33rd or below. – arne.b Sep 25 '14 at 14:43
0

If your memory is correct, your teacher was wrong.

The percentile tells you the value below which a certain percentage of the observations fall.

Thus, if the median score on the test was $80$, a score of $80$ would put you at the fiftieth percentile regardless of what the high score was.

N. F. Taussig
  • 79,074
  • 1
    In test theory, the percentile rank of a raw score is interpreted as the percentages of examinees in the norm group who scored at or below the score of interest. – Nick Sep 25 '14 at 12:33
-1

First, consider the possibility that you misunderstood your teacher or that your words above do not quite capture what (s)he meant. That said, the "percentage with respect to the score of the highest achiever" has nothing to do with percentiles, and I am not sure there is a single word to express "I got within 89% of the best".

Percentiles (or, more generally, quantiles) are about relative positions compared to everyone else. It is not required that whatever you are looking at has numerical values, only that the values can be ordered. Taking an example in the spirit of @Nick's first link, consider a test where

  • 60 people got a D
  • you and no one else got a C
  • 39 people got a B
  • no-one got an A or worse than D.

How many % of a B are a C? However, one can still make statements in terms of quantiles, for example:

  • Everyone in the lower half got a D. (Since some in the upper half did so, too, the median grade is a D, too.)
  • Everyone in the highest (fourth) quartile got a B.
  • Everyone in the sixth decile got a D. (= those who scored better than the bottom 50%, but worse than the top 30%.)
  • Those in the 61st percentile got a C.
  • Those in the 62nd percentile got a B.

Thus, quantiles are best imagined as lining up everyone in (ascending) order and putting (ascendingly numbered) separators at n equidistant steps (n=100 for percentiles, 10 for deciles, 4 for quartiles)

Your percentile rank is then the number of the marker closest to you towards the "worse" side. (Note that percentiles make most sense if the considered set has >>100 elements. See the aforementioned link on how handle sets with < 100 elements.)

arne.b
  • 395