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How do we calculate percentile? I think it should be calculated as:

P = Total number of candidates  
L = Number of candidates whose marks are below yours

Percentile = (L/P)*100
That means if you are the highest in the range, and there are 200,000 candidates and if your marks are same as 7 others then;

your percentile = (199992/200000)*100 = 99.996

That means in any circumstances you can't have perfect 100 percentile.

Then how come this is possible, see links:-

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Can you find any quoted example of an individual with a percentile showing more than four significant figures? – Henry Apr 17 '11 at 20:44
up vote 6 down vote accepted

The simple answer is rounding.

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There are different definitions of "percentile."

Usually a percentile is computed by first ranking all the data with 1 the lowest, 2 the next lowest, up through $N$. (The possibility of ties is a complication but does not change the essential idea.) Ranking from lowest to highest instead of highest to lowest is arbitrary but it gives definite rules. However, it would be nice if the percentile computed from ranking in one direction agreed with the percentile from ranking in the other.

You can convert a rank $k$ into a percentile by:

  • Computing $100 k /N$. This value will range from $100/N$ through $100N/N = 100$. Note the asymmetry: the highest is 100 but the lowest is nonzero.

  • Computing $100(k-1)/N$. This is the rule quoted in the question. The value will range from $0$ through $100(N-1)/N \lt 100$.

  • You can make the range of percentiles symmetric. This means that the percentile corresponding to rank $k$ is $100$ minus the percentile corresponding the rank in reverse order, which is $N+1-k$. To do this, compute $100(k-1/2) / N$. The values range from $100/(2N)$ to $100(1 - 1/(2N))$.

  • There are other ways to make the range symmetric. For instance, compute $100(k-1)/(N-1)$. Values range from $0$ through $100$.

(There are yet other rules, used especially for constructing probability plots, but you get the idea.)

Either using the first rule, the last rule, or rounding to the nearest percent, can produce a 100th percentile. As I recall, Excel's function for computing percentiles can produce 100 for the top-ranked value.

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The question is about %, LaTeX is still with $ ;-) – Asaf Karagila Apr 17 '11 at 17:56
@Asaf Thanks for fixing the typo. – whuber Apr 17 '11 at 17:58

To put it in words, being in the 100 percentile would mean that 100% of the group has marks below yours. But since 100% of the group would include you, and your mark could never be below your mark, then 100% of the group could not be below you. Therefore you could never be in the 100 percentile.

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That is WRONG! There is one circumstance that you can have 100% percentile. That is when the population is only 1!

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No need to shout. – Stefan Hansen Jan 11 '13 at 7:46
If there is only one member of the population, then nobody, i.e. $0\%$ of the population, ranks lower than that one. (Of course, that depends on the conventional definition of percentile: You're at the $x^\text{th}$ percentile if $x\%$ of the population ranks strictly lower than you.) – Michael Hardy Dec 29 '13 at 23:55

How to project a percentile between a range of numbers:

Suppose you have a range of integers between: 5 -> 12

The current value to be calculated is 6. What percentile is 6 in the range? Answer:

(current - min) / (max - min)

Which breaks down to:

(6-5) / (12-5)  = (1/7) = .1429

So that means 6 is about 14% on the way between 5 and 12.

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It depends. There are two definitions of percentile that I know of. If you use the "percentage below or equal to" definition, then, yes, you can have a 100th percentile. However, if you use the "percentage below" definition, then, no, you cannot have a 100th percentile. I use the first one, so I'm used to dealing with 100th percentiles.

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For percentiles, there are actually only 99 equal partitions of the population being ranked: 1 to 99. It is thoughtless hand waving to say there are 100 equal percentile bands when calculating percentiles.

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For a population of 1, the single entry is in the 50th percentile. – Woody Pidcock Nov 12 '14 at 23:54
Challenge question: for a test with 2 participants, where the test question has a yes/no answer and one answers "yes" and the other "no" what are the percentile ranks of these two participants (assuming "yes" is the correct answer)? – Woody Pidcock Nov 12 '14 at 23:59

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