agreseza

2021-12-23

How to calculate percentile? Is it possible to get 100 percentile?
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
$\text{Percentile}=\left(\frac{L}{P}\right)\cdot 100$
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;
$\text{your percentile}=\left(\frac{199992}{200000}\right)\cdot 100=99.996$
That means in any circumstances you can't have perfect 100 percentile.

Travis Hicks

Expert

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 100k/N. This value will range from 100/N through $100\frac{N}{N}=100$. Note the asymmetry: the highest is 100 but the lowest is nonzero.
- Computing $100\frac{k-1}{N}$. This is the rule quoted in the question. The value will range from 0 through $100\frac{N-1}{N}<100$.
- 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 $100\frac{k-\frac{1}{2}}{N}$. The values range from .
- There are other ways to make the range symmetric. For instance, compute $100\frac{k-1}{N-1}$. 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.

Melissa Moore

Expert

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.

user_27qwe

Expert

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:
$\frac{\left(current-min\right)}{\left(max-min\right)}$
Which breaks down to:
$\frac{6-5}{12-5}=\frac{1}{7}=.1429$
So that means 6 is about 14% on the way between 5 and 12.

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