[Math] the meaning of percentile

percentagespercentileterminology

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.

Best Answer

"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.

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