Q.In an entrance test taken by many candidates, a student's score is reported to be at the $80$th percentile, $P_{80} = 68$ marks. Interpret this statement. What is the percentile rank of a score of $68$?

A percentile states relative standing: $P_{80}$ is the value with about $80\%$ of scores below it.

A percentile describes where a value stands within the distribution, not the value itself.

Interpretation of $P_{80} = 68$. The $80$th percentile is the score below which about $80\%$ of all candidates lie. So $P_{80} = 68$ means roughly $80\%$ of the candidates scored below $68$ marks, and about $20\%$ scored above — the student is near the top fifth of the group.

Percentile rank of $68$. The percentile rank of a value is the percentage of observations at or below it. Since $68$ is the $80$th percentile, its percentile rank is about $80$. …

If the total number of candidates were known — say $5000$ — the interpretation can be made concrete: about $80\%$ of $5000 = 4000$ ca …

Confusing the $80$th percentile with a mark of $80\%$. A percentile ranks a value against the rest of the data; it is not the raw score. Also, 'below the perc …