Q.In a national scholarship examination taken by $2000$ candidates, the cut-off for an interview call is set at the $90$th percentile. Explain what this means, and estimate how many candidates are called for interview.

The $90$th percentile has about $90\%$ of candidates below it, so only the top $10\%$ clear the cut-off.

Meaning of a $90$th-percentile cut-off. The $90$th percentile $P_{90}$ is the score below which about $90\%$ of candidates fall. Setting the interview cut-off at $P_{90}$ therefore means only candidates scoring at or above $P_{90}$ — the top $10\%$ — qualify.

Estimating the number called. With $2000$ candidates, the top $10\%$ is

So about $200$ candidates are called for interview, and about $1800$ (the lower $90\%$) are not. …

The same reasoning scales to any percentile cut-off: a $P_k$ cut-off admits the top $(100 - k)\%$. A $75$th-percentile ($Q_3$) cut-off, for i …

Reading a $90$th-percentile cut-off as admitting $90\%$ of candidates. It is the threshold at the $90\%$ mark, so those *at or ab …