The technical definition of a "percentile" in statistics is taken from the quantile function; it is the value below (or below or equal to) which a given percentage of values falls. For example, the 20th percentile is the point where 20% of values fall below (or below or equal to) that value.

However, in a previous answer to a question here, I got into a little debate with other users about whether or not there exists an alternative practice of people reversing the meaning of "percentiles" so that it now refers to a value above (or above or equal to) which a given percentage of values falls (e.g., when the writer refers to the 1% "percentile" as a cut-off where 1% of values are above that level). Here is one example of the reversed usage in an article in the Wall Street Journal. We came to the conclusion that this practice does exist, but now I would like to try to get a sense of how common it is. So, let's collect some data (albeit non-systematically).

My question: Can anyone identify other examples of this non-standard usage? (I.e., examples where a source refers to a "percentile", but uses this to refer to a value above which a certain percentage of values lie. More authoritative sources are best, but I am interested in any published examples.

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    $\begingroup$ There's yet a third usage to disentangle from those, which is when "percentile" (or other terms like decile and quartile) refer to an interval. e.g. the third quartile being used to refer to the interval from the median to the upper quartile rather than to the upper quartile. This usage is fairly common in some of the social sciences and also sometimes in economics and demography. $\endgroup$ – Glen_b -Reinstate Monica Jul 11 at 2:34
  • $\begingroup$ That is a very interesting third use. Would you be interested in finding some examples and converting your comment to an answer? It would be a useful addition. $\endgroup$ – Reinstate Monica Jul 11 at 4:02
  • $\begingroup$ This seems likely to be common. I'd guess that the top 1%, 5%, 10%, whatever on income or wealth are at least sometimes referred as the top 1% percentile, etc. $\endgroup$ – Nick Cox Oct 8 at 0:17

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