What EXACTLY do percentiles (/does which) mean, how are they distributed exactly (equally/weighed)?
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$\begingroup$ The 50th percentile is the median. It need not in general be either halfway between the minimum and the maximum or equal to the average — although each of those might be true in particular cases. If the data were 1 2 4 then neither condition is true. If the data were 1 2 3 both would be true. $\endgroup$– Nick CoxCommented Oct 15, 2022 at 14:35
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$\begingroup$ The most common name for (minimum + maximum)/2 is midrange and a different name is needed because the main idea is different from both the idea of the mean and that of the median. $\endgroup$– Nick CoxCommented Oct 15, 2022 at 14:41
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Let’s assume values to be on a continuum. (The problem gets annoying for technical reasons if we do not assume this.)
Then percentile $1$ is the smallest number such that $1\%$ of values are below.
Then in general, percentile $p$ is the smallest number such that $p\%$ of the values are below.
