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If you use @Stata to compute/estimate quantiles/percentiles there's a Statalist thread that may be of interest. (Spoiler: Different commands can yield different results—except for the median—so exercise care with tail-probability, IQR, etc. calculations.)…
This is probably a negligible concern when analyzing most "large" samples, but not necessarily so for "small" ones.
Here's an example—
Note: The Stata documentation ("Methods and Formulas") makes clear that different formulae are used, so—just as many of us were told growing up—read the instructions.
P.S. While here it might be noted that medians are computed as the avg. of the .5N and .5N+1 order stats. when N is even. This is not the same as the def'n min{y|F(y)≥.5} which is the .5N order statistic with N even. Likely no concern in large samples, maybe so in smallish ones.
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