I am teaching a basic statistics course for psychology students. The lecturer provided a formula for the rank of a quantile rank = alpha n + 1/2, alpha being the proportion which corresponds to the quantile and $n$ the number of observations The students asked why it is a half for all quantiles. Is this so that you always round up to the next integer? Basically I am looking for an intuitive explanation for this formula and would like to know if it works in all cases and for all quantiles. Cheers!
quantile rank formula
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descriptive-statistics
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0sorry should have been: "rank of a quantile. Rank = alpha n + 1/2" – 2011-10-07