Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.


Another numerical descriptor for the span of frequency distributions is the quantile (or fractile). A p-quantile is defined as the x-value of the distribution which includes p*N observations, with 0<p<1 and N being the number of observations.

An example may clarify this: the 0.1-quantile (0.1-fractile) of the distribution shown below is 14.6, as it includes 10 % of all observations (starting from the left).

The p-quantile is also called P-percentile, with P=p*100; a 0.12-quantile could be designated as 12-percentile, as well.

There are a few special quantiles which have their own definition: Quartiles refer to quarters of the distribution, deciles to the tenth part: