Quantiles

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:

• 1. quartile = 0.25-quantile
• 2. quartile = 0.5-quantile = 5. decile = median
• 3. quartile = 0.75 quantile