Quantiles
Published on 30 Mar 2005Tags #Statistics
For a series of measurements $x_i = x_1, \dots, x_n$
, it is useful to examine the magnitude of a certain fraction of the number of values.
NOTE: The following descriptions assume that the series of measurements is available in a sorted manner.
The pquantile ($0 \le p \le 1$
) is the value that devides the series of measurements into $i=p*n$
measurements that are smaller than $x_i$
and the rest of the measurements. It is important to note that the previously calculated value $x_i$
cannot be considered to be final. There are two rules that need to be obeyed:

$i$
is a whole number: The pquantile is calculated by interpolating$x_i$
and$x_{i+1}$
:$Q(p)=\frac{(x_i+x_{i+1})}{2}$

$i$
is not a whole number: The pquantile is calculated by rounding down:$Q(p)=x_{\lfloor \irfloor)}$
The 0.5quantile is called the median. It represents the value for which 50% of all measurements are smaller and 50% are greater or equal.
Quantiles are very useful to examine a series of measurements for outliers. Low outliers can be identified by comparing the minimum value and the 0.1quantile. Whereas high outliers can be discovered by comparing maximum value and the 0.9 quantile.
NOTE: YYMV, so please consider using slightly higher or lower quantiles to identify outliers.