QuantilesPublished on 30 Mar 2005
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 p-quantile (
$0 \le p \le 1$) 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 p-quantile is calculated by interpolating
$i$is not a whole number: The p-quantile is calculated by rounding down:
The 0.5-quantile 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 0.1-quantile. 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.