How does PPM calculate percentiles?
Percentiles are position parameters of a frequency distribution. A p-percentile splits the data of a series of measurements into two parts, so that p% of the data are left of the percentile and (1-p)% of the data are right of the percentile. The value of a percentile is greater than or equal to the value below this percentile (that is, left of this percentile in the distribution). If the entire distribution is split into n=100 even parts, the result is n-1=99 percentiles, that is, interfaces between these parts. Depending on the size of n, the terms quartile (n = 4), quintile (n = 5), and decile (n = 10) are used. The general term for all these position parameters is quantiles.
Median
The median corresponds to the mean percentile p=50%. That is, the median splits the distribution into two halves. Statisticians often prefer the median over the average (that is, the arithmetic mean) because it is more useful as a "typical" value if the values are distributed unevenly.
The following data points are saved in PPM:
90, 15, 10, 20
The average of these values is 67.5.
The median of these values is 20.
Nomenclature
PPM allows the calculation of general quantiles, but they must be specified as percentiles. This means in addition to the above definition of the percentile, non-integer values are also allowed for p (for example, p=99.9).
Special cases p=0, p=1
Some statisticians allow the notation of p=0% and p=100% as percentiles. PPM does not support this notation. Since these two cases are nothing but the minimum or maximum value of a measure, you can query the minimum and maximum comparison values.
Returning specific values
Various frequently used calculation methods for percentiles exist but they differ only marginally. PPM uses this one:
When calculating percentiles, the values that the calculation is based on are not considered as random samples, but in their entirety. This means that a specific, actually existing value will always be returned.
N be the number of values. If the rank of the element to be found r = p × N is not an integer, the figure will be rounded up to the next higher integer number, and this element will be returned as a percentile. If the rank of the element to be found r is an integer, the next higher integer is applied. In the case of the median this applies to the upper median.