A measure of position determines the position of a single value in relation to other values in a sample or a population data set. Unlike the mean and the standard deviation, descriptive measures based on quantiles are not sensitive to the influence of a few extreme observations. For this reason, descriptive measures based on quantiles are often preferred over those based on the mean and standard deviation (Weiss 2010)).

Quantiles are cut points dividing the range of the data into contiguous intervals with equal probabilities. Certain quantiles are particularly important: The median of a data set divides the data into two equal parts: the bottom 50% and the top 50%. Quartiles divide the data into four equal parts and percentiles divide it into hundredths, or 100 equal parts. Note that the median is also the 50th percentile. Deciles divide a data set into tenths (10 equal parts), and quintiles divide a data set into fifths (5 equal parts). There is always one less quantile than the number of groups created (e.g. There are 3 quartiles dividing the data into 4 equal parts!).


The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

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You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: Hartmann, K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.