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
50^{th} 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!).

**Citation**

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.

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.*