The central limit theorem is one of the most useful concepts in statistics. It is all about drawing samples of a finite size \(n\) from a population. The theorem states that if one collects samples of a large enough sample size \(n\) and calculates each sample’s mean (or sum), the shape of the histogram of those means (or sums) approximates a normal distribution bell shape.

Note: The usefulness of the central limit theorem is due to the fact, that it does not matter what the distribution of the original population is, the distribution of sample means and the sums tends to follow the normal distribution.

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The following functions and R-packages are used in this section (in alphabetical order):

R-packages

Functions

• abs()
• c()
• cat()
• length()
• list()
• matrix()
• mean()
• paste()
• print()
• rbeta()
• rgamma()
• rep()
• rnorm()
• runif()
• round()
• sample()
• sd()
• seq()

Plotting Functions

• abline()
• curve()
• legend()
• mtext()
• par()
• plot()
• stripchart()
• text()

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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.