Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.


Whenever some measurements are taken, one has to deal with variability (or dispersion) in the data. As a matter of fact, virtually all natural processes vary - even those which yield "constant" results show up fluctuations if either the observation time is long enough or the scale of the measurement is zoomed in (see random experiment).


  • The actual amount of sugar in a 1 kg package of sugar may vary between 0.95 and 1.05 kg.
  • The temperature of boiling water varies with pressure and with the amount of dissolved substances. Thus, the boiling points of several brands of different mineral waters differ slightly from each other.
  • A time of reaction to a certain event may vary according to your physical and psychological condition (don't drink and drive). Let's perform an experiment by starting the following  interactive example 
  • The amount of rain in July varies from place to place, and from year to year.

Statistics helps in coping with situations in the presence of variability. The reason for the variability may be twofold:

  • process variability - introduced by the process under investigation
  • measurement variability - introduced by the measuring procedure

The variability in the data is often referred to as the noise that obscures the true signal.