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


Home Univariate Data Measures of Variation Variance
See also: precision of results, fractile, variability, standard deviation, mean, Exercise - Measure your reaction time 

Variance

In addition to the measures of location for describing the position of the distribution of a variable, one has to know the spread of the distribution (and, of course, about its form). Maybe you want to have a look at the following  interactive example  in order to see some examples of common means but different spreads.

The spread of a distribution may be described using various parameters, of which variance is the most common one. Mathematically speaking, the variance v is the sum of the squared deviations from the mean divided by the number of samples less 1:

Examination of this formula should lead to at least three questions:
  • Why take the sum of squares and not, for example, the sum of absolute deviations from the mean? The answer to this is quite simple: the mathematical analysis is simpler, if the sum of squares is used.
  • Why is the sum divided by n-1; wouldn't it be more logical to take just n? Here again, the answer is simple, but requires the introduction of the concept of the degree of freedom.
  • What about the s² in the formula? The parameter s which is apparently the square root of the variance is called the standard deviation.
Please note the notation concerning the variance and the standard deviation: it is depicted as s² (or s, respectively) if it has been calculated from a sample. If it is computed from a population the standard deviation is depicted by the Greek letter s (sigma)

The variance of some data is closely related to the precision of a measuring process, as can be seen in the following  interactive example .

Last Update: 2009-Mär-29