Brief on variance

Variance surrounds us. Despite our desire to have the same thing every day, we will face a slight variation of something we want to encounter again.

A mathematical definition of the variance is quite straight forward:
it is a measure of how far are the data values are located from the mean.

The population variance is defined as : \sigma_{N}^2 =  {\frac{1}{N}\sum\limits_{i = 1}^N {\left( {x_i - \mu } \right)^2 } }  , where N is the population size (the number of values in the set), x_i is a selected value,  \mu  is the population mean (the average).

If we take Coca-Cola’s share price as an example and calculate the variance for all available data, we get \sigma_{N}^2 = 193.43 .

The minimum, mean and maximum in the same data are min  = 0.64, \mu = 19.20, max = 47.13 .

The square root of the variance will give us a more firm view on the deviation from the mean and the spread of the data values: \sqrt \sigma_{N}^2 = 13.91 .


Information sources:

  1. An R introduction to statistics (link)
  2. StatisticsHowTo (link)

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