# 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)