FORMULAS FOR MEAN OR AVERAGE

1. Mean of all observed data (running average)

   

   where X(i) is the value of the i-th individual observation

   n is the total number of observations

   i is the sum index over all n-observed data values.

2. Mean of frequency grouped data (ranked and stacked )

   

   where X _k is the nominal value of the k-th cell

   f _k is the frequency of observations occurring in the k-th cell

   n _c is the number of cells or data groups (n _c ‰ n)

   

3. Mean of discrete probability density function (pdf)

   

   where f(X _k ) = is probability of cell random variable X _k