If x₁, x₂, … , x_n are observations with frequencies f₁, f₂, … , f_n i.e. x₁ occurs f₁ times and x₂ occurs f₂ times and so on, then we have

Sum of the values of the observations = f₁x₁ + f₂x₂ + … + f_nx_n

and Number of observations = f₁ + f₂ + … + f_n

So, mean() of observations is given by

Or,

In summation form, it can be shorted to

Which also can also be written as,

And it is understood i varies from 1 to n.