The mean or average of observations, is the sum of the values of all the observations divided by the total number of observations.
If x1, x2, … , xn are observations with frequencies f1, f2, … , fn 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 + … + fnxn
and Number of observations = f1 + f2 + … + fn
So, mean() of observations is given by
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.
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