Harmonic mean is another mathematical average. It is defined as the “Reciprocal of the arithmetic average of the reciprocals of the values of a variable
Thus, the fundamental formula for its calculation in the different series are as follows:
H = reciprocal of ∑rx/N or N/∑rx
Where, H = Hormonic mean
∑rx = Sum of the reciprocals of the variable or mid values
N = No. of observations or ∑F
The above formula can also be can also be modified as under:
Where, X1, X2, X3 etc. = Values of the variables
F1, F2, F3 etc. = Frequencies of the respective variables
∑r(x) = Total of the products of reciprocals of the variables, and
And their corresponding frequencies.
All other factors carry the same meaning as before.
Weighted Harmonic Mean:
Further, for computing the weighted harmonic mean, the formula is to be modified as under:
Where, H(w) represents the weighted harmonic mean,
And ∑wr(x), the total of the products of the reciprocals of the values, and their corresponding frequencies.
Combined Harmonic Mean:
In order to compute the combined harmonic mean of two, or more series at a time, the formula is as under:
From the above definition and the different formula it follows that computation of harmonic mean depends entirely on the reciprocals of the values.