if one of the observations is zero. . . Harmonic mean Harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocal of the individual observations.
It is denoted by HM. Thus, HM = X n ..... When the number of items is large the computation of harmonic mean in the above manner becomes tedious. To simplify calculations we obtain reciprocals of the various items from the tables and apply the following formulae: (i) In individual observations HM X n .....
(or) HM Σ where n is number of observations or items or values. (ii) In discrete frequency distribution HM N Σ where N = total frequency= ∑ f (iii) In continuous frequency distribution HM N m Σ Where m is midpoint and N is total frequency Example . Calculate the Harmonic Mean of the following values: , . , , .
. . Σ Table : . n = HM Σ Example .
From the following data compute the value of Harmonic Mean Marks No. of students Calculation of Harmonic Mean Marks No. of Students . .
Σ Table : . HM N Σ Example . Calculate Harmonic Mean for the following data given below: Value - - - - - Frequency Calculation of Harmonic Mean Value