Statistics - Harmonic Mean of Individual Series



When data is given on individual basis. Following is an example of individual series:

Items 5 10 20 30 40 50 60 70

In case of individual items, Harmonic Mean is computed using following formula.

Formula

$H.M. = \frac{N}{\sum (\frac{1}{X})}$

Where −

  • ${H.M.}$ = Harmonic Mean

  • ${N}$ = Number of observations.

  • ${X}$ = Variable value

Example

Problem Statement:

Calculate Harmonic Mean for the following individual data:

Items 14 36 45 70 105

Solution:

Based on the given data, we have:

${x}$ ${\frac{1}{X}}$
14 0.7142
36 0.2777
45 0.0222
70 0.0142
105 0.0095
Total 1.0378

Based on the above mentioned formula, Harmonic Mean $H.M.$ will be:

$H.M. = \frac{N}{\sum (\frac{1}{X})} \\[7pt] \, = \frac{5}{1.0378} \\[7pt] \, = 4.81$

The Harmonic Mean of the given numbers is 4.81.

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