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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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