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Statistics - Harmonic Mean of Discrete Series
When data is given alongwith their frequencies. Following is an example of discrete series:
| Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 12 | 0 | 5 | 7 |
In case of discrete series, Harmonic Mean is computed using following formula.
Formula
$H.M. = \frac{N}{\sum (\frac{f}{X})}$
Where −
${H.M.}$ = Harmonic Mean
${N}$ = Number of observations.
${X}$ = Variable value
${f}$ = Frequency of variable X
Example
Problem Statement:
Calculate Harmonic Mean for the following discrete data:
| Items | 14 | 36 | 45 | 70 | 105 |
|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 2 |
Solution:
Based on the given data, we have:
| ${x}$ | ${f}$ | ${\frac{f}{X}}$ |
|---|---|---|
| 14 | 2 | 0.1428 |
| 36 | 5 | 0.1388 |
| 45 | 1 | 0.0222 |
| 70 | 3 | 0.0428 |
| 105 | 2 | 0.0190 |
| Total | 0.3656 |
Based on the above mentioned formula, Harmonic Mean $H.M.$ will be:
$H.M. = \frac{N}{\sum (\frac{f}{X})} \\[7pt]
\, = \frac{5}{0.3656} \\[7pt]
\, = 13.67$
The Harmonic Mean of the given numbers is 13.67.
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